GAXEX jaargang 33, editie 2

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De geschiedenis van het geld VESTING Magazine - Jaargang 33 - Editie 2 Hoofdsponsor: Interview ICT Commissie Zal de website nog radicaal veranderen?! The Olympic 1000m Speed Skating Event

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GAXEX jaargang 33, editie 2

Transcript of GAXEX jaargang 33, editie 2

Page 1: GAXEX jaargang 33, editie 2

De geschiedenis van het geld

VESTING

Magazine - Jaargang 33 - Editie 2

Hoofdsponsor:

Interview ICT Commissie

Zal de website nog radicaal veranderen?!

The Olympic 1000m Speed Skating Event

Page 2: GAXEX jaargang 33, editie 2

VoorwoordHet doel is dat je zelf initiatief neemt. Ga naar aegon.nl/werk

Eerlijk over werken bij AEGON.

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Björn WijbengaVESTING Voorzitter

Voorwoord

Jurjen BoogGAXEX Hoofdredacteur

Geld speelt wel een rolMijn eerste les economie op de middelbare school werd gevraagd wat economie precies inhoudt. “Geld!” was het meest gehoorde antwoord, wat volgens de docent niet correct is. “Economie is de kunst die zich je bezig houdt met de verdeling van schaarse goederen.”

Toch is het opvallend dat de meesten die nog nooit economie-lessen hebben gehad, geld als eerste met economie in verband brengen. Geld heeft immers een belangrijke rol in het dagelijks leven ingenomen. Het is hét ruilmiddel voor de mens en zorgt ervoor dat een on-handige driehoeksruil tot het verleden behoort.

Het coverartikel gaat juist over dit laatste verschijnsel. Hoe komt het dat we tegenwoordig niet net zo lang rui-len met anderen tot we een product hebben dat degene met wie we willen ruilen, wel wil hebben? Behalve naar het verleden, wordt ook gekeken naar de toekomst en de vraag gesteld: hoe gaat de manier van betalen zich ontwikkelen?

Naast het coverarikel staat deze GAXEX vol met verha-len over de vereniging. Er staat een uitgebreid interview met de ICT Commissie in deze editie. Voor iedereen die zich afvraagt wat de ICT Commissie doet en hoe ze te werk gaat, het antwoord is te vinden in deze editie van de GAXEX.

Tenslotte is voor deze GAXEX gekozen om een artikel te plaatsen met betrekking tot de actualiteiten. Het onder-zoek van Richard Kamst, Gerard Kuper en Gerard Sierk-sma over de 1000m schaatsen op de Olympische Spe-len staat in deze tweede GAXEX van dit collegejaar.

Kortom, in deze editie staat voor ieder weer wat wils. De redactie heeft haar uiterste best gedaan om weer een kwalitatief goede GAXEX te presenteren. Mocht de lezer nog op- of aanmerkingen hebben naar aanleiding van deze editie, of op een andere manier tips of vragen over de GAXEX hebben, dan kun je naar gaxex@deves- ting.nl mailen.

Veel leesplezier!

Jaargang 33 - GAXEX 2 3

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Jaargang 33 - GAXEX 2 5

12 Kort door de bocht

20 Durf jij het wél aan?

22 VESTING Pagina

23 Bèta BedrijvenDagen

28 Landelijke Econometristendag

30 Interview ICT Commissie

32 Column VESTING Voorzitter

34 Colofon

AC Activiteiten

Lees alles over de laatste drie AC Activiteiten: het Pooltoernooi, de Pub-quiz en het Schaatsen.

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The Olympic 1000m Speed Skating Event

After analysing 1000m races, Richard Kamst, Gerard Kuper and Gerard Sierksma argue that the skater starting in the outer lane have an advan-tage.

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De geschiedenis van het geldWanneer is het concept ‘geld’ ont-staan? En wat waren de voorlo-pers van het moderne geld? Lees hier alles over in de coverstory van deze GAXEX Editie.

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Tekst: Kevin MannCOVERSTORY

Geschiedenis van geldHet wiel, de taal en het leren maken, beheersen en gebruiken van vuur. Zij worden beschouwd als de belangrijkste uitvin-dingen van de mens. Kunnen wij ons ook maar enigszins een moderne maatschappij voorstellen als deze drie ontdekkingen nooit waren gedaan? Geenszins! Zonder deze ontdekkingen zouden wij als soort onszelf nooit verheven kunnen hebben naar de toestand waarin wij ons nu bevinden. Een andere uit-vinding die vaak in dit rijtje genoemd wordt is het concept van geld. Hoort geld in dit rijtje thuis? Er bestaan zeker samenle-vingen waarin het concept van geld niet geïntegreerd is. Een noodzaak is geld dus niet. Toch komt geld veelvuldig in onze geschiedenis voor. Waar en waarom is geld uitgevonden?

Iedereen gebruikt geld. Het hoort zó bij ons dagelijks bestaan, dat we amper stil staan bij het gebruik er van. Zin een kopje koffie? Lever een muntje of strookje papier in en het is van jou. Geen chartaal geld bij de hand? Met de pin wordt het giraal zonder probleem overgemaakt. De eerste functie van geld is hiermee meteen opengelegd: geld is een betaalmiddel.

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BetaalmiddelStel dat we in een maatschappij zouden leven zonder dat geld daarin geïntegreerd is. De meest eenvoudige manier om aan onze primaire behoeften, zoals eten en onderdak, te voldoen ligt voor de hand: ieder individu, of in een wat ruimere context de familie of groep, ver-bouwt zijn eigen eten en verzorgt zijn eigen onderdak. Dit is echter zeer tijd-inefficiënt, bovendien is niet ieder-een voor elke taak goed toegerust. Beter zou zijn als ieder individu een eigen specialiteit of taak heeft en door middel van uitwisseling van goederen en diensten met andere individuen aan zijn behoeften voldoet. Deze uit-wisseling kan op meerdere manieren plaats vinden: door middel van gift, door middel van ruil of door middel van betaling.

GifteconomieënBinnen een gifteconomie worden goederen en diensten uitgewisseld zonder dat daar een vergoeding tegenover staat, in een ideale wereld doet ieder individu waar zij goed in is en circuleren goederen en diensten binnen de gemeenschap waardoor iedereen in zijn behoeften kan voorzien. We kunnen ons voorstellen dat de eerste groe-pen jagers en verzamelaars binnen hun gemeenschap gebruik maakten van een gifteconomie. Er zal een groep mannen geweest zijn die zich voornamelijk toelegde op de jacht, anderen zullen wapens hebben moeten ver-vaardigen. De vrouwen legden zich voornamelijk toe op het verzamelen van bessen en kruiden en het bereiden van het eten. Binnen dit soort kleine en eenvoudige ge-meenschappen kan een gifteconomie floreren.

Voorbeelden van moderne gifteconomieën zijn vrijwel niet te vinden, wel kunnen op kleinere schaal voorbeel-den gevonden worden, zoals een feest bij iemand thuis waarbij geen entree betaald hoeft te worden en iedereen mag eten en drinken wat hij wil. Orgaan- en bloeddonatie werkt vrijwel overal ter wereld op basis van gift, men stelt zonder daarvoor een betaling te ontvangen een deel van hun bloed beschikbaar voor zij die dat nodig hebben. Denk klein en talloze andere voorbeelden kunnen ge-vonden worden, zoals het achterlaten van boeken op de camping of het weggeven van sigaretten en kauwgom.

Op grotere schaal komt het giftensysteem echter niet voor, blijkbaar wegen de nadelen van het systeem zwaarder dan de voordelen. Nadelen van een gifteco-nomie liggen erg voor de hand. Zo is de wereld helaas niet ideaal en zullen enkele mensen zich niet verplicht voelen volledig mee te doen met het systeem, waardoor profiteurs ontstaan: mensen die wel in hun eigen behoef-

ten voorzien, maar geen verdere bijdrage leveren aan de gemeenschap. Tevens is het systeem weinig stimu-lerend voor het verrichten van wetenschappelijk onder-zoek, aangezien niet direct duidelijk is wat de bijdrage van de wetenschapper aan de gemeenschap is (zelfs in onze moderne maatschappij wordt helaas vaak met hoon neergekeken op wetenschappers, maar dat terzij-de), waardoor vooruitgang belemmerd wordt. Een laat-ste probleem doet zich voor bij bijvoorbeeld een tekort aan een noodzakelijk goed binnen de gemeenschap. Wederom leent zich de vergelijking met de groep jagers en verzamelaars, stel je voor dat die groep een tekort aan vlees voor de winter heeft. Wellicht dat de groep een andere groep tegenkomt die ruim voldoende vlees voor de winter heeft. Een probleem doet zich voor dat het giftensysteem niet werkt tussen twee verschillende gemeenschappen. De tweede groep heeft geen reden om het vlees met de andere groep te delen, immers, een deel van het vlees wordt uit de stroom van goederen binnen de gemeenschap gehaald, zonder dat daar voor andere goederen of diensten in zijn plaats komen. De oplossing blijkt al uit de formulering van het probleem.

RuilhandelNatuurlijk zal de tweede groep bereid zijn een deel van hun voorraad aan de eerste groep beschikbaar te stellen als de die daar iets tegenover zet. Wellicht dat de tweede groep door een brand een groot deel van zijn graan is kwijtgeraakt, voor een enkele kilo’s graan willen zij best een hoeveelheid vlees beschikbaar stellen. De ruilhan-del, een systeem waarin goederen en diensten worden geruild, is geboren.

Al lijkt een systeem gebaseerd op ruilhandel op het eer-ste gezicht stabiel en een logische substitutie voor geld, zijn er geen aanwijzingen dat er economieën bestaan hebben die enkel hiervan afhankelijk waren. Ruilhandel lijkt vooral veel voor te komen in combinatie met andere systemen, zoals giften. Ook vandaag de dag wordt er volop geruild, volgens een onderzoek van de Internatio-nal Reciprocal Trade Association werd er in 2008 globaal door bedrijven voor ruim 10 miljard dollar aan goederen

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verruild. Ook in tijden van hyperinflatie, of in gebieden waar zeer weinig geld voor handen is, wordt veelvuldig gebruik gemaakt van ruilhandel. Immers, de goederen die verkregen zijn door ruil zijn vaak ook morgen nog beschikbaar, terwijl geld morgen de helft aan waarde verloren kan hebben.

Als bijzaak of in tijden van crisis bewijst ruilhandel dus ze-ker zijn nut. Echter, als voornaamste manier van betaling is ruilhandel om verscheidene redenen niet geschikt. Zo moet er bij een ruil eerst iemand gevonden worden die gelijktijdig geïnteresseerd is in hetgeen jij als ruilmiddel aanbied. Dit zal zeker niet altijd het geval zijn, vooral niet als hetgeen jij aanbiedt niet houdbaar en daardoor niet geschikt voor sparen is. Ook voor sparen, het opslaan van waarde, zijn grote goederen niet bijzonder geschikt, aangezien ze veel ruimte innemen en moeilijk verplaats-baar zijn.

Grote goederen brengen vaak nog een probleem met zich mee: vaak zijn ze veel waard en niet deelbaar. Bij het kopen van een brood zou het praktisch zijn slechts dat deel van het goed aan te bieden dat evenveel waard is als een brood, echter weinig bakkers zullen in enkel een stoelpoot geïnteresseerd zijn.

Om deze nadelen te omzeilen is het proces van betalen door middel van ruil langzaam maar zeker geëvolueerd naar een proces waarbij betaald wordt met een betaal-middel zoals gouden munten. Een betaalmiddel moet aan enkele voorwaarden voldoen, waardoor de hierbo-ven beschreven problemen omzeilt worden. Allereerst is het belangrijkste dat een betaalmiddel

schaars en algemeen begeerd is, waardoor je er altijd mee kunt betalen. Gras zou als betaalmiddel niet ge-schikt zijn, als je niet genoeg gras hebt om iets leuks te kopen zou je het gewoon kunnen plukken. Zelfs als gras-velden door de overheid gereguleerd zouden worden, is het niet bijzonder moeilijk om thuis gras te kweken.Daarnaast moet een betaalmiddel draagbaar en goed transporteerbaar zijn: een betaalmiddel moet een niet te groot volume hebben. Hieruit volgt dat een betaalmiddel in kleine hoeveelheden veel waard moet zijn. Een laat-ste voorwaarde is dat het betaalmiddel niet voor bederf gevoelig moet zijn.In de geschiedenis hebben vele voorwerpen als betaal-middel gediend: schelpen, kostbare metalen zoals goud en zilver en zelfs thee of zout.

Van ruil naar geldKooplieden van voor onze jaartelling ruilden goederen veelal met vee. In de achtste eeuw na Christus werd in bepaalde gebieden de os als rekeneenheid gebruikt, de waarde van goederen werd dus in ossen uitgedrukt. Het woord ‘pecunia’, synoniem voor geld, dateert ook die tijd, het is afgeleid van het Latijnse woord ‘pecus’, dat vee be-tekent. Voor reizende kooplieden is vee echter geen ide-aal betaalmiddel: het vee neemt veel ruimte in, vertraagt in veel gevallen de mars en moet gevoerd worden. In latere gevallen werd er dan ook steeds minder met vee geruild, maar nam tabak, thee of zout hun plek in.

Zout komt op veel plekken in de geschiedenis naar voren als betaalmiddel, dat is niet verwonderlijk want zout was

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erg kostbaar. Zout kan gemakkelijk vervoerd worden, be-derft niet en was, zeker in het binnenland, niet ruim voor-handen. Bovendien is zout een goed conserveermiddel, bewaar vlees in zout en het is langer houdbaar, vraag naar zout was daardoor vrijwel altijd aanwezig. Marco Polo meldde dat er in het China van de 13e eeuw met ba-ren zout werd betaald, ook in de Romeinse tijd was zout een algemeen betaalmiddel en dat terwijl de Romeinen ook al munten kenden. Met dit in ons achterhoofd is ook het woord ‘salaris’ af te leiden, ‘sal’ is Latijn voor zout.

Net als zout zijn ook bepaalde schelpen een tijd lang als betaalmiddel gebruikt, zoals bijvoorbeeld de kaurischelp. De herkomst van deze schelp ligt op de Malediven (die vandaar ook de Kauri-Eilanden genoemd worden), hier wordt de schelp voor het eerst als ruilmiddel gebruikt. De schelp verspreidt zich echter al snel, het wordt al in de veertiende eeuw voor Christus in China als ruilmiddel

gebruikt. Ook op Nederlands Nieuw-Guinea en in Su-riname werden de schelpen als zodanig gebruikt. In de gouden eeuw waren de schelpen ook in Nederland bij-zonder populair. De Verenigde Oost-Indische Compag-nie nam de schelpen mee om ze in Nederland aan de West Indische Compagnie te verkopen. De W.I.C. kocht met deze schelpen slaven in Afrika. Tijdens het hoogte-punt van de slavenhandel was Amsterdam een van de grootste distributiecentra van de kaurischelp.

MuntenIn tegenstelling tot zout komen schelpen al behoorlijk in de buurt van moderne betaalmiddelen. Zout kan door de

ontvanger gebruikt worden als consumptiegoed even-als zout kan dienen als puur betaalmiddel waar de ont-vanger later zelf goederen mee zal kopen, bij schelpen ligt de zaak iets anders. Immers, schelpen dienen geen praktisch nut, behalve dat ze als sieraad gebruikt kunnen worden. Schelpen worden enkel als betaalmiddel geac-cepteerd omdat de ontvanger weet dat deze schaars zijn en er ook door anderen waarde aan toegekend wordt, waardoor ook hij de schelp als betaalmiddel kan gebrui-ken. Echter, we zullen schelpen nog wel als goederen-geld blijven beschouwen, omdat ze als rekeneenheid lastiger te gebruiken zijn. Een schelp kan groter dan een andere schelp zijn, of van betere kwaliteit. Echter, een prijs uitgedrukt in schelpen voorziet hier niet in. Met de komst van de eerste munten werd dit probleem verhol-pen. Geld kan hierdoor niet alleen gebruikt worden om mee te betalen, of mee te sparen, een derde functie kan worden toegevoegd: geld is een rekenmiddel.

De eerste geslagen munten komen uit het staatje Ly-dië, gelegen in het westen van het huidige Turkije, uit de zesde eeuw voor Christus. De inwoners van Lydië waren handelaren en hadden als zodanig behoefte aan een handig betaalmiddel. Daarvoor gebruikten zij aan-vankelijk klompjes electrum, een legering van goud en zilver dat in de natuur voorkomt, die zij in de rivierbed-ding vonden. Een probleem dat zich met dit betaalmid-del voordeed was dat de samenstelling van de klompjes electrum nooit gelijk was. Soms bestond een klompje voornamelijk uit goud, weer een ander bestond voorna-melijk uit zilver. En aangezien zilver en goud in waarde niet gelijk waren, kon de waarde van een klompje elec-trum behoorlijk schommelen. Vandaar dat koning Croe-sus (561-546 v.Chr.) besloot het zilver en het goud te

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scheiden en in muntvorm te gieten. Hij kiemde de afme-tingen van de munten dusdanig uit dat een gouden munt precies twintig zilveren munten waard was. Deze munten kregen vervolgens een stempel, zodat voor alle Lydiërs duidelijk was dat het een echte munt was, die precies die waarde vertegenwoordigde die ook op de munt stond.

Ook de Grieken zagen wel iets in een dergelijk beta-lingssysteem. In Athene werden vanaf 545 voor Christus drachmen geslagen. Deze zilveren drachme was on-derverdeeld in zes koperen obolen (welke in de Griekse mythologie diende als betaling om rivier de Styx naar de onderwereld over te steken), tevens bestonden er andere munten zoals de didrachmon en tetradrachmon die respectievelijk twee en vier zilveren drachme waard waren. Met de komst van Alexander de Grote (356 – 323 v.Chr.) die het Macedonische rijk flink uitbreidde, werd de drachme in heel het Middellandse Zeegebied als betaalmiddel geaccepteerd. De drachme, althans een gemoderniseerde versie, is tot 2002 het betaalmiddel geweest in Griekenland, daarna werd deze door de euro vervangen.

In West-Europa wordt muntgeld door de Romeinen ge-introduceerd met als voornaamste reden het heffen van belastingen aan Rome gemakkelijker te maken. Met het

vertrek van de Romeinen in de vijfde eeuw vertrekt ook het gebruik van munten als betaalmiddel met hen. Pas aan het eind van de achtste eeuw wordt het muntenstel-sel door Karel de Grote heringevoerd. Halverwege de Middeleeuwen (vanaf pakweg het jaar duizend) gaat het bijzonder goed met West-Europa, de economieën flore-ren en verschillende landen en gebieden introduceren een eigen munt. De Engelse sterling doet zijn intrede en in de Nederlanden wordt in 1253 de eerste florijn ge-slagen.

PapiergeldIs het systeem dat tot dusver beschreven staat ideaal of bevat het nog enkele knelpunten? Tegenwoordig beta-len we niet enkel met munten, maar ook met papiergeld of zelfs met de bankpas, deze zullen niet zonder reden bestaan. Een systeem waarbij enkel met munten betaald wordt is dan ook niet ideaal.

We hebben gezien dat de invoering van een muntstel-sel veelal gepaard gaat met veelvuldig handelende eco-nomieën, mensen die in een dergelijk systeem kansen om waarde te creëren goed benutten, zullen rijk worden. Echter, in een stelsel waar enkel munten geïntegreerd

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zijn, houdt rijk zijn in dat de persoon erg veel munten be-zit. Het opslaan van economische waarde geschiedde in werkelijkheid door het kopen van goudstaven, welke veel waard en bijzonder waardevast zijn. Ook grote transac-ties werden, gezien hun geringe waarde, meestal niet met munten verricht, maar met goudstaven. Het bewa-ren en transporteren van deze goudstaven nam een groot risico met zich mee, goudtransporten waren een gewild doelwit voor overvallers.

Vandaar dat veel handelaren hun goudstaven bij de goudsmid lieten bewaren. De goudsmid had altijd goud voor handen en om dit te bewaren was hij in bezit van een grote kluis, waarin het goud met een miniem risico bewaart kon worden. Als bewijs dat de goudsmid een schuld bij de handelaar had, schreef hij waardepapieren uit waarop dit vermeld stond. De handelaren gebruikten deze waardepapieren niet alleen om op een veilige ma-nier te sparen, maar gingen ook transacties aan waar-mee zij betaalden met de waardepapieren.

Al snel circuleerden deze waardepapieren door de eco-nomie waarbij de nominale waarde van het waardepa-pier daadwerkelijk garant stond voor een opgeborgen hoeveelheid goud. Aangezien de goudsmeden bekend stonden als zeer vermogend, was het niet verwonderlijk

dat handelaren hen al snel benaderden voor leningen. Een goudsmid schreef vervolgens een waardepapier uit, waarbij hij er van uitging dat hij later die hoeveelheid aan goud plus rente terug zou krijgen. Aangezien alleen de goudsmid wist hoeveelheid goud hij daadwerkelijk in zijn kluis had en wat de totale waarde was van de waardepa-pieren die hij had uitgeschreven, kon hij meer waardepa-pieren uitschrijven dan hij daadwerkelijk aan goud in kas had. Zolang de goudsmid bekend bleef staan als vermo-gend is dit systeem over het algemeen stabiel. Een beta-lingssysteem met papiergeld gebaseerd op vertrouwen is geïntroduceerd.

Tegenwoordig hebben bankiers de rol van goudsmid overgenomen en is de koppeling van papiergeld aan goud grotendeels verdwenen. Wat zal de toekomst bren-gen? Wellicht een globale munteenheid, misschien dat chartaal geld wel in zijn geheel afgeschaft zal worden en alle betalingen giraal plaats zullen vinden. Wij als econo-metristen zullen een van velen zijn die er over na mogen denken.

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KORT DOOR DE BOCHT

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Tekst: Kevin Mann

Versier een econometrist (1)

Met Valentijnsdag weer in het verschiet, worden we door de media overspoelt met informatie over liefde en aantrekkingskracht. Voor de vrouwelijke lezer die geïn-teresseerd is in hoe zij zichzelf het best op de markt kan plaatsen heeft ondergetekende het nodige samengevat.Zo blijkt uit onderzoek van psycholoog David Holmes dat de meeste mannen mooie rondingen prefereren bo-ven een mager alternatief. Hij ontwikkelde een formule die voorspelt in hoeverre een man zich tot een bepaald vrouwenlichaam aangetrokken voelt. De formule ziet er als volgt uit: ((Cupmaat + dij-lengte ratio + heup-middel ratio) * rondingsindex) + symmetrie-index.Uit deze formule blijkt onder andere dat een DD of E cup, een zandloperfiguur en een symmetrisch voorkomen de man erg blij maakt. De herkomst van de deze voorkeur moet gezocht worden in ons evolutionaire verleden: het zien van een vrouw met de juiste rondingen prikkelt het hormonale systeem van de man, waardoor lust opge-wekt wordt, aldus Holmes.Valt Valentijnsdag dit jaar precies samen met je ovula-tie, terwijl tevens je parfum op is? Dat betekent volgens onderzoekers Saul Miller en Jon Maner van de Florida State University dat je kans een man te versieren nog groter geworden is. Zij testten wat het effect van geur op mannen is, door enkele vrouwen, die in verschillende periodes van hun cyclus zaten, drie nachten lang in het-zelfde shirt te laten slapen. Een groep mannen moest vervolgens aan deze shirts ruiken en ze beoordelen. Het bleek dat mannen die shirts die tijdens de vruchtbare periode van de vrouw gedragen waren, als het lekkerste beoordeelden. Bovendien werd bij reuk aan deze shirts een verhoging van het testosterongehalte in het speek-sel van de mannen waargenomen, terwijl dit bij de an-dere shirts vrijwel niet het geval bleek.

Tekst: Jurjen Boog

De oplossing van het filepar-keren

Simon Blackburn van de University of London heeft de minimale lengte die een auto nodig heeft bij het filepar-keren berekend. In zijn artikel bekijkt hij hoe groot de parkeerplek moet zijn om in één beweging netjes in het vak te belanden.

Uiteindelijk kwam Blackburn tot de volgende conclusie: de minimale benodigde ruimte bij het fileparkeren is ge-lijk aan de lengte van de auto plus

waar r staat voor de draaicirkel van de auto, l de afstand tussen de middens van de voor- en achterwielen, k de afstand tussen de neus van de auto en het midden van de voorste wielen, en w de breedte van de auto waar achter geparkeerd wordt.

Zijn bewijs voor de formule maakt gebruik van de stelling van Pythagoras en een aantal simpele eigenschappen van een cirkel. De beweging van de voorwielen maken bij het inparkeren een perfecte cirkel, aldus Blackburn.

Voor bijvoorbeeld een Honda Civic met straal van de draaicirkel r = 5,5m, wielbasis l =2,6m , van neus tot wiel k =1,3m , en met de breedte van de auto voor het plaats-je w = 1,8m, is de minimaal benodigde ruimte de lengte van de auto plus 1,52 meter.

Voortaan hoeft dus niet meer uitgeprobeerd te worden of de auto op een plek past. Met een lineaal of stok in de auto kan het exact bekeken worden.

√(r2 − l2) + (l + k)2 − (

√r2 − l2 − w)2 − l − k

1

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Jaargang 33 - GAXEX 2 13

Tekst: Kevin Mann

Versier een econometrist (2)

Nu je als vrouw de keuze gemaakt hebt op Valentijns-dag geen parfum te dragen, kan ook de make-up wel overboord. Een onderzoek uitgevoerd door een Engels kauwgummerk onder ruim duizend Britse mannen heeft namelijk aangetoond dat mannen liever zien dat een vrouw lacht dan dat ze opgemaakt is. Tijdens het on-derzoek kregen de mannen telkens twee foto’s te zien van dezelfde vrouw: op een van de foto’s droeg ze geen make-up, maar keek ze lachend naar de camera, ter-wijl ze op de andere foto wel make-up droeg, maar niet lachte. Zeventig procent van de mannen gaf de voorkeur aan de lachende de vrouw, van wie zij aangaven een leukere en bereikbare indruk te hebben. Over lachende vrouwen met make-up en chagrijnig kijkende vrouwen zonder make-up wordt in het onderzoek niet gerept. On-dergetekende begrijpt wel waarom.

Klaar om zowel parfum- als make-uploos op de econo-metrist af te stappen kan het nog wel eens gebeuren dat je als vrouw flink bloost. Gelukkig is ook hier aan de uni-versiteit van St. Andrews onderzoek naar gedaan. Het blijkt dat mannen vrouwen met een rode blos aantrekke-lijker vinden en gezonder inschatten. De onderzoekers vroegen een groep vrijwilligers om een digitale foto van een persoon zo te bewerken dat deze er gezonder en aantrekkelijker uitzag. Het bleek dat vrijwel alle vrijwil-ligers roodtinten aan de wangen toevoegden. Conclusie: met blozen is niets mis.

Tekst: Jurjen Boog

”Mens kan 65 km/u lopen”

In mei 2008 verbeterde Usain Bolt het wereldrecord op de 100m atletiek voor de eerste keer naar 9,72 secon-den. Onderzoekers stelden zich naar aanleiding van deze verbetering de vraag wat de maximale snelheid is die de mens te voet kan behalen. Het resultaat was het volgende: de maximale tijd op een 100m sprint is 9,6 seconden, met een maximale snelheid van 43,06 km/u. Als de mens sneller rent, wordt de belasting op de spie-ren te groot en zal de bovenbeenspieren van hun plek af trekken.

Op 16 augustus 2009 liep Usain Bolt echter onder deze minimaal geachte tijd. In Berlijn rende hij in 9,58 secon-den naar de finishlijn – een verbetering van het record met 11 honderdste van een seconde. Zelf doet hij de uitspraak dat hij de afstand in 9,4 seconden kan over-bruggen. Hoe reageerden wetenschappers op deze ver-plettering van het wereldrecord, en daarmee de gestelde ondergrens?

Amerikaans onderzoek verwerpt de aanname dat de maximale belasting op de ledematen de beperkende factor voor de maximumsnelheid voor de mens is. De druk op de bovenbenen van een atleet bleek inderdaad niet de reden voor de ondergrens te zijn.

De nieuwe ondergrens wordt gesteld door de kracht waarmee de spieren kunnen samentrekken op het mo-ment dat de voeten met de grond in contact komen. Met behulp van deze nieuwe aanname, wordt de maximale snelheid van de mens op 55-65 km/u geschat. Misschien dat Bolt zijn uitspraak nog kan waarmaken.

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14

Text: Richard KamstPhoto: Huub Snoep

The Olympic 1000m Speed Skating Event

Richard Kamst, Gerard Kuper, and Gerard Sierksma

November 2009

The Olympic 1000m Speed Skating Event

Richard Kamst, Gerard Kuper, and Gerard Sierksma

November 2009

University of GroningenThe Netherlandse-mail: [email protected]

1

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Jaargang 33 - GAXEX 2 15

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

In order to establish the difference between 1000m times skated with a start in the inner and the outer lane, we must correct for the fact that performances are achieved during different seasons and on different rinks. Conse-quently, we introduce the dummy variables

and for each and . The dummy variable Seasonc;j;i is equal to 1 if the ith finishing time of skater c is skated during season j. Similarly, the dummy variable Rinkc;k;i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore,

The set of skaters in the data set; Skater index, ; The set of contests in which skater participated; Contest index of skater , ; The set of seasons in the data set ( contains nine seasons); Season index, ; The set of rinks in the data set ( contains 19 rinks); Rink index, ; The set of contests during season in which skater participated; The set of contests skated at rink in which skater participated; The 1000m finishing time of skater skated on rink during contest i in season j.

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

IntroductionSpeed skating has matured so much during the last de-cade that small differences in race circumstances may determine whether or not a skater wins a medal. The widely accepted hypothesis that the start position (inner vs. outer) significantly inuences nishing times is conrmed by an analysis of 1000m times skated during the Olym-pic Games, the World Championships Single Distances, and World Cups in the period 2000-2009. Our analysis strongly suggests that the 1000m should be skated twice during Olympic Games and World Championships Sin-gle Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skated are the sections of a 1000m race that might cause the signicant dierence between 1000m times skated. The first lane change oc-curs immediately after the second curve, when a skater starting in the inner lane moves to the outer lane, and

vice versa. The last lane change occurs after passing the fourth curve. During the first lane change, the skater starting in the outer lane may have an advantage be-cause he/she can utilize the slipstream of the skater starting in the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, as the skater start-ing in the inner lane enters the last curve via the outer lane, then crosses to the inner lane for the finish. Many believe that skating a final curve of the outer lane is more difficult than a final curve of the inner lane for an ex-hausted skater.

The statistical modelIndices and parameters describing clock times for the 1000m finishing times are as follows:

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Page 16: GAXEX jaargang 33, editie 2

16

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

we introduce the dummy variable Vc;i for the inner-outer information, so that Vc;i equals 1 if skater c starts in the outer lane during his/her ith race. The dummies are in-cluded in a regression function, together with a constant and a measure of individual ability, yielding the following model for each , , , ,

with

As the season and rink dummies correspond to categori-cal variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewritten as follows,

In model (2), the season parameter ~ is the average level of performance during season l compared to the season 2000-2001, while the rink parameter ~ is the average level of speed on rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specic intercept c as a fixed effect (Mundlak, 1978).

Deciding on outliersSpeed skating is a technical sport that includes falls and minor slips, leading to results that deviate from `average’ performances. It is necessary to eliminate these devia-tions from our inference of the parameter that mea-sures the dierence between the 1000m nishing times when skated with a start in the inner and the outer lane. Therefore, we select 1000m times of error-free races by eliminating times of skaters in races containing a fall or slip. In order to do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

Introduction

Speed skating has matured so much during the last decade that small differences in racecircumstances may determine whether or not a skater wins a medal. The widely acceptedhypothesis that the start position (inner vs. outer) significantly influences finishing timesis confirmed by an analysis of 1000m times skated during the Olympic Games, the WorldChampionships Single Distances, and World Cups in the period 2000-2009. Our analysisstrongly suggests that the 1000m should be skated twice during Olympic Games and WorldChampionships Single Distances.

After analysing 1000m races, we argue that the change of lanes and the last curve skatedare the sections of a 1000m race that might cause the significant difference between 1000mtimes skated. The first lane change occurs immediately after the second curve, when a skaterstarting in the inner lane moves to the outer lane, and vice versa. The last lane change occursafter passing the fourth curve. During the first lane change, the skater starting in the outerlane may have an advantage because he/she can utilize the slipstream of the skater startingin the inner lane, while the reverse holds true during the second change of lanes.

The last lane change (last curve) may account for the greatest discrepancy in finish times, asthe skater starting in the inner lane enters the last curve via the outer lane, then crosses tothe inner lane for the finish. Many believe that skating a final curve of the outer lane is moredifficult than a final curve of the inner lane for an exhausted skater.

The statistical model

Indices and parameters describing clock times for the 1000m finishing times are as follows:

C The set of skaters in the data set;c Skater index, c ∈ C;Nc The set of contests in which skater c participated;i Contest index of skater c, i ∈ Nc;J The set of seasons in the data set (J contains nine seasons);j Season index, j ∈ J ;K The set of rinks in the data set (K contains 19 rinks);k Rink index, k ∈ K;Nc,j The set of contests during season j in which skater c participated;Nc,k The set of contests skated at rink k in which skater c participated;Finishi,c,j,k The 1000m finishing time of skater c skated on rink k during contest i in season j.

In order to establish the difference between 1000m times skated with a start in the inner andthe outer lane, we must correct for the fact that performances are achieved during differentseasons and on different rinks. Consequently, we introduce the dummy variables Seasonc,j,i

and Rinkc,k,i for each c ∈ C, j ∈ J and k ∈ K. The dummy variable Seasonc,j,i is equal to 1if the ith finishing time of skater c is skated during season j. Similarly, the dummy variableRinkc,k,i equals 1 if the ith finishing of skater c is skated at rink k. Furthermore, we introducethe dummy variable Vc,i for the inner-outer information, so that Vc,i equals 1 if skater c startsin the outer lane during his/her ith race.

2

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

Constant; Parameter that measures the average level of performance of skater c; Parameter that measures the average level of performance of all skaters in season j; Parameter that measures the average speed of skaters at rink k; Parameter that measures the average advantage that a skater starting in the inner lane has over a skater starting in the outer lane during a 1000m race.

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

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Jaargang 33 - GAXEX 2 17

Detecting outliers with box plots By introducing bounds on the 1000m finishing times, based on box plots of the Finishi;c;j;k values, we re-move times of races containing a fall or slip. However, box plots of pooled finishing times neglect technological progress of equipment and the fact that races are skat-ed on different rinks. Therefore, we make box plots of 1000m times that are skated on the same rink and during the same season. If a finishing time is an outlier in a par-ticular box plot, the corresponding bound is lowered and the finishing time is removed. This procedure is repeated until there are no more outliers in the box plots.

Detecting outliers with test statisticsIn this section we use the same test statistic for the de-tection of outliers as in Hjort(1994). The test statistic reads

where dVar (Finishi;c;j;k) represents the estimated vari-ance of the finishing time corresponding to the ith race of skater c on location k in season j. The test statistic is the standardized value of Finishi;c;j;k or the differ-ence of Finishi;c;j;k and its expectation, divided by the estimated standard deviation of Finishi;c;j;k . The 1000m time of a male skater is defined to be an outlier if the value of Ti;c;j;k exceeds 2.60; for female skaters this value equals 2.80. We validated the selected bound values by means of a sensitivity analysis which will not be presented here. A negative value of the test statistic corresponds to a good performance, suggesting that the 1000m time skated is not an outlier.

Estimates of the fixed effects modelWe analyzed all finish times for the men’s and women’s 1000m races of the Olympic Games, World Champion-ships Single Distances, World Sprint Championships, and World Cup events in the period 2000-2009 using the website of the International Skating Union (ISU). The second 2002-2003 World Cup in Heerenveen could not be traced. The original data sets consist of 2860 and 2650 finishing times for male and female skaters, respec-tively. After removing 1000m times of races containing an error, we are left with 2697 and 2529 observations for men and women, respectively, corresponding to a dele-tion rate of 5.70% and 4.57%, respectively.

The estimates of the parameter of model (2), the clus-ter robust standard errors, and the bounds of 95% confi-dence intervals are presented in Table 1. For our analy-sis, we made use of the program STATA.

We are primarily interested in the estimated value of , which measures the difference in time between 1000m races skated with a start in the inner and the outer lane. Based on Table 1, we conclude that there is a difference of 0.120 seconds between starting in the inner and the outer lane for female skaters, and 0.030 seconds for male skaters. When standard errors are taken into ac-count, it follows that the figures are significant for wom-en, but insignificant for men.

Detecting outliers with test statistics

In this section we use the same test statistic for the detection of outliers as in Hjort(1994).The test statistic reads

Ti,c,j,k =Finishi,c,j,k − F̂inishi,c,j,k√

V̂ar (Finishi,c,j,k), (3)

where V̂ar (Finishi,c,j,k) represents the estimated variance of the finishing time correspondingto the ith race of skater c on location k in season j.

The test statistic is the standardized value of Finishi,c,j,k, or the difference of Finishi,c,j,k

and its expectation, divided by the estimated standard deviation of Finishi,c,j,k. The 1000mtime of a male skater is defined to be an outlier if the value of Ti,c,j,k exceeds 2.60; for femaleskaters this value equals 2.80. We validated the selected bound values by means of a sensitivityanalysis which will not be presented here. A negative value of the test statistic correspondsto a good performance, suggesting that the 1000m time skated is not an outlier.

Estimates of the fixed effects model

We analyzed all finish times for the men’s and women’s 1000m races of the Olympic Games,World Championships Single Distances, World Sprint Championships, and World Cup eventsin the period 2000-2009 using the website of the International Skating Union(ISU). The sec-ond 2002-2003 World Cup in Heerenveen could not be traced. The original data sets consistof 2860 and 2650 finishing times for male and female skaters, respectively. After removing1000m times of races containing an error, we are left with 2697 and 2529 observations for menand women, respectively, corresponding to a deletion rate of 5.70% and 4.57%, respectively.

The estimates of the parameter δ of model (2), the cluster robust standard errors, and thebounds of 95% confidence intervals are presented in Table 1. For our analysis, we made useof the program STATA.

Men WomenPar. Regressor Est. SE 95% C.I. Est. SE 95% C.I.δ V I/O 0.030 0.019 -0.008 0.068 0.120 0.029 0.063 0.177

Table 1: Estimates of the fixed effects model using data of tournaments between 2000-2009.Par.=Parameter, Est.=Estimate, SE=Standard Error, and 95% C.I.=95% Confidence Inter-val.

We are primarily interested in the estimated value of δ, which measures the difference in timebetween 1000m races skated with a start in the inner and the outer lane. Based on Table 1,we conclude that there is a difference of 0.120 seconds between starting in the inner and theouter lane for female skaters, and 0.030 seconds for male skaters. When standard errors aretaken into account, it follows that the figures are significant for women, but insignificant formen.

4

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

Detecting outliers with test statistics

In this section we use the same test statistic for the detection of outliers as in Hjort(1994).The test statistic reads

Ti,c,j,k =Finishi,c,j,k − F̂inishi,c,j,k√

V̂ar (Finishi,c,j,k), (3)

where V̂ar (Finishi,c,j,k) represents the estimated variance of the finishing time correspondingto the ith race of skater c on location k in season j.

The test statistic is the standardized value of Finishi,c,j,k, or the difference of Finishi,c,j,k

and its expectation, divided by the estimated standard deviation of Finishi,c,j,k. The 1000mtime of a male skater is defined to be an outlier if the value of Ti,c,j,k exceeds 2.60; for femaleskaters this value equals 2.80. We validated the selected bound values by means of a sensitivityanalysis which will not be presented here. A negative value of the test statistic correspondsto a good performance, suggesting that the 1000m time skated is not an outlier.

Estimates of the fixed effects model

We analyzed all finish times for the men’s and women’s 1000m races of the Olympic Games,World Championships Single Distances, World Sprint Championships, and World Cup eventsin the period 2000-2009 using the website of the International Skating Union(ISU). The sec-ond 2002-2003 World Cup in Heerenveen could not be traced. The original data sets consistof 2860 and 2650 finishing times for male and female skaters, respectively. After removing1000m times of races containing an error, we are left with 2697 and 2529 observations for menand women, respectively, corresponding to a deletion rate of 5.70% and 4.57%, respectively.

The estimates of the parameter δ of model (2), the cluster robust standard errors, and thebounds of 95% confidence intervals are presented in Table 1. For our analysis, we made useof the program STATA.

Men WomenPar. Regressor Est. SE 95% C.I. Est. SE 95% C.I.δ V I/O 0.030 0.019 -0.008 0.068 0.120 0.029 0.063 0.177

Table 1: Estimates of the fixed effects model using data of tournaments between 2000-2009.Par.=Parameter, Est.=Estimate, SE=Standard Error, and 95% C.I.=95% Confidence Inter-val.

We are primarily interested in the estimated value of δ, which measures the difference in timebetween 1000m races skated with a start in the inner and the outer lane. Based on Table 1,we conclude that there is a difference of 0.120 seconds between starting in the inner and theouter lane for female skaters, and 0.030 seconds for male skaters. When standard errors aretaken into account, it follows that the figures are significant for women, but insignificant formen.

4

Detecting outliers with test statistics

In this section we use the same test statistic for the detection of outliers as in Hjort(1994).The test statistic reads

Ti,c,j,k =Finishi,c,j,k − F̂inishi,c,j,k√

V̂ar (Finishi,c,j,k), (3)

where V̂ar (Finishi,c,j,k) represents the estimated variance of the finishing time correspondingto the ith race of skater c on location k in season j.

The test statistic is the standardized value of Finishi,c,j,k, or the difference of Finishi,c,j,k

and its expectation, divided by the estimated standard deviation of Finishi,c,j,k. The 1000mtime of a male skater is defined to be an outlier if the value of Ti,c,j,k exceeds 2.60; for femaleskaters this value equals 2.80. We validated the selected bound values by means of a sensitivityanalysis which will not be presented here. A negative value of the test statistic correspondsto a good performance, suggesting that the 1000m time skated is not an outlier.

Estimates of the fixed effects model

We analyzed all finish times for the men’s and women’s 1000m races of the Olympic Games,World Championships Single Distances, World Sprint Championships, and World Cup eventsin the period 2000-2009 using the website of the International Skating Union(ISU). The sec-ond 2002-2003 World Cup in Heerenveen could not be traced. The original data sets consistof 2860 and 2650 finishing times for male and female skaters, respectively. After removing1000m times of races containing an error, we are left with 2697 and 2529 observations for menand women, respectively, corresponding to a deletion rate of 5.70% and 4.57%, respectively.

The estimates of the parameter δ of model (2), the cluster robust standard errors, and thebounds of 95% confidence intervals are presented in Table 1. For our analysis, we made useof the program STATA.

Men WomenPar. Regressor Est. SE 95% C.I. Est. SE 95% C.I.δ V I/O 0.030 0.019 -0.008 0.068 0.120 0.029 0.063 0.177

Table 1: Estimates of the fixed effects model using data of tournaments between 2000-2009.Par.=Parameter, Est.=Estimate, SE=Standard Error, and 95% C.I.=95% Confidence Inter-val.

We are primarily interested in the estimated value of δ, which measures the difference in timebetween 1000m races skated with a start in the inner and the outer lane. Based on Table 1,we conclude that there is a difference of 0.120 seconds between starting in the inner and theouter lane for female skaters, and 0.030 seconds for male skaters. When standard errors aretaken into account, it follows that the figures are significant for women, but insignificant formen.

4

Detecting outliers with test statistics

In this section we use the same test statistic for the detection of outliers as in Hjort(1994).The test statistic reads

Ti,c,j,k =Finishi,c,j,k − F̂inishi,c,j,k√

V̂ar (Finishi,c,j,k), (3)

where V̂ar (Finishi,c,j,k) represents the estimated variance of the finishing time correspondingto the ith race of skater c on location k in season j.

The test statistic is the standardized value of Finishi,c,j,k, or the difference of Finishi,c,j,k

and its expectation, divided by the estimated standard deviation of Finishi,c,j,k. The 1000mtime of a male skater is defined to be an outlier if the value of Ti,c,j,k exceeds 2.60; for femaleskaters this value equals 2.80. We validated the selected bound values by means of a sensitivityanalysis which will not be presented here. A negative value of the test statistic correspondsto a good performance, suggesting that the 1000m time skated is not an outlier.

Estimates of the fixed effects model

We analyzed all finish times for the men’s and women’s 1000m races of the Olympic Games,World Championships Single Distances, World Sprint Championships, and World Cup eventsin the period 2000-2009 using the website of the International Skating Union(ISU). The sec-ond 2002-2003 World Cup in Heerenveen could not be traced. The original data sets consistof 2860 and 2650 finishing times for male and female skaters, respectively. After removing1000m times of races containing an error, we are left with 2697 and 2529 observations for menand women, respectively, corresponding to a deletion rate of 5.70% and 4.57%, respectively.

The estimates of the parameter δ of model (2), the cluster robust standard errors, and thebounds of 95% confidence intervals are presented in Table 1. For our analysis, we made useof the program STATA.

Men WomenPar. Regressor Est. SE 95% C.I. Est. SE 95% C.I.δ V I/O 0.030 0.019 -0.008 0.068 0.120 0.029 0.063 0.177

Table 1: Estimates of the fixed effects model using data of tournaments between 2000-2009.Par.=Parameter, Est.=Estimate, SE=Standard Error, and 95% C.I.=95% Confidence Inter-val.

We are primarily interested in the estimated value of δ, which measures the difference in timebetween 1000m races skated with a start in the inner and the outer lane. Based on Table 1,we conclude that there is a difference of 0.120 seconds between starting in the inner and theouter lane for female skaters, and 0.030 seconds for male skaters. When standard errors aretaken into account, it follows that the figures are significant for women, but insignificant formen.

4

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

Detecting outliers with test statistics

In this section we use the same test statistic for the detection of outliers as in Hjort(1994).The test statistic reads

Ti,c,j,k =Finishi,c,j,k − F̂inishi,c,j,k√

V̂ar (Finishi,c,j,k), (3)

where V̂ar (Finishi,c,j,k) represents the estimated variance of the finishing time correspondingto the ith race of skater c on location k in season j.

The test statistic is the standardized value of Finishi,c,j,k, or the difference of Finishi,c,j,k

and its expectation, divided by the estimated standard deviation of Finishi,c,j,k. The 1000mtime of a male skater is defined to be an outlier if the value of Ti,c,j,k exceeds 2.60; for femaleskaters this value equals 2.80. We validated the selected bound values by means of a sensitivityanalysis which will not be presented here. A negative value of the test statistic correspondsto a good performance, suggesting that the 1000m time skated is not an outlier.

Estimates of the fixed effects model

We analyzed all finish times for the men’s and women’s 1000m races of the Olympic Games,World Championships Single Distances, World Sprint Championships, and World Cup eventsin the period 2000-2009 using the website of the International Skating Union(ISU). The sec-ond 2002-2003 World Cup in Heerenveen could not be traced. The original data sets consistof 2860 and 2650 finishing times for male and female skaters, respectively. After removing1000m times of races containing an error, we are left with 2697 and 2529 observations for menand women, respectively, corresponding to a deletion rate of 5.70% and 4.57%, respectively.

The estimates of the parameter δ of model (2), the cluster robust standard errors, and thebounds of 95% confidence intervals are presented in Table 1. For our analysis, we made useof the program STATA.

Men WomenPar. Regressor Est. SE 95% C.I. Est. SE 95% C.I.δ V I/O 0.030 0.019 -0.008 0.068 0.120 0.029 0.063 0.177

Table 1: Estimates of the fixed effects model using data of tournaments between 2000-2009.Par.=Parameter, Est.=Estimate, SE=Standard Error, and 95% C.I.=95% Confidence Inter-val.

We are primarily interested in the estimated value of δ, which measures the difference in timebetween 1000m races skated with a start in the inner and the outer lane. Based on Table 1,we conclude that there is a difference of 0.120 seconds between starting in the inner and theouter lane for female skaters, and 0.030 seconds for male skaters. When standard errors aretaken into account, it follows that the figures are significant for women, but insignificant formen.

4

Detecting outliers with test statistics

In this section we use the same test statistic for the detection of outliers as in Hjort(1994).The test statistic reads

Ti,c,j,k =Finishi,c,j,k − F̂inishi,c,j,k√

V̂ar (Finishi,c,j,k), (3)

where V̂ar (Finishi,c,j,k) represents the estimated variance of the finishing time correspondingto the ith race of skater c on location k in season j.

The test statistic is the standardized value of Finishi,c,j,k, or the difference of Finishi,c,j,k

and its expectation, divided by the estimated standard deviation of Finishi,c,j,k. The 1000mtime of a male skater is defined to be an outlier if the value of Ti,c,j,k exceeds 2.60; for femaleskaters this value equals 2.80. We validated the selected bound values by means of a sensitivityanalysis which will not be presented here. A negative value of the test statistic correspondsto a good performance, suggesting that the 1000m time skated is not an outlier.

Estimates of the fixed effects model

We analyzed all finish times for the men’s and women’s 1000m races of the Olympic Games,World Championships Single Distances, World Sprint Championships, and World Cup eventsin the period 2000-2009 using the website of the International Skating Union(ISU). The sec-ond 2002-2003 World Cup in Heerenveen could not be traced. The original data sets consistof 2860 and 2650 finishing times for male and female skaters, respectively. After removing1000m times of races containing an error, we are left with 2697 and 2529 observations for menand women, respectively, corresponding to a deletion rate of 5.70% and 4.57%, respectively.

The estimates of the parameter δ of model (2), the cluster robust standard errors, and thebounds of 95% confidence intervals are presented in Table 1. For our analysis, we made useof the program STATA.

Men WomenPar. Regressor Est. SE 95% C.I. Est. SE 95% C.I.δ V I/O 0.030 0.019 -0.008 0.068 0.120 0.029 0.063 0.177

Table 1: Estimates of the fixed effects model using data of tournaments between 2000-2009.Par.=Parameter, Est.=Estimate, SE=Standard Error, and 95% C.I.=95% Confidence Inter-val.

We are primarily interested in the estimated value of δ, which measures the difference in timebetween 1000m races skated with a start in the inner and the outer lane. Based on Table 1,we conclude that there is a difference of 0.120 seconds between starting in the inner and theouter lane for female skaters, and 0.030 seconds for male skaters. When standard errors aretaken into account, it follows that the figures are significant for women, but insignificant formen.

4

Detecting outliers with test statistics

In this section we use the same test statistic for the detection of outliers as in Hjort(1994).The test statistic reads

Ti,c,j,k =Finishi,c,j,k − F̂inishi,c,j,k√

V̂ar (Finishi,c,j,k), (3)

where V̂ar (Finishi,c,j,k) represents the estimated variance of the finishing time correspondingto the ith race of skater c on location k in season j.

The test statistic is the standardized value of Finishi,c,j,k, or the difference of Finishi,c,j,k

and its expectation, divided by the estimated standard deviation of Finishi,c,j,k. The 1000mtime of a male skater is defined to be an outlier if the value of Ti,c,j,k exceeds 2.60; for femaleskaters this value equals 2.80. We validated the selected bound values by means of a sensitivityanalysis which will not be presented here. A negative value of the test statistic correspondsto a good performance, suggesting that the 1000m time skated is not an outlier.

Estimates of the fixed effects model

We analyzed all finish times for the men’s and women’s 1000m races of the Olympic Games,World Championships Single Distances, World Sprint Championships, and World Cup eventsin the period 2000-2009 using the website of the International Skating Union(ISU). The sec-ond 2002-2003 World Cup in Heerenveen could not be traced. The original data sets consistof 2860 and 2650 finishing times for male and female skaters, respectively. After removing1000m times of races containing an error, we are left with 2697 and 2529 observations for menand women, respectively, corresponding to a deletion rate of 5.70% and 4.57%, respectively.

The estimates of the parameter δ of model (2), the cluster robust standard errors, and thebounds of 95% confidence intervals are presented in Table 1. For our analysis, we made useof the program STATA.

Men WomenPar. Regressor Est. SE 95% C.I. Est. SE 95% C.I.δ V I/O 0.030 0.019 -0.008 0.068 0.120 0.029 0.063 0.177

Table 1: Estimates of the fixed effects model using data of tournaments between 2000-2009.Par.=Parameter, Est.=Estimate, SE=Standard Error, and 95% C.I.=95% Confidence Inter-val.

We are primarily interested in the estimated value of δ, which measures the difference in timebetween 1000m races skated with a start in the inner and the outer lane. Based on Table 1,we conclude that there is a difference of 0.120 seconds between starting in the inner and theouter lane for female skaters, and 0.030 seconds for male skaters. When standard errors aretaken into account, it follows that the figures are significant for women, but insignificant formen.

4

Detecting outliers with test statistics

In this section we use the same test statistic for the detection of outliers as in Hjort(1994).The test statistic reads

Ti,c,j,k =Finishi,c,j,k − F̂inishi,c,j,k√

V̂ar (Finishi,c,j,k), (3)

where V̂ar (Finishi,c,j,k) represents the estimated variance of the finishing time correspondingto the ith race of skater c on location k in season j.

The test statistic is the standardized value of Finishi,c,j,k, or the difference of Finishi,c,j,k

and its expectation, divided by the estimated standard deviation of Finishi,c,j,k. The 1000mtime of a male skater is defined to be an outlier if the value of Ti,c,j,k exceeds 2.60; for femaleskaters this value equals 2.80. We validated the selected bound values by means of a sensitivityanalysis which will not be presented here. A negative value of the test statistic correspondsto a good performance, suggesting that the 1000m time skated is not an outlier.

Estimates of the fixed effects model

We analyzed all finish times for the men’s and women’s 1000m races of the Olympic Games,World Championships Single Distances, World Sprint Championships, and World Cup eventsin the period 2000-2009 using the website of the International Skating Union(ISU). The sec-ond 2002-2003 World Cup in Heerenveen could not be traced. The original data sets consistof 2860 and 2650 finishing times for male and female skaters, respectively. After removing1000m times of races containing an error, we are left with 2697 and 2529 observations for menand women, respectively, corresponding to a deletion rate of 5.70% and 4.57%, respectively.

The estimates of the parameter δ of model (2), the cluster robust standard errors, and thebounds of 95% confidence intervals are presented in Table 1. For our analysis, we made useof the program STATA.

Men WomenPar. Regressor Est. SE 95% C.I. Est. SE 95% C.I.δ V I/O 0.030 0.019 -0.008 0.068 0.120 0.029 0.063 0.177

Table 1: Estimates of the fixed effects model using data of tournaments between 2000-2009.Par.=Parameter, Est.=Estimate, SE=Standard Error, and 95% C.I.=95% Confidence Inter-val.

We are primarily interested in the estimated value of δ, which measures the difference in timebetween 1000m races skated with a start in the inner and the outer lane. Based on Table 1,we conclude that there is a difference of 0.120 seconds between starting in the inner and theouter lane for female skaters, and 0.030 seconds for male skaters. When standard errors aretaken into account, it follows that the figures are significant for women, but insignificant formen.

4

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

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18

Correcting the 1000m times between 2000-2009Hjort’s(1994) correction of the 500m times of the Olym-pic Games in Calgary(1988), Albertville(1992), and Lillehamer(1994) showed that a reversed draw of lanes changed the medal winners. For example, Jan Ykema won the silver medal in Calgary with a 500m time of 36.76 sec; however, when his time was corrected for the advantage of his start (inner lane), the result was 36.81 sec and a fourth-place finish.

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As an illustration of what could have happened with a re-versed inner/outer track draw during the Olympic Games and the World Championships Single Distances in the period 2000-2009, we subtracted the estimate of from 1000m times skated with a start in the outer lane. Table 2 shows the actual ranking together with the ranking based on a reversed draw for the 2008-2009 World Champion-ships Single Distances and the 2010 Olympic Games.

Correcting the 1000m times between 2000-2009

Hjort’s(1994) correction of the 500m times of the Olympic Games in Calgary(1988), Al-bertville(1992), and Lillehamer(1994) showed that a reversed draw of lanes changed the medalwinners. For example, Jan Ykema won the silver medal in Calgary with a 500m time of 36.76sec; however, when his time was corrected for the advantage of his start (inner lane), theresult was 36.81 sec and a fourth-place finish.

As an illustration of what could have happened with a reversed inner/outer track draw duringthe Olympic Games and the World Championships Single Distances in the period 2000-2009,we subtracted the estimate of δ from 1000m times skated with a start in the outer lane.Table 2 shows the actual ranking together with the ranking based on a reversed draw for the2008-2009 World Championships Single Distances and the 2010 Olympic Games.

World Championships Single Distances. Vancouver 2009Realized ranking Corrected ranking1 T. Marsicano I 1:08.96 1 T. Marsicano I 1:08.962 D. Morrison I 1:09.00 2 S. Davis I 1:08.993 S. Davis O 1:09.02 3 D. Morrison I 1:09.004 S. Groothuis O 1:09.25 4 S. Groothuis I 1:09.225 J. Bos O 1:09.27 5 J. Bos I 1:09.24

Realized ranking Corrected ranking1 C. Nesbitt I 1:16.28 1 C. Nesbitt I 1:16.282 A. Friesinger I 1:16.32 2 A. Friesinger I 1:16.323 M. Boer O 1:16.44 2 M. Boer I 1:16.324 N. Bruintjes I 1:16.80 4 N. Bruintjes I 1:16.805 S. Yoshii I 1:16.82 5 S. Yoshii I 1:16.82

Olympic Games. Vancouver 2010Realized ranking Corrected ranking1 S. Davis O 1:08.94 1 S. Davis I 1:08.912 T.-B. Mo O 1:09.12 2 T.-B. Mo I 1:09.093 C. Hedrick I 1:09.32 3 C. Hedrick I 1:09.324 S. Groothuis I 1:09.45 4 S. Groothuis I 1:09.455 M. Tuitert I 1:09.48 5 M. Tuitert I 1:09.48

Realized ranking Corrected ranking1 C. Nesbitt I 1:16.56 1 A. Gerritsen I 1:16.462 A. Gerritsen O 1:16.58 2 C. Nesbitt I 1:16.563 L. van Riessen O 1:16.72 3 L. van Riessen I 1:16.604 K. Groves I 1:16.78 4 K. Groves I 1:16.785 N. Kodaira I 1:16.80 5 N. Kodaira I 1:16.80

Table 2: Realized and corrected ranking of the 2008-2009 World Championships Single Dis-tances and the 2010 Olympic Games.

What immediately catches the eye are the differences between the top three finishers in the2008-2009 World Championships Single Distances and the 2010 Olympic Games. For ex-ample, Boer was third in the actual ranking of the 2008-2009 World Championships SingleDistances, but would have won the silver medal when we correct for the average advantage

5

The dummies are included in a regression function, together with a constant and a measureof individual ability, yielding the following model for each c ∈ C, j ∈ J , k ∈ K, i ∈ Nc,

Finishi,c,j,k = α + θc +∑l∈J

Seasonc,l,iβl +∑m∈K

Rinkc,m,iγm + Vc,iδ + εi,c,j,k, (1)

with

α Constant;θc Parameter that measures the average level of performance of skater c;βl Parameter that measures the average level of performance of all skaters in season j;γm Parameter that measures the average speed of skaters at rink k;δ Parameter that measures the average advantage that a skater starting in the inner lane has

over a skater starting in the outer lane during a 1000m race.

As the season and rink dummies correspond to categorical variables, we take the season 2000-2001 and the rink situated in Berlin as the reference categories, so that the model is rewrittenas follows,

Finishi,c,j,k = α̃ + θc +∑l∈J

Seasonc,l,iβ̃l +∑m∈K

Rinkc,m,iγ̃m + Vc,iδ + εi,c,j,k, (2)

In model (2), the season parameter β̃l is the average level of performance during season lcompared to the season 2000-2001, while the rink parameter γ̃m is the average level of speedon rink m compared to the rink in Berlin.

We conclude from a Mundlak test that we need to treat the skater-specific intercept θc as afixed effect (Mundlak, 1978).

Deciding on outliers

Speed skating is a technical sport that includes falls and minor slips, leading to results thatdeviate from ‘average’ performances. It is necessary to eliminate these deviations from ourinference of the parameter δ that measures the difference between the 1000m finishing timeswhen skated with a start in the inner and the outer lane. Therefore, we select 1000m timesof error-free races by eliminating times of skaters in races containing a fall or slip. In orderto do so, we introduce bounds for the 1000m finishing times, together with an outlier test.

Detecting outliers with box plots

By introducing bounds on the 1000m finishing times, based on box plots of the Finishi,c,j,k

values, we remove times of races containing a fall or slip. However, box plots of pooledfinishing times neglect technological progress of equipment and the fact that races are skatedon different rinks. Therefore, we make box plots of 1000m times that are skated on the samerink and during the same season. If a finishing time is an outlier in a particular box plot, thecorresponding bound is lowered and the finishing time is removed. This procedure is repeateduntil there are no more outliers in the box plots.

3

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Jaargang 33 - GAXEX 2 19

What immediately catches the eye are the differences between the top three finishers in the 2008-2009 World Championships Single Distances and the 2010 Olympic Games. For example, Boer was third in the actual rank-ing of the 2008-2009 World Championships Single Dis-tances, but would have won the silver medal when we correct for the average advantage of starting in the in-ner lane. For female skaters, there is a even a difference between the gold medal winners of the 2010 Olympic Games. In fact, when we correct for the draw of lanes of the 2010 Olympic Games, Gerritsen, starting in the outer lane, becomes the gold medal winner, whereas her actual result is the silver medal. Similar changes were evident for men, as well. For instance, when the draw of lanes of the 2008-2009 World Championships Single Distances was changed, Davis, starting in the outer lane, becomes silver medal winner, whereas his actual result was the bronze medal.

Additionally, we added the estimate of to 1000m times skated with a start in the inner lane. The resulting rank-ings, which are the so called reversed draw rankings, show the influence of the draw of lanes on finishing times. Actually, for all World Championships Single Dis-tances and Olympic Games between 2000 and 2009, the percentage of differences between the realized and reversed draw rankings is 22.89% and 48.29% for male and female skaters, respectively.

ConclusionBoth for male and female skaters we have found an in-ner/outer lane difference for the 1000m, namely 0.030 seconds for men, with a standard error of 0.019, and for women 0.120 seconds, with a standard error of 0.029. For female skaters this difference is even statistically significant. Hence, we may conclude that two 1000m competitions are needed at Olympic Games and World Championships Single Distances.

An additional argument is that the inner/outer difference might still exert influence on future results, as speed skating has matured during the last decade and is still maturing, so that small differences between race cir-cumstances may make the difference between a gold medal or nothing. For instance, the difference between the gold and bronze medal winners of the 2008-2009 World Championships Single Distances for men is only 0.06 seconds. Obviously, starting in the inner or the outer lane becomes of great influence for the division of medals during future tournaments.

AcknowledgementWe would like to thank our colleague Bertus Talsma for his comments and suggestions. We would like to thank Huub Snoep for providing the photograph on the front page.

ReferencesA.J. Cameron and P.K. Trivedi, Microeconometrics (3rd Ed.), Cambridge University Press, 2007

J.A. Rice, Mathematical Statistics and Data Analysis (2nd Ed.), Duxbury Press, 1995

N.L. Hjort, Should the Olympic Sprint Skaters Run the 500 Meter Twice?, Statistical Research Report, Univer-sity of Oslo, 1994

G.H. Kuper, E. Sterken, Endurance in Speed Skating: The Development of World Records, European Journal of Operational Research (148), 2003, pp. 293-301

Y. Mundlak, On the Pooling of Time Series and Cross Section Data, Econometrica (46), 1978, pp. 69-85

http://ww2.isu.org/speed/worldcup/0001/sswc0001.html

www.skateresults.com

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Tekst: Ruben te Wierik

Bobsleeën is als sport ontdekt halverwege de negen-tiende eeuw. In St. Moritz, Zwitserland werd destijds door Britse toeristen voor het eerst een stuurmechanis-me toegepast op een slee, waardoor het mogelijk werd bochten te maken. Een Zwitserse hoteleigenaar legde vervolgens, vooral vanwege de commerciële belangen, een baan aan, waarop ook aan rodelen en skeleton werd gedaan. Het was ook hier, waar in 1884 de eerste offi-ciële wedstrijden werden gehouden. In 1897 werd in St. Moritz dan ook de eerste bobsleevereniging opgericht en in zowel 1928 als 1948 werd op de St. Moritz-Celeri-na Olympische Bosleebaan de Olympische bobsleewed-strijd gehouden.

Deze natuurlijke ijsbaan wordt nog steeds elk jaar mid-den november opnieuw aangelegd door vijftien speci-alisten. Hiervoor wordt gedurende drie weken gebruik gemaakt van 5000 m3 sneeuw en 4000 m3 water. Aan het einde van bobsleeseizoen, eind februari, wordt de baan weer afgebroken. Dit in tegenstelling tot de kunst-matige banen, die een metalen ondergrond hebben, met daarop een laag ijs. Deze banen worden ook kunstmatig gekoeld en zijn daardoor van veel betere kwaliteit. Hier-door zijn wedstrijden op dit soort banen eerlijker en is het mogelijk om tijden tussen verschillende jaren te vergelij-ken, omdat de baan niet elk jaar veranderd.

De eerste Nederlandse bobsleedeelname aan de Olym-pische Spelen dateert van 1928, toen het team van pi-loot Van der Sandt met remmers Delprat, Teixeira de Mattos, Dekking en Menten twaalfde werd in een veld van 25 sleeën. Weinig Nederlands succes volgde, tot de bob van Arend Glas in 2002 enige medaillekansen werd toegedicht. In de jaren die volgden stopte Glas en nam

Edwin Van Calker zijn plek als piloot van de Nederlandse bob over. Een samenwerking tussen de TU’s en enkele bedrijven, leverde een kwalitatief zeer goede slee op. Prompt haalde Van Calker tijdens een wereldbekerwed-strijd in Königssee de eerste Nederlandse podiumplek ooit.

Door deze prestatie in de vernieuwde bob, werd Neder-land plots een outsider voor een Olympische medaille. Vooral van de Nederandse tweemansbob werd gedacht dat ze een kleine kans hadden op een medaille. De vier-mansbob zou zeker op een top-10 plek gerekend kunnen hebben.

Tijdens een trainingsafdaling ging de Nederlandse twee-mansbob nogal hard onderuit, zoals vrijwel elke favoriet al wel een keer het ijs van zeer dichtbij zag. Bovendien is het niet raar wanneer piloten tijdens de eerste paar runs op een onbekende baan wel eens onderuit gaan.

Op 21 en 22 februari werkten Van Calker en Jansma de vier runs van de Olympische tweemanswestrijd af. Hun snelste tijd, 52.37 seconden, stak schril af bij de gemiddelde tijd van de winnaars Lange en Kuske: 51.59. Bovendien ging de Nederlandse slee tot twee keer toe bijna op zijn kant door zwak stuurwerk van Van Calker. Deze trok zich dit dusdanig aan dat hij twee dagen later bekend maakte het niet aan te durven om deel te nemen aan de wedstrijd in de viermansbob.

Dat bobsleeën niet ongevaarlijk is, heeft de historie be-wezen. In totaal vonden zeker zes mannen en één vrouw de dood in de bob. De Zwitser Reto Capadrutt was tij-dens het WK van 1939 in Cortina d’Ampezzo voor zo-

Durf jij het wél aan?Op 23 februari maakte piloot Edwin van Calker bekend niet van start te gaan tijdens de Olympische bobsleewedstrijd van een paar dagen later. Zijn reden was zijn gebrek aan zelfvertrouwen na een belabberd optreden in de tweemansbob. Hij was bang te crashen op de zeer moeilijke Olym-pische baan. Was zijn afzeggen een laffe daad of was het terecht en ver-dient hij respect voor deze moeilijke keuze?

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Jaargang 33 - GAXEX 2 21

ver bekend de eerste die omkwam tijdens een afdaling, het meest recente slachtoffer was Yvonne Cernota, die in 2004 tijdens een training op de baan van Königssee crashte en overleed. Verder zijn er tal van ongelukken geweest met zeer ernstige verwondingen.

De Olympische baan in Whistler staat bovendien bekend als één van de snelste en moeilijkste banen in de we-reld. Tijdens de wereldbekerwedstrijd van februari 2009 haalde de rodelaar Felix Loch met 153 km/h de hoogste rodelsnelheid ooit. De gevaarlijkheid werd nogmaals be-wezen door de dood van de Georgische rodelaar Nodar Kumaritashvili. Hij raakte met 143 km/h de kant van een recht stuk en werd tegen een pilaar gelanceerd. De crash van Kumaritashvili was de zoveelste al in korte tijd op deze baan en wakkerde de discussie over de veilig-heid van de baan opnieuw aan.

Rodelaar Patrick Singleton, uitkomend voor Bermuda, beweert dat de Canadezen met hun olympisch program-ma ‘Own the podium’ hebben bijgedragen aan de dood van Kumaritashvili, omdat ze bewust buitenlandse spor-ters hebben weggehouden van de wedstrijdfaciliteiten in Whistler en Vancouver. Hierdoor hebben buitenlanders veel minder trainingsafdalingen kunnen maken, waar-door ze de baan lang niet zo goed kennen als de gang-bare wereldbekerbanen.

Verschillende aanpassingen aan de baan volgden. Voor de veiligheid van de mannelijke rodelaars, begonnen zij één bocht verder, bij de vrouwenstart, waardoor zij de moeilijkste passages met een iets lagere snelheid pas-seerden. Ook werden in de bocht waar Kumaritashvili verongelukte enige aanpassingen gedaan en werden de

pilaren afgedekt. Voor de bobsleewedstrijden werd nog extra ijs uit de baan genomen, waardoor de baan minder snel werd.

Van Calker was niet de enige die besloot niet van start te gaan. Twee Zwitserse sleeën, een Letse, een Austra-lische en een slee uit Liechtenstein gingen ook niet van start, vanwege crashes. Tijdens de wedstrijd gingen ver-schillende bobsleeën op hun kant, zonder al te veel erg.

Al met al valt er veel te zeggen voor het besluit van Van Calker, de baan in Whistler is ook gewoon heel gevaarlijk en hij heeft inderdaad niet veel afdalingen gehad. Het zegt genoeg dat de andere teams zijn keuze respecteren en niet verwerpen. Toch blijft het jammer dat je zelfver-trouwen zo ver zakt na twee slechte runs in het beste seizoen van je leven. Bovendien hebben vele mensen er jaren aan gewerkt, is er miljoenen geïnvesteerd in het project en wilden remmers Jansma en Beck wél graag naar beneden.

De voorzitter van de Bob en Slee Bond Nederland (BSBN) was woedend toen hij het besluit van Van Cal-ker vernam. Hij ontviel Van Calker publiekelijk en maakte direct duidelijk dat Van Calker zijn plek als piloot van de Nederlandse bob wel kan vergeten. Op de website van de BSBN staat al een bericht, waarin de bond zegt op zoek te zijn naar nieuwe bobslee- en skeletontalenten, die het avontuur wél aandurven.

De nederlandse bob op 10 januari 2010 in Königssee De Olympische baan in Whistler

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Activiteiten Agenda08 maart Landelijke Econometristendag

16 maart Algemene Ledenvergadering

16 maart VESTING Borrel

16/17 maart Bèta BedrijvenDagen

23 maart Algemene Activiteit

24 april Batavierenrace

Graag wil VESTING de volgende mensen feliciteren met het behalen van hun bul:

11-12-2009 Margriet van der Wal Speeding up Value-at-Risk calculations for option portfolios

26-01-2010 Pieter van der Hoek An Empirical Study of Mean Reversion in International Stock Market In dexes and the Implications for the FTK Continuity Analysis

12-02-2010 Jingjing Liu Income Inequality in China, 1989 to 2006

VESTING Bestuur 2009-2010

Johan Sanders Voorzitter

Fred Heijnen Vice-voorzitter Intern coördinator

Chris Jensma Secretaris

Martijn Westra Penningmeester

Eelke de Jong Bedrijfscontacten

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Jaargang 33 - GAXEX 2 23

Tekst: Renske van Raaphorst, secretaris BBD ‘10

Met trots stel ik hier het bestuur van de Bèta Bedrijven-Dagen 2010 aan u voor. Een bestuur dat enthousiast, gedreven en ambitieus is. Dat natuurlijk erg gezellig is. En dat maar één ding voor ogen heeft: van de BBD 2010 het mooiste evenement van het jaar maken.

De Bèta BedrijvenDagen is een tweedaags evenement waar studenten in contact kunnen komen met bedrijven op verschillende manieren. Als je je wilt oriënteren, is er de bedrijvenmarkt en zijn er een aantal presentaties. Mocht je op zoek zijn naar een stageplaats of een baan, dan zijn er workshops door bedrijven en individuele ge-sprekken. Daarnaast is er nog de mogelijkheid om in-formeel contact te leggen met je toekomstige werkgever tijdens het ontbijt, de lunch of de beroemde borrels.

Het leuke van de Bèta BedrijvenDagen is dat het erg ge-makkelijk is om contact te maken met de bedrijven. De prachtige locatie van het Kasteel maakt de sfeer heel speciaal, de bovengenoemde borrels zorgen voor een

feestelijk einde van de dag. Het is geen massaal evene-ment, waardoor je makkelijk je weg zal kunnen vinden op de BBD.

Als student zal je beide dagen helemaal in de watten worden gelegd. Alles wat er op de dagen wordt aange-boden is gratis. Jij, de student, staat immers centraal.

Misschien vraag je je af wat je als econometrie-student op de BBD moet? Ik kan je vertellen dat er ook dit jaar weer een hoop interessante bedrijven zullen zijn. Van techniek-bedrijven als Technolution, tot energiebedrijven als Nuon en Shell. Hou voor de actuele informatie in fe-bruari de site in de gaten!

Ik kan dus niet meer zeggen dan dat de Bèta Bedrijven-dagen van 2010 gewoon niet te missen vallen. Of je nu voor het eerst kennis maakt met de arbeidsmarkt, of echt op zoek bent naar jouw carrièrestart: op de BBD kun je het vinden.

Bèta BedrijvenDagen 2010: Make the world a Bèta place

Datum: dinsdag 16 en woensdag 17 maart

Meer informatie? kijk op: www.beta-bedrijvendagen.nl of mail naar: [email protected]

Vlnr: Ömer Arslan, Yoep Hoekzema, Warun Bhola, Valerie

Siahaan, Renske van Raaphorst en Sjoerd Bielleman

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24

PooltoernooiOp 10 november was het zover: de eerste algemene ac-tiviteit voor VESTING Leden van het nieuwe collegejaar, een pooltoernooi. De avond begon met een heerlijke maaltijd, speciaal voor mentorgroep Roze bereidt door papa-Thomas, waarna we ons richting Cue Action bega-ven waar het pooltoernooi zou gaan plaatsvinden. Tom zorgde er voor dat alle deelnemers wisten tegen wie ze moesten spelen en aan welke tafel dat dan zou gaan plaatsvinden. Toen de eerste ronde was afgelopen, was nog maar de helft van alle deelnemers over en begon de volgende ronde. Zodra er wat pooltafels over waren werd daar goed gebruik van gemaakt door een deel van de afgevallen deelnemers. Anderen dronken een biertje aan de bar en keken met veel plezier toe hoe alle ballen, ook de zwarte en witte bal uiteraard, gepot werden. Nog wat rondes en dus ook afvallers later, waren alleen Luuk en Kenneth nog over. Zij zouden gaan strijden voor de hoofdprijs. Na een spannende wedstrijd bleek Luuk toch net wat beter te zijn dan Kenneth en ging er dus met de hoofdprijs vandoor: onder andere een bioscoopbon en een heuse beker! Na deze victorieuze overwinning was het tijd om richting Chaplin’s pub te gaan waar de avond werd afgesloten met een borrel.

AC ActiviteitenTekst: Mariska van Ham

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PubquizToen bekend werd dat de eerstvolgende activiteit een pubquiz zou worden, werden deVESTING Leden meteen enthousiast. Er barstte een hef-tige discussie los op het VESTING Forum over wie zou gaan winnen en dat moesten de deelnemende teams na-tuurlijk waar gaan maken. De pubquiz zou gaan plaats-vinden op 1 december, in Jut&Jul. Op een aantal boetes na vanwege het fietsen zonder licht, was iedereen zon-der problemen gearriveerd. De deelnemers kregen de kans om even bij te praten onder het genot van een bier-tje voordat we aan de eerste ronde begonnen: De nut-teloze weetjes. Aan het eind van deze ronde was het ook tijd voor het eerste ‘tussendoortje’. Toen alle vragen van de eerste ronde gesteld waren en de antwoordbladen ingeleverd had iedereen een kwartiertje pauze, behalve de AC die snel de antwoorden nakeek. Na de pauze en bekend maken van de scores, begonnen we aan de vol-gende rondes: sport, showbizz en topografie. Vreemd genoeg had iedereen bij het onderdeel showbizz de 5 vragen over Paris Hilton goed. Ik weet niet of ik me zor-gen moet gaan maken over het feit dat iedereen weet dat Tinkerbell de naam is het van het hondje van Paris.Ook in de plaatjesronde werd goed gescoord. De ori-ginaliteitprijs voor de vraag waarom piet niet kon auto-rijden, was terecht gewonnen door Bestuur ‘09-’10. En schande aan de mensen die niet wisten dat de prachtige zonnewijzer op de martinitoren zat!Na een spannende finale tussen Bestuur ‘08-‘09 en ‘Bas zijn bierbende der ellende’, bleek ‘Bas zijn bierbende der ellende’ uiteindelijk toch beter te zijn. Dat bekent dat de (heerlijke) hoofdprijs, chocoladeletters en 2 flessen La Chouffe, aan het Bestuur ’08-’09 voorbij ging. Na de quiz en het plakken van VESTING Stickers op met name studiegenoten, werd het hoog tijd om nog even in de 9e cirkel een aantal biertjes te gaan drinken, want daar was iedereen na de vermoeiende quiz wel aan toe.

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SchaatsenNa kerst en oud en nieuw was iedereen wel wat kilootjes aangekomen, en wat is er nou beter voor de lijn dan een sportief avondje? Dus besloot de AC te gaan schaatsen in Kardinge, alvorens we ons naar de Rumba zouden begeven waar de VESTING Borrel zou plaatsvinden, en waar de onthulling van het kandidaatsbestuur zou plaats-vinden. Zodra bekend werd dat er geschaatst zou gaan worden, werden de schaatsen uit de kast gehaald en van te voren ondergebonden voor een korte training. Dit om genante valpartijen tijdens de activiteit zelf te voor-komen. Kandidaatsvoorzitter Jurjen had de opdracht gekregen om bier, glühwein, sinaasappels, vlammetjes en meer van zulks mee te nemen naar de schaatsbaan. Terwijl langzamerhand iedereen binnendruppelde, wer-den de toegangsbewijzen gekocht en uitgedeeld. Toen ongeveer alle sportievelingen er waren, werden de schaatsen aangetrokken en werden de eerste rondjes ietwat voorzichtig gereden. Na wat rondjes werd het vertrouwen in de schaatsen groter, met als gevolg dat er wat harder gereden werd. Jurjen, als voorzitter van het kandidaatsbestuur, moest natuurlijk wel opgemerkt worden en had daarom ook een prachtig hanenpak aan. Dit was dan ook uiteraard oorzaak voor flink wat gelach, aangezien niet alle schaatsers op de baan VESTING Lid waren. Toen iedereen zich flink had uitgeleefd, werd het tijd om de schaatsen uit te trekken en nog een mok war-me chocolademelk te drinken, voor er aan de lange en koude reis terug kon worden begonnen. Eenmaal aan-gekomen in de Rumba werd alles weer vergeten en wer-den de laatste weddenschappen gesloten. Wie zouden er in Jurjen’s kandidaatsbestuur komen?! Dat werden Pim, Pieter en Fonkei, en uiteindelijk kwam Myrthe het team nog versterken. Toen kon het kandidaatsbestuur zich wagen aan de beruchte vuurproef. Niet veel later werden er felicitaties uitgedeeld en werd er weer gezellig gekletst en gedronken tot het hoog tijd was om het bed op te zoeken.

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Alfabetfeest

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Het alfabetfeest vond plaats op maandag 22 februari in Huize Maas. Het feest werd georganiseerd door 14 stu-dieverenigingen uit Groningen, en zoals je al kan zien was het thema: “Superhelden en sprookjesfiguren”. Het was een schitterend feest en aangezien foto’s meer zeg-gen dan woorden, hierbij twee fotopagina’s!

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Tekst: Jurjen Boog

Interview ICT Commissie

Hartstikke leuk dat jullie als commissie tijd hebben kun-nen vinden voor dit interview. Veel VESTING Leden ken-nen jullie al, maar weinig mensen hebben een idee van wat het inhoudt om deel uit te maken van de ICT com-missie. Hoe zien jullie vergaderingen er uit?

Martin: Meestal vergaderen we pas als er iets gedaan moet worden. Sinds Maarten in oktober de ICT commis-sie kwam versterken, hebben we twee vergaderingen gehad. Op dit moment zijn we bijvoorbeeld hard bezig met de nieuwe website, daar is Maarten hard mee be-zig.

Maarten: In de vakantie heb ik er heel hard aan gewerkt, nu ligt alles even stil in verband met tentamens. De be-doeling is dat deze voor de ALV in maart helemaal klaar is.

Wat is de functieverdeling in de ICT commissie?

Maarten: Ik doe op dit moment vooral het ontwerp van de nieuwe website. Daarnaast houd ik me bezig met de structuur van de website opbouwen. Bram helpt vervol-gens door het programmeren te doen.

Martin: Administratie en bestuurscontacten lopen via Chris. Als het bes tuur iets veranderd wil hebben, geeft Chris het in de commissie aan. En ik leid alles in goede banen, wat me meestal goed af gaat.

Martin, waarom heb je voor de ICT commissie gesolli-citeerd?

Martin: Volgens mij heb ik daar nooit voor gesolliciteerd. Volgens mij ben ik een van de founding fathers van de ICT commissie. Ik weet niet meer precies hoe dat ging, maar volgens mij was het altijd zo dat Bram de website in zijn eentje deed. In 2006 bedacht ik dat ik Bram wel kon assisteren met creatieve ideeën bedenken.

Chris: Bram heeft de huidige versie van het CMS ge-bouwd. Daarvoor gebruikten we een andere, oudere versie. Deze versie heeft Bram uitgebreid, waardoor het grootste deel nu wel door hem is gemaakt. Hetzelfde geldt voor de website.

Chris, denk je dat je volgend jaar nog in de ICT commis-sie zult blijven, na je bestuursjaar?

Chris: Daar moeten we nog over nadenken, maar ik denk waarschijnlijk niet. Na mijn bestuur ben ik geen inten-sief gebruiker van de website en het CMS meer, dus dan denk ik dat er misschien geschiktere mensen zijn om mijn plaats in te vullen.

Wat zijn dingen waar jullie op dit moment mee bezig zijn, naast de nieuwe website?

Martin: De laatste tijd hebben we een paar dingen geïn-troduceerd, zoals de verjaardagskalender. Het zou ech-ter fijn zijn als VESTING Leden met voorstellen komen van wat ze op de VESTING Site zouden willen zien. We hebben zelf een aantal dingen bedacht, maar dat staat allemaal al online. Google Streetview op de website is een van de ideeën die nog open ligt.

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Maarten: Een overzicht met de top vijf posters op het forum is ook geopperd als idee. Chris heeft gisteren toe-vallig de 9000e post geplaatst op het forum.

Hoe vaak lezen jullie de GAXEX eigenlijk?

Maarten: Ik heb de GAXEX wel gelezen toen ik hem vo-rige keer in de bus kreeg.

Chris: Ik lees de GAXEX een aantal keer per editie. Als bestuurstaak heb ik ook de eindredactie, dus dan moet ik alle artikelen wel minstens twee keer doorlezen. Maar voor ik in het bestuur zat, las ik de GAXEX sowieso wel.

Martin: Ik lees de GAXEX niet zo heel vaak. Heel af en toe blader ik het blad door. Meestal lees ik de verslagen over de artikelen wel door, ik vind een verenigingsblad veel leuker.

Laatste vraag: willen jullie nog iets kwijt richting de GAXEX lezers?

Martin: Ik zou graag meer ideeën vanuit de leden wil-len krijgen met hoe de website nog meer verbeterd kan worden.

Maarten: Er zijn de laatste tijd weinig eerstejaars studen-ten op de informele activiteiten, zoals borrels. Het zou gezellig zijn als meer mensen, dus ook minder actieve leden, op komen dagen.

Nogmaals bedankt voor jullie tijd

Vlnr: Chris Jensma, Martin Haringa, Maarten Ruissaard en Bram de Jonge

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Column VESTING Voorzitter

32

Ten eerste zou ik graag van de gelegenheid gebruik wil-len maken om Jurjen Boog van harte te feliciteren met zijn benoeming als kandidaatsvoorzitter van VESTING. Namens mijn hele bestuur wens ik hem heel veel succes toe voor aankomend jaar. Daarnaast wil ik de VESTING Buitenlandse Reis Commissie (Gerdie Knijp - Voorzit-ter, Lisanne Cock, Fonkei Chan en Martin Haringa) van harte feliciteren met hun benoeming. Ook hun wens ik heel veel succes toe met het organiseren van de vol-gende VESTING Buitenlandse Reis.

Met het inluiden van het nieuwe jaar komen traditioneel ook de goede voornemens voor het aankomend jaar. Het is een moment van zelfreflectie, een tijd waarin men ve-randeringen en verbeteringen aan zichzelf en anderen belooft. Velen van ons zullen onder meer sporten, ge-zonder leven en afvallen op het rijtje van voornemens hebben staan. Ook de Rijksuniversiteit heeft zo haar voornemens, namelijk het verbeteren van de onderwi-jskwaliteit voor studenten. Dit jaar zal daarom vol staan met veranderingen in het studieprogramma. Zo zal er hoogst waarschijnlijk vanaf 2010 het Bindend Studie Ad-vies worden ingevoerd. Dit zal inhouden dat iedereen die

in zijn/haar eerste jaar nog geen 40 ECTS heeft behaald of na zijn/haar tweede jaar zijn propedeuse nog niet heeft behaald van de studie zal worden gestuurd. Een ander gevolg van het BSA zal zijn dat de augustus her-kansingen zullen verdwijnen, wat zou kunnen betekenen dat de studiedruk nog verder vergroot gaat worden. Er zullen nu immers minder collegeweken te vergeven zijn. Of dit werkelijk tot beter onderwijs zal leiden is nog de vraag. Feit blijft wel dat BSA eraan komt, voor sommigen van ons misschien een reden om ook harder studeren bij de goede voornemens van 2010 te plaatsen.

Hoewel iedereen zijn/haar voornemens heeft voor een spoedig 2010 zal er ook veel onzekerheid zijn, zowel binnen en buiten ons mooie Groningen. Hoe gaat het BSA ons raken? Houden we met de verscherping van de regels nog wel tijd over om deel te nemen aan alle activiteiten van VESTING? Zal de instroom van eerste jaars niet halveren uit angst dat ze niet aan het BSA kun-nen voldoen? Hoe staan mijn arbeidskansen ervoor na het halen van mijn studie? Dit klinkt allemaal wel heel dramatisch en serieus, maar ik ben ervan overtuigd dat de gevolgen niet zo extreem voor ons econometristen

Goede voornemens

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Johan SandersVESTING Voorzitter

zullen zijn. Wat betreft het BSA: we zijn al zo’n kleine studie waar iedereen elkaar kent en ook veel contact heeft met de opleiding. Het is bovendien ook voor de professoren van belang dat de opleiding zal blijven te bestaan. Ik heb daarom goede hoop dat de opleiding flexibiliteit zal geven, en met een schuin oog het BSA tegemoet zal zien.

Ook buiten ons stadje zijn er zorgen: Is de vrijheid van meningsuiting in gevaar? Kijk alleen al naar de vervolg-ing van Geert Wilders, de aanslag op de deense cartoon-ist Kurt Westergaard en de controles van China op het nieuws en internet betreffende een de demonstraties in Urumqi. Moeten wij als student hier niet op reageren?,Wij zijn immers de aankomende elite van Nederland. Heb-ben wij dan niet de plicht om te melden dat niet zom-aar alles kan, dat we het niet moeten dulden dat ons de mond wordt gesnoerd door een kleine groep extremisten of extremistische ideeën? Het opkomen voor onszelf en voor anderen staat daarom bij mij ook hoog op het lijste van goede voornemens voor 2010.

Binnen VESTING zullen er ook veranderingen plaats-

vinden. Zo zal er op 16 maart de bestuurswissel plaats-vinden, en zal Jurjen Boog samen met zijn bestuur het stokje van mij overnemen. Hij zal ongetwijfeld een aantal vernieuwende activiteiten neerzetten, maar éénn ding blijft zeker. VESTING zal een rots in de branding zijn, ondanks alle tumult binnen en buiten Groningen. VEST-ING zal zoals ieder jaar weer garant staan voor vele acit-viteiten van zowel formele en informele aard voor haar leden.

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Colofon / Adverteerders

02 AEGON

04 Ernst & Young

35 All Options 36 Towers Watson

34

HoofdredacteurJurjen Boog

RedactieKevin MannArne WoltersFred HeijnenJurjen BoogSebastiaan Oude Groeniger

Lay-outFred HeijnenArne Wolters

SpellingPaula HylkemaArno de Wolf

Externe contactenFred Heijnen

Ontwerp lay-outFred HeijnenMelinda JagersmaBram de JongeArne Wolters

AcquisitieEelke de Jong

EindredactieVESTING Bestuur

RedactieadresVESTING GAXEX CommissiePostbus 8009700 AV GroningenTel: (050) 363 70 62Email: [email protected]

Oplage1000

DrukkerFlyeralarm

VESTING is geliëerd aan deEconomische en BedrijfskundigeFaculteitsvereniging

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