The hot hand in basketball On the misperception of

COGNITIVEPSYCHOLOGY17,295-314(1985)TheHotHandinBasketball:OntheMisperceptionofRandomSequencesTHOMASGILOVICHCornellUniversiiyANDROBERT~ALLONEANDAMOSTVERSKYStanfordUni\sersityWeinvestigatetheoriginandthevalidityofcommonbeliefsregarding“thehothand”and“streakshooting”inthegameofbasketball.Basketballplayersandfansaliketendtobelievethataplayer’schanceofhittingashotaregreaterfollowingahitthanfollowingamissonthepreviousshot.However,detailedanalysesoftheshootingrecordsofthePhiladelphia76ersprovidednoevidenceforapositivecorrelationbetweentheoutcomesofsuccessiveshots.Thesameconclusionsemergedfromfree-throwrecordsoftheBostonCeltics,andfromacontrolledshootingexperimentwiththemenandwomenofCornell’svarsityteams.TheoutcomesofpreviousshotsinfluencedCornellplayers’predictionsbutnottheirperformance.Thebeliefinthehothandandthe“detection”ofstreaksinrandomsequencesisattributedtoageneralmisconceptionofchanceaccordingtowhichevenshortrandomsequencesarethoughttobehighlyrep-resentativeoftheirgeneratingprocess.G1985AcademicPress.Inc.Indescribinganoutstandingperformancebyabasketballplayer,re-portersandspectatorscommonlyuseexpressionssuchas“LarryBirdhasthehothand”or“AndrewToneyisastreakshooter.”ThesephrasesexpressabeliefthattheperformanceofaplayerduringaparticularperiodThisresearchwassupportedinpartbyafacultyresearchgrantfromtheCollegeofArtsandSciencesatCornellUniversitytothefirstauthorandbyGrantNR197-058fromtheU.S.OfficeofNavalResearchtothethirdauthor.WethankHarveyPollackofthePhila-delphia76ersandToddRosensweigoftheBostonCelticsforprovidingtheirteams’shootingstatistics,toBillyCunninghamofthe76ersforallowinghisteamtobeinterviewed,andtoCornell’sTomMillerandLindaLerchforrecruitingtheirplayersforourshootingexperi-ment.WealsothankKathyStrattonforcollectingalargepartofthedatareportedhere.ThisworkhasbenefitedfromdiscussionswithPersiDiaconis,DavidFreedman,LeeRoss,andBrianWandell.SendrequestsforreprintstoDr.ThomasGilovich,PsychologyDe-partment,CornellUniversity,Ithaca,NY14853.295OOIO-0285/85$7.50CopyrightC1985byAcademicPress.Inc.Allrightsofreproductioninanyformreserved.296GILOVICH,VALLONE,ANDTVERSKYissignificantlybetterthanexpectedonthebasisoftheplayer’soverallrecord.Thebeliefin“thehothand”andin“streakshooting”issharedbybasketballplayers,coaches,andfans,anditappearstoaffecttheselectionofplaysandthechoiceofplayers.Inthispaperweinvestigatetheoriginandthevalidityofthesebeliefs.People’sintuitiveconceptionsofrandomnessdepartsystematicallyfromthelawsofchance.’Itappearsthatpeopleexpecttheessentialcharacteristicsofachanceprocesstoberepresentednotonlygloballyintheentiresequence,butalsolocally,ineachofitsparts.Forinstance,peopleexpectevenshortseqeuncesofheadsandtailstoreflectthefair-nessofacoinandcontainroughly50%headsand50%tails.Thiscon-ceptionofchancehasbeendescribedasa“beliefinthelawofsmallnumbers”accordingtowhichthelawoflargenumbersappliestosmallsamplesaswell(Tversky&Kahneman,1971).Alocallyrepresentativesequence,however,deviatessystematicallyfromchanceexpectation:Itcontainstoomanyalternationsandnotenoughlongruns.Aconceptionofchancebasedonrepresentativeness,therefore,pro-ducestworelatedbiases.First,itinducesabeliefthattheprobabilityofheadsisgreaterafteralongsequenceoftailsthanafteralongsequenceofheads-thisisthenotoriousgambler’sfallacy(see,e.g.,Tversky&Kahneman,1974).Second,itleadspeopletorejecttherandomnessofsequencesthatcontaintheexpectednumberofrunsbecauseeventheoccurrenceof,say,fourheadsinarow-whichisquitelikelyinase-quenceof20tosses-makesthesequenceappearnonrepresentative(Falk,1981;Wagenaar,1972).Sequencesofhitsandmissesinabasketballgameofferaninterestingcontextforinvestigatingtheperceptionofrandomnessoutsidethepsy-chologicallaboratory.Consideraprofessionalbasketballplayerwhomakes50%ofhisshots.Thisplayerwilloccasionallyhitfourormoreshotsinarow.Suchrunscanbeproperlycalledstreakshooting,how-ever,onlyiftheirlengthorfrequencyexceedswhatisexpectedonthebasisofchancealone.Theplayer’sperformance,then,canbecomparedtoasequenceofhitsandmissesgeneratedbytossingacoin.Aplayerwhoproduceslongersequencesofhitsthanthoseproducedbytossingacoincanbesaidtohavea“hothand”orbedescribedasa“streakshooter.”Similarly,thesetermscanbeappliedtoaplayerwhohasabetterchanceofhittingabasketafteroneormoresuccessfulshotsthanafteroneormoremisses.Thisanalysisdoesnotattempttocaptureallthatpoeplemightmean’Feller(1968)describessomestrikingexamplesofthenonintuitivecharacterofchanceprocesses(e.g.,matchingbirthdatesorthechangeofsigninarandomwalk),whichheattributesto“faultyintuitions”aboutchanceandcommonmisconceptionsof“thelawofaverages.”THEHOTHANDINBASKETBALL297by“thehothand“or“streakshooting.”Nevertheless,wearguethatthecommonuseofthesenotions-howevervagueorcomplex-impliesthatplayers’performancerecordsshoulddifferfromsequencesofheadsandtailsproducedbycointossingintwoessentialrespects.First,thesetermsimplythattheprobabilityofahitshouldbegreaterfollowingahitthanfollowingamiss(i.e.,positiveassociation).Second,theyimplythatthenumberofstreaksofsuccessivehitsormissesshouldexceedthenumberproducedbya