Papa Chakravarthy Presented to the Department of Economics ...€¦ · My junior research paper on...
Transcript of Papa Chakravarthy Presented to the Department of Economics ...€¦ · My junior research paper on...
SalaryAllocationandRiskPreferencesintheNationalFootballLeague:
TheImplicationsofSalaryAllocationinUnderstandingthePreferencesofNFL
Owners
PapaChakravarthy
PresentedtotheDepartmentofEconomics
Inpartialfulfillmentoftherequirements
ForaBachelorofArtsdegreewithHonors
HarvardCollege
Cambridge,Massachusetts
March8th,2012
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Abstract
ThestudyofriskpreferencesintheallocationoftheNationalFootball
League’ssalarycaphasnotseenmuchacademicresearch.Previousanalysis
showsthatthesalarycapimprovesparityacrosstheNFLandmaybepartially
responsibleforthegrowthoftheUnitedStates’mostpopularsportsleague.
Allocatingsalarytoplayers,however,canrevealagreatdealofinformation
regardingtheutilityfunctionofNFLOwners.Thispaperillustrates,usingdataon
widereceiversintheNFLfrom2005to2009,variablespredictingfuture
performanceintheNFLdonotpredictfuturesalary,meaningOwnersvalue
somethinginadditiontofutureexpectedperformancewhenallocatingsalary.
Thepotentialtobecomeastar,leadershiporpopularitymaybethe
characteristicvaluedbyOwnersthatisnotshownbyOLSregression.A
comparisonofNFLOwnerstofantasyfootballownersshowsthatwhilethe
methodofriskaversiondiffersbetweenthetwo,itisimpossibletoruleoutrisk
aversionbyNFLOwnerstryingtoretainagedplayerswithhighsalaries.Finally,it
ispossiblethatNFLteamsmayimproveteamperformancewhilestayingwithin
thesalarycapbycuttingplayersmorefrequentlyandsigningshortercontracts,
thuseliminatingtheneedtooverpayplayersandfieldingamorecompetitive
team.
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Acknowledgements
Thisthesiswouldnotbepossiblewithoutmyadvisor,Professor
ChristopherAvery,whoseenthusiasm,guidanceandsupportwereinvaluable.I
neverleftameetingwithhimwithoutfeelingoptimisticIcouldhandlethework
ahead.IamtrulyindebtedtoDr.NielsRosenquistwhoconvincedmetostep
forwardtothemostsatisfyingundertakingofmyundergraduateexperience.
Finally,IoweagreatdealtoCathyBarerra,withoutwhomthispaperwouldbe
largelyinaccessible;ProfessorSusanAthey,whoseadvicewasincrediblyhelpful;
andmyparents,whomaynotknowexactlywhatthispaperconcernsbut
providedaconstantstreamofencouragementnonetheless.
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TableofContents
Introduction....................................................................................................................................4
Background.....................................................................................................................................7
PreviousResults............................................................................................................................15
TheoryandTestableHypotheses..................................................................................................25
ProblemI:PlayerSalaryandSalaryGrowth.............................................................................26
ProblemII:PlayerPerformanceandPerformanceGrowth.......................................................28
ProblemIII:LaggedValues........................................................................................................30
ProblemIV:RiskPreferencesandCuttingPlayers....................................................................33
Methods........................................................................................................................................36
Data...............................................................................................................................................43
Results...........................................................................................................................................46
PartI:PlayerSalaryandSalaryGrowth....................................................................................48
PartII:PlayerValue..................................................................................................................51
PartIII:LaggedValues..............................................................................................................54
PartIV:RiskPreferencesandCuttingPlayers...........................................................................56
Limitations....................................................................................................................................59
Conclusion.....................................................................................................................................60
Tables............................................................................................................................................64
Figures...........................................................................................................................................71
References....................................................................................................................................82
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Introduction
TherecentAcademyAwardnominatedfilm“Moneyball”broughtsabermetrics
asevaluationofbaseballplayersintothemainstream.Evaluationoftalentinthe
NationalFootballLeague(“NFL”),however,hasnotyetseenthelevelsofstatistical
analysiscommoninMajorLeagueBaseball.Thestudyofsalaryallocationandtalent
evaluationintheNFLisavaluablepursuitbecauseitfocusesonahugemarketthathas
seenlittletonoacademicstudy.NFLplayerstogethermakeapproximately$3.5billion
peryear,butthedivisionofthatmoneyandthereasoncertainplayersmakemorethan
theirpeershasnotbeenconsideredfromaneconomicperspective.Often,teams
appeartopayplayersinadifferentwaythantheiron‐fieldperformancewouldindicate
–apossibleinefficiencyinincentivizingfutureperformancethatmeritsinvestigation.
ThispaperconcernstheprocessgoverningNFLsalaryallocationswithmulti‐year
contracts,thereasonsforplayerpaymentstrategies,aswellastheinducedrisk
preferencesshownbyNFLteams.Implicitinthatqueryistheneedtounderstand
exactlythesetofpreferencesespousedbyNFLOwners,amajorfocusofthisthesis.For
example,perhapsOwners1preferolder,morepopularplayerstoyounger,less
experiencedathletesbecauseoftheprofitsgainedfromjerseysalesofpopularplayers.
Ifso,thoseOwnerswouldprobablyweightdifferentcharacteristicsthanon‐field
production,likepopularityorteamwork,andwouldpayplayersdifferentlyasaresult.If
weassumethateveryOwnerhasthesolegoalofwinningmoregames,wecanexamine
1Todistinguishfromownersinthegameoffantasyfootball,Ihavecapitalized“Owner”whenreferringtothoseintheNFL.
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theinducedriskpreferencesfromon‐fieldcharacteristics.Studyingplayercontribution
toteamwins,throughon‐fieldstatisticalresults,andrelatingthatvaluetoaplayer’s
salaryisimperativeforastronganalysis.Ifplayer’son‐fieldvaluetohisteamislargely
uncorrelatedtoplayersalary,ownersprobablyvaluecharacteristicsinvisibleduringthe
footballgames,renderingmypreviousassumptioninvalid.However,sucharesult
wouldprovidegreatinsightintotheutilitycurvesofOwnersandGeneralManagers,by
showingthatwinninggamestakesabackseattosomeothergoal.
Myjuniorresearchpaperonmarketdesigncouldelucidatefindingsinthisstudy
(P.Chakravarthy,2010).Ifoundrisk‐aversepreferencesamongownersinfantasy
football,awidelyplayedgameinwhichagroupofindividualsselectrealfootballplayers
andcompetewitheachothertoearnpointsbasedonthoseplayers’performance.This
risk‐aversionismostlyevidencedbyanownerspendingalargerallocationofhis/her
limitedbudgetonplayerslikelytobeinabenchrolethanwouldbeexpectedbyon‐field
contributionsandappearstobearesultofoverestimatingtheprobabilityofaninjuryor
otherperformancelimitationtoaplayerinastartingrole.Benchplayersarethose
wouldnotcontributetotheteamexceptinthecaseofreplacingabetterstartingplayer.
Risk‐aversiononthepartofmanyownerswouldincreasethepriceofmanyplayersas
themarketfindsequilibrium.Spendingahigherallocationonbackupsformsatypeof
insuranceagainstinjuryorperformance‐risk.Suchastrategymaybeinducedbythe
typeofmarket–certainownersmayderiveutilityfromfactorsotherthantheirsuccess
inaleague,perhapstheygeneratemoreutilityfromavoidingapoorrankthanattaining
ahighrank.IntheNFL,OwnersandGeneralManagersofteamsmightexpresssimilar
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behavior.Ateamthatwantstoavoidfinishinglastinitsdivisionorconferencewilltake
arisk‐aversesetofchoicesbyallocatingmoneytobackupsandavoidingtheriskofan
injuryderailingaseason.Alternatively,ifateamisweakatagivenposition,theymay
overspendrelativetovaluecontributedtotheteamtogarnertoplevelplayers.This
inducedriskpreferencediffersfromtherisk‐aversepreferenceabove,butmaybea
resultofscarcityoftalent,whichwoulddriveuppricesfortoptierplayers.While
fantasyfootballusuallyconsistsofonlytenteams,theNationalFootballLeaguehas32
teams.Thismeansthatthesamepooloftopplayersisbeingdividedintofarmore
teams,andtherelativelackofhugelytalentedplayersmakesthemmorevaluableinthe
NFL.Thequestionofhowtherisk‐aversepreferencesoffantasyfootballownersapply
totheirNFLcounterpartsisaninterestingonebecauseofthecompetingeffects
describedabove.
Thequestionsabovewillbediscussedasoutlinedhere.First,Iwilldetailthe
backgroundoftheNFL,includinginformationonhowplayersareallocatedandprevious
findingsregardingthesalarycap’simpactonateam’soperations.Thisisfollowedbya
sectiondetailingmypreviousresearchconcerningfantasyfootballandthehypotheses
formedfromthatwork.IntheTheoryandTestableHypothesessection,Idetailexactly
whichtestswillprovidetheanswerstoeachquestion,andwhateachpossibleresult
impliesabouttheanalysis.Followingthisbreakdownoftests,areData,Methodsand
Resultssections,explainingtestresults.TheConclusionssectionprovidessummarizing
ofthoughtsandareiterationofthepointslearnedfromtestinghypotheses.
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Background
TheNFListhemostpopularsportsleagueintheUnitedStatesandamongthe
mostpopularintheworld(A.Heller,2000).Thedirectconsequenceofthispopularityis
thespecialnichewhichateamholdsintheheartsandmindsofitsfollowers,notunlike
areligion.Becausefootballteamshavesuchacult‐likefollowingandallcitieshosting
NFLteamscontributefinanciallytobuildingandmaintainingastadiumwithouttaking
directprofit,2manypeoplefeelthatOwnersshouldnottreattheteamasafinancial
investment,butratherasanopportunitytoprovideapublicgoodwhilestillgaining
somefinancialbenefit.Thisgeneralattitudeisthefoundationfortheassumption
discussedearlier–thatownershaveonegoalaboveallothers–tofieldasuccessful
footballteamasmeasuredbywinningpercentage.WhileOwnershavethepowertodo
whatevertheywantwiththeirteam,whentheyareseenasmiserlyitcanhaveasevere
effectontheirfinances.Thisinferenceisbasedinpartonamajormovementamongthe
followersoftheCincinnatiBengalsfranchise,angeredbyaconsistentlypoorteamand
anOwnerunwillingtochange.Theangerofthemovementisbasedinlargepartonthe
perceivedgoaloftheteam’sOwner–tomakemoneyratherthantowingames.3While
anangrygroupmayfeelanOwnerisresponsibleforprovidingacompetitiveteam,the
2Citygovernmentscontributetostadiumsbecauseoftheassociatedrevenueteamsbringintotowns.Also,theriskthatateammaytransfertoanothercityisamajorfactor.AnexampleistherecentnegotiationsbetweentheMinnesotaVikingsandMinneapolis,inwhichtheVikingsthreatenedtomovetoLosAngeles.http://espn.go.com/nfl/story/_/id/7190566/stadium‐drama‐stoking‐fears‐minnesota‐vikings‐move3WhoDeyRevolution,namedforthechant“Whodeythinkgon’beatthemBengals,”believesindestabilizingtheorganizationbyaffectingthefranchise’sticketintakeanddirectlylimitingtheirfinancialsuccess.Groupmembersroutinelyboycottthegamesandadviseagainstpurchaseofanymemorabilia.Onenotableprotestinvolvedanudemanstreakingthroughthestadiumwhileholdingaposterreading“FireMike[Brown,theBengals’Owner].”http://www.whodeyrevolution.com/
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followinganalysiscanshowwhetherthatis,infact,anOwner’sprimaryobjectiveorif
thereareothermotivationsinchoosingplayersbesidesexpectedon‐fieldperformance.
TheNFLismadeupof32clubs,splitupintoeightdifferentdivisions.Eachteam
plays16gamesinaseason.Forthesakeofparity,onlyacertainnumberofplayersmay
playinanygivengame.Teamsmayhave53playersontheirroster,butonly45ofthose
playersmay“dressfor”andparticipateinanygivengame(R.Goodell,2011).Finding
andreplacingplayersisdifficultbecauseoftheparticularskillsetrequiredforsuccess
playingfootball,makingthelabormarketextremelythin,whichcouldhaveasignificant
effectontherelationshipbetweenplayercontributionandsalary.Thefootballplayer’s
marketisgovernedbyaCollectiveBargainingAgreement(“CBA”)negotiatedbetween
Ownersandplayers.AllteamshaveOwners4andmosthaveGeneralManagersor
Presidents.Officerssuchastheserunthedailyoperationsofateam,including
acquisitionofplayersandinteractionwithfansormedia.
NFLteamsmayacquireplayersinthreeways:freeagency,drafts,andtrades.
FreeagencyasweknowitnowaroseduringtheCBAnegotiationsofthelate1980’s(E.
Garvey,1989).Garveydetailsthesourceofthedisagreementsurroundingthose
negotiations–playerdesireforcompletefreeagencywithitsaccompanyingincreasesin
paymentandownerdesiretoavoidsalaryhikesassociatedwiththefreemarket.Afree
agentisaplayerwhohascompletedtherequirementsofhiscontractandiscurrently
4ThenotableexceptiontothisstatementistheGreenBayPackers.ThePackersareapubliclyownedcompanywithaBoardofDirectors.Thereasonforthisdivisionisafundraisingone–theteamneededmoneytosurvivein1950andsoldsharesofownership.Thereareoverfourmillionshares,buttheymaynotbetradedorsold.IndividualsholdingshareshavetherighttovoteforBoardmembers,whointurnelectaPresidenttoruntheteam.http://www.packers.com/history/birth‐of‐a‐team‐and‐a‐legend.html
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availabletonegotiatenewcontractwithanyteam(M.Truelock,1993).Hemaybe
signedbywhicheverteamheselectsandhascompletecontroloverhisdecision,beit
motivatedbyfinancesorotherreasons.Aresultoffreeagency,asidefromincreased
playersalaries,ismoresophisticatedcoachingschemesfueledbytheabilitytofind
specificskillsinpersonnel(S.E.Backman,2002).Freeagencyhasalsoincreased
competitivebalanceandparity(A.Larsenetal.,2006)alongwithplayerpayment
inequality(M.A.LeedsandS.Kowalewski,2001,G.W.Scully,2004).Consequently,
teamsuselucrative,longtermcontractsusedtolurefreeagents.Oneimportant
concessionoffreeagency,whichisnotseeninanyothermajorsportsleague,isa
team’srightto“cut”aplayerbeforetheseasonbeginsbyremovinghimfromtheir
rosterwithouthavingtopayanynon‐guaranteedcontractualobligations,suchasa
bonusorfuturesalary.Theabilitytocutaplayerdrasticallylowersateam’sriskand
helpslimitthedamagepossiblefromapoorcontractdecision,bylimitingtheeffectofa
salaryonateam’ssalarycap.Itmayhaveaneffectonthelargesseofcontracts–teams
givemoremoneythanexpectedforplayers,knowingthatifthecontractbecomes
unwieldytheycancuttheplayer.Teamsmayalsorenegotiatecontractswithplayers
duringthetermofthecontract,allowingteamstofindcreativewaystoallocatesalaries,
usuallythroughtheuseofincreasedbonuses,whileremainingundertheleague‐wide
salarycap.5Signingarenegotiatedcontractputsplayersatriskofbeingcutbefore
5BenRoethlisbergerofthePittsburghSteelersrecentlyagreedtosucharestructuringforthereasonsoutlinedabove.http://espn.go.com/nfl/story/_/id/7609160/pittsburgh‐steelers‐ben‐roethlisberger‐restructures‐contract
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reachingtheirhighestpaidyearsbutalsoallowsforthesigningofbetterteammatesand
beingpartofabetterteam,thereasonplayersoftenagreetosuchanoption.
NewplayersusuallyentertheNFLthroughtheleague’samateurdraft.Most
playersinthedraftplayedinacollegeastheleaguedoesnotallowplayerswhoareless
thanthreeyearsremovedfromtheirhighschoolgraduation(R.Goodell,2011).Teams
enterthedraftrankedinreverseorderofperformanceanddraftforsevenroundsinthe
sameorder.Thismeansthattheworstteamin2011willdraftfirstforeachround,one
toseven,in2012’sdraft.TheteamthatwontheSuperBowlthisFebruary,theNewYork
Giants,willdraft32ndineachround.MasseyandThaler(2005)detailtheovervaluation
ofearlydraftpickswithregardtocontributiontoateam,aneffectwhichreiteratesthe
importanceanddifficultyofpredictingfutureperformanceintheNFL–amajorfocusof
thisstudy.Highlytoutedcollegeplayersarepaidfarmorethantheiron‐field
contributiontotheteamwouldindicate,perhapsbecauseofthepotentialsuchaplayer
hastobecomeateam’smainattraction,therebygeneratingrevenuefortheteam.This
overvaluationmaybeimportanttounderstandingriskpreferencesasitisacommon
threadinmanysports,whichvaluehavinga“star”capableofdrawingfanstobuy
ticketsandmerchandise(S.Rosen,1981).Themotivebehindpayingforstarpotential–
theideaonegreatplayerisworthfarmorethananynumberofgoodplayersbecauseof
associatedfinancialbenefit–couldbeadrivingfactorinhowowner’sallocatetheir
fundsinacquiringandretainingplayers.
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Tradesalsoimprovecompetitivebalancethroughplayermovement(A.Nissim,
2004)byallowingteamstofindplayersmatchingtheiridealschemes.Aplayertradeis
executedbytradingtherightsforaplayer.Thismeansthataplayermaynotbeunder
contractwhilebeingtraded;onlythathehasbeenassignedtoateam.6Whenaplayeris
drafted,theteamownstherightstothatplayer,whichmeansnootherNFLteammay
signacontractwiththatplayerforonecalendaryear.Duringthattime,aplayermay
stillbetradedevenifhehasnotsignedacontract.Theresultofthesetradesisthat
teamshaveplayerswhofitwithinamalleablesystemandcanbemaximallyutilized
accordingtofitwithinateamratherthantopureability,twoattributesthatdonot
alwayscorrelatedirectly.Tradingrightsmakessalaryfiguresmoreaccuratepredictors
ofplayervaluetotheteaminsteadofsimplyindicatorsofplayerability,whichmeans
thereislessnoiseincomparingsalarytoplayercontribution.Moreover,studyingthe
utilizationofplayerscangiveinsightintoaplayer’sskill.Whilethismaynotalwaysbe
thecase,playerswhoareusedmoreoftenaregenerallybeingusedbecausetheir
coachesbelievetheygivetheirteamthebestchanceofwinning.Measuringutilizationis
awayofmeasuringateam’sfaithinaplayer.
Themostimportantfactorinaclub’sacquisitionofplayersisthesalarycap.The
NFLusesahardsalarycap,whichmeansthatteamsmaynotexceedacertainnumberin
yearlysalary(B.Richard,2008).ThesalarycapbecameapartoftheNFLin1994.It
startedatjustmorethan$34millionperteam,buthassincegrownrapidly.Currently,
6ThisdistinctionallowedthefamousEliManning–PhillipRiverstradein2004,whenneitherplayerhadsignedacontractandManningforcedatradebecausehedidn’twanttoplayinSanDiego.http://espn.go.com/blog/afcwest/post/_/id/39688/poll‐eli‐manning‐trade
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thesalarycapstandsat$128millionperteam(NFLEnterprises,2010).7Despitethe
changesintheNFLCollectiveBargainingAgreementduringthesummerof2011,the
basicrulesregardingplayersalaryhavenotbeenchangedagreatdealsincefreeagency
began.Underthecap,theallocationofsalariesbetweenplayersislargelyunregulated.
TheonlylimitationisthattheNFLhasminimumsalariesforplayersdependingonyears
intheleague.Playersintheleagueformorethanadecadecanmakenolessthanthe
“veteranminimum”of$810,000butyoungerplayerscanbepaidaslittleas$405,000
(NFLEnterprises,2010).Thismeansthatwithacapofmorethan$100million,ateam
couldtheoreticallydevoteahugeamountofmoneytoasingleplayerandspreadtheir
remainingsalaryamonglotsofplayersortheycouldopttogivethesameamountto
everyplayer.Acommonassumptionisthatplayersarecompensatedaccordingto
expectedfutureperformance(C.MasseyandR.Thaler,2005).Thisisaconsistenttheme
throughoutmajorsportscontracts–youngerplayerswithsimilarimmediate
performancetoolderplayersareexpectedtoearnmoremoneybecauseofthe
likelihoodofimprovedperformanceinthefuture.
AgreatdealofresearchstudiestheeffectsofthiscapontheNFL.Richard(2008)
showsthatteamsorientedaroundpayingasingleplayerahugeamounttendto
performworseonaverage,perhapsbecauseofdissatisfactionfromteammates.Other
literaturesuggeststhatthesalarycapexiststokeepplayersalariesevenlydistributed
amongteams(M.J.ReddingandD.R.Peterson,2009),whichincreasesparityand
7Thecaphasgrownbecauseofincreasesinrevenuefromtelevisionandmerchandising,butalsobecauseplayersaredemandingahigherratiooftherevenuetakeninbyclubs.Thisdebatewasthecenterofthe2011NFLlockout.http://sports.espn.go.com/nfl/news/story?id=6687485
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thereforeconsumerinterest(A.Larsen,A.J.FennandE.L.Spenner,2006).Alternatively,
Heller(2000)focusesonhowthesalarycapincentivizesownersandplayersworking
togethertoimproveeveryone’srevenue.Allocatingthatmoneytoplayersisadifficult
taskandunderstandingthatallocationisimportantintheNFLbecauseofthehuge
salariesinvolved.Thegeneralfindingofthisresearchisthatthesalarycap’slimitations
requireteamstodevelopanunderstandingofhowbesttoallocatetheirfundsinterest
(A.Larsen,A.J.FennandE.L.Spenner,2006).Althoughdifferentteamshavevery
differentstrategiestheyallneedtounderstandhowthesalarycapworks–indeed,this
isbackedupbyanecdotalevidence.Mostteamshaveseveralemployeeswhowork
exclusivelywithcapallocations.However,itisworthnoticingthatwhilemanyhave
studiedtheeffectsofasalarycaponfootballgamesandhowteamsworkunderacap
(L.M.Kahn,2000)thereisadearthofinformationregardingevaluationofplayersunder
thecapandunderstandinghowOwnersviewriskindefiningsalaryallocation.
Whenateamhasasignedcontractwithaplayer,theymayaddhimtoaroster.
Tosignacontract,ateammustknowtheexpectedcontributionofaplayertoan
Owner’sutility(S.Rosen,1981).Understandingallthewaysaplayercontributestohis
team’sperformancecanhelptojudgeaplayer’sworthtohisteam.Alsoimportantbut
hardertodefineisaplayer’soff‐fieldcontributionstohisteam,suchasrevenue
benefits.Theseattributesmaymakeaplayermoreorlessdesirableandaffectasalary.
Thecomplexityoffootballcomplicatestheadditionorremovalofaplayerfroma
team.Coachesspendweeksgeneratingplaybookswithproprietaryinformationsuited
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towardthepersonnelinplaceonateam.Thismeansthereisanadditionalcostin
addingorremovingaplayer.Suchacostisadirecteffectoftheeffortrequiredtotrain
him.Similarly,tradingawayaplayercostsmorethanproductionlost,italsoleadstolost
trainingtime.AnexampleofthiscostisplayerChadOchocinco,whowaslargely
successfulduringhistenurewiththeCincinnatiBengalsbuthadanexceedinglypoor
seasonwiththeNewEnglandPatriotsin2011.Thereareavarietyofpossiblecausesfor
poorperformancethisseason–includingsuchmundaneaspectsastheweatherofhis
newhome.However,onepossibleexplanationisthecomplexityoftheNewEngland
Patriotsplaybook–widelyknownasbeingamongthemostdifficulttounderstandin
theNFL–inconjunctionwiththe2011NFLlockout,whichdrasticallyshortenedtheoff
seasontimeforplayerstobecomeacclimatedtotheirnewteamsandnewschemes.In
thecaseofOchocinco,suchalimitedtimetolearnanincrediblycomplexplaybook
undoubtedlylimitedhisabilitytoperformathisexpectedhighlevel.
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PreviousResults
Mostofthefollowingisarestatementofinformationandconclusionsfrommy
juniorpaper:OptimizingDraftStrategiesinFantasyFootball(Chakravarthy,2010).
Fantasyfootballisaninteractive,oftenonline,gameplayedwithinagroupofeightor
tenpeople.8Suchagroupistermeda“league.”Eachofthepeopleinvolvedis
consideredan“owner”andrunsa“team.”Eachownerselectstenplayersinthe
NationalFootballLeagueforhisteam.Basedontheperformanceofthoseplayersinreal
gamesagainstNFLopponents,theownerreceivespointsforhisteam.Thenumberof
pointsreceivedvariesslightlydependingontheleague,butasarule,betterplayers
earntheirownersmorepointsasaresultofbetterperformance.Themorepointsa
teamreceivesrelativetootherteamsintheleague,themorelikelyateamistowinits
league,whichmayearnitsownermoneyorsimplybraggingrights.Thestrengthof
fantasyfootballasamodelforstatisticalanalysisoftheNFLliesintheabilitytoisolate
performancefrominducedrevenue.Infantasyfootball,ownersdonotcareaboutthe
revenueaplayerearnsandareonlyinfluencedbytheutilityheprovidesthem.Thus,we
canisolatethewaysaplayermaygeneratevalueforhisteam.Moreover,acquiringnew
playersdoesnotaffecttheperformanceofplayersontheteam–playersare
independentfromeachotherandqualitieslikeleadershipandteamwork.
Evenwithonlyasuperficialunderstandingofthegame,itisimmediately
apparentthatobtainingthebestplayersprovidesanownerwiththebestchanceto
8Estimatesofthenumberoffantasyfootballparticipantsvarywidely,becausemanyparticipantsdonotuseonlineclientstomanagetheirleagues.ThenumberoftotalplayersintheUnitedStatesmaybeashigh50millionpeople(C.Harris,2008)
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placewellintheleague.AcquiringplayersoccursjustpriortothebeginningoftheNFL
seasoninaprocessknownasadraft.Mostleaguesdothisdraftonlineusingadraft
engine,likeESPN.comorYahoo’sFantasyFootballportal.Thesedraftsareseparated
intotwomajorcategories:snakeandauction.Asnakedraftrequiresarandomnumber
generatortopredeterminedraftorderforeveryteamintheleague.Then,eachteam
makesaplayerselectioninthatdefinedorder.Theprocessisrepeated,butin
alternatingforwardandreverseorderuntileveryteamhasafullroster.Thistypeof
draftiscurrentlypopularbutthatpopularityistrendingdownwardsinfavorofthemore
complexauctiondraft,whichresemblestheNFLfreeagencymarket.
Inanauctiondraft,ownersareagainrandomlydefinedinanorder,butinstead
ofselectingplayersinthatorder,ownersnominateplayers.Then,eachteambidson
thoseplayersinaslightlymodifiedEnglishauction.Whicheverownerbidshighest
retainsthatplayerfortheyear.Inthisinternet‐drivenage,everyownerhasthesame
informationabouteachplayer.Moreover,theonlinedraftportalprovidesanestimated
valuationfortheplayer.ThisEnglishauctionhassomeimportantdistinctionsfroma
standardauction:Becauseeachownerneedstofillhisroster,thedraftconsistsofa
seriesofauctionswhichaffectoneanother;additionally,eachownerhasasalarycap,a
numbersetbytheleaguetoprotectparityandpreventoneownerwithmoremoney
frombuyingallofthebestplayers.Still,becausetheauctionisanEnglishauction,itis
efficientwithregardtoallocatingplayerstotheownerwiththehighestvaluationofthat
player.
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Themethodofallocatingplayersinanauctionisverysimilartothefreeagency
marketplaceintheNFLbecauseeachplayercanbeofferedvaryingamountsofmoney
fromdifferentteams.Whiletheremaybeotherfactorstobeconsideredinchoosinga
locationtoplay,moneyisdefinitelyamajorpartofthedecisionmakingprocessforreal
players.Mypreviousworkwasinthisaspectoffantasyfootball–understandinghow
andwhyplayerswerepricedatcertainlevelsandwhetherthereisabetterwaytoprice
playersorstrategicallyoperateinthedraftgivenanowner’sriskpreferences.Aplayer’s
pricecanbeimpactedbytwomajoreffects–theexpectedperformanceandthe
possibilityofinjuryorsomeotherrisktotheexpectedperformance.Theownermay
alsohavehisownreasonsforwantingornotwantingacertainplayer–thingsliketeam
allegiancesandfavoritismmaycomeintoinfantasyfootballjustastheymightinthe
NFL.Oneimportantfactortonoteindefiningpriceiswhethertheplayerwillearnhis
teampoints.Teamsarelimitedinthatonlyfirst‐stringplayerscanearnpoints.Even
thoughaplayermaybeafirst‐stringplayerintheNFL,hemayperformlesswellthan
anotherfirst‐stringplayerandbeafantasyfootballbackup.9Sincefantasybackupsare
lesslikelytoearntheteammorepointsthanfantasyfirst‐stringplayers,fantasybackups
arerarelyutilized.Thus,evenifafantasybackupcouldearnhisownerfiftypoints,since
thefirst‐stringplayerwouldearnonehundredpoints,thebackupwouldneverbe
utilizedanddidnotearntheowneranypoints.Insuchasituation,thebackup’szero
9AnexampleofthissituationwouldbethewidereceiversontheNewEnglandPatriotsin2012.EventhoughbothDeionBranchandWesWelkerstartedintheNFLatwidereceiver,BranchperformedlesswellthanmanyotherNFLstartersandinfantasyfootballwasabackup.http://espn.go.com/nfl/player/_/id/3593/deion‐branch
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pointsareworthnothingtoanownerasidefrompossibleutilitygainedfrompreventing
hispresenceonanotherowner’steam.
Gleaningriskpreferencesfromfantasydatarequiresamajorassumption:all
fantasyfootballownershavethesamegoal–towintheirleagues.Therefore,an
owner’sutilitywouldbedeterminedexclusivelybytheprobabilityofwinninghisorher
league.Therearetwowaystoimproveprobabilityofwinningaleague:onemay
improvehisownteamoronemaytrytohoardgoodplayerstopreventotherteams
frombeingabletoscorepoints.Thelatterstrategywouldgreatlycomplicateany
analysisofplayerprice.Unfortunatelytrackingindividualleaguesisimpossible;however
thereisasimplewaytodetectwhethertoptierplayersarebeinghoarded.Becausea
teammusthavefivewidereceiversonlythreeofthosewidereceiversarebeingusedat
anytime,sotwowidereceiverswillnotbestartedandwillbesecond‐stringplayersfor
theirteam.Iftopplayersarebeinghoarded,wewouldseesometopplayerswhoare
notbeingstartedasoftenaswouldbeexpected.Figure1,Figure2andFigure3are
repetitive,butreinforcethepatternofstartingplayersovermultipleyears.Bothscatter
plotsareassociatedwithregressionshavingstatisticallysignificantpositivecoefficients
onpoints,meaningthatbetterplayersmust,infact,bestartedmoreoftenthanworse
players.Unfortunately,Idonothavestartingdataconcurrentwithmypricinganalysis,
howeverwecanseethepatternin2011and2012issufficientlystrongthatanyother
yearoffantasyfootballwouldlikelynothavesignificantlydifferentwaysofstartingand
benchingplayers.Therefore,wecanruleouttheideaofasystematicattempttohoard
toptierplayerstopreventotherteamsfromscoringpoints.Thus,wecaninferteams
19
usuallyhopetowinbyimprovingtheirownperformanceratherthanhinderingtheir
competitors.
Thedistinctionbetweenstartingandbenchplayersisanimportantonetomuch
ofthisstudyandparticularlyinthecaseofinducedrisk‐aversion.Thereasonforthisis
thatteamscanonlyreapeffectivefantasypoints,notallfantasypoints.Aneffective
pointisafantasypointscoredbyaplayerwhostarted.Consequently,regardlessofthe
numberoffantasypointsabenchplayerwouldscore,sincehedoesn’tstart,his
effectivefantasypointsarezero.Becauseastartingplayercouldalwaysbeeasily
replacedbyabenchplayer,astarter’svaluetohisteamisthedifferenceinperformance
aboveabenchplayer.Thedirectconclusionofsuchasituationisthatbenchplayers
wouldallbeinterchangeableandhavenegligiblevalue,whilestartingplayerswould
havevaluetoteamsaccordingtotheirperformancewithrespecttobenchplayers.
Therefore,ateam’svaluationfunctionforplayerswouldlookjustlikeFigure4.An
effectivepointisameasureofpointsscoredmultipliedbypercentstarted,orameasure
ofvaluetoateam.Thus,ifaplayerisnotstarted(i.e.isabenchplayer)hewillnotbe
abletoearnanypoints.Wecanseeinthefigurethatthevalueprovidedtoateambya
benchplayeriszero10andthenvalueincreasesamongstartingplayerswithincreased
performance.Onewouldexpectthatthebidsinanauctionforplayerswouldseea
similardistinctbreakbetweenstartersandbenchplayers.
10TheslopeoftheOLSregressionofeffectivepointsonpointsamongbenchplayersisnotstatisticallysignificant.
20
Totestrisk‐aversion,Iregressedfantasypriceonpointsscoredforstartersand
benchplayers,andstudiedthedifferenceinslopeoftheOLSregressionbetweenthe
twopools.Figure5andFigure6showthatthereisnodifferenceinpricewith
performanceamongfantasyplayersregardlessofwhethertheplayerwillbeastarteror
benchplayer.Althoughwithoutdatatotrackspecificleagues,onecannotcompletely
ruleoutthepossibilityofteamshoardingtopplayersonamicroscale.However,given
thestrengthofthepatternoffantasypricesonbenchplayersin2008and2009aswell
asthepatternofstartingplayersgivenearlier,itisreasonabletostatethatitis
extremelyunlikelyfantasyfootballownersbidmoreonbenchplayersthanwouldfollow
iftheironlymotivewastoincreasetheprobabilityofwinning.Infact,onewouldexpect
adistinctlypiecewisefunctionbasedontheeffectivepointsaplayercouldscoreforhis
team.Suchafunctionforpricewouldbeflatforbenchplayersatthelowestpossible
price–inthiscase$1–andthenhavepositiveslopeforstartingplayers.
Thistypeoffunction–flatforbenchplayersandincreasingforstartingplayers–
isnottheoneseeninpractice.Thereareseveralreasonsthatslopewouldbepositive
forbenchplayersinpracticeeventhoughitwouldbezerointheoryevenwithoutrisk‐
aversepreferences.Apossibleexplanationforanoverpaidbenchplayerisa
misperceptionregardingfuturecontributions,althoughsuchamisperceptionproblemis
unlikelytobesystematicbecausethereisverylittleinformationasymmetryinfantasy
football.However,themostobviousreasonisthatthereisalwaysariskofastarting
playergettinginjuredorperformingpoorlyforsomeotherreason,andhavingagood
backuptoreplacesuchaplayerhedgesriskandlowersthestandarddeviationofpoint
21
total.Decidingwhethertheequalityofslopesisjustifiedbythesereasonscangive
insightintofantasyowners’riskpreferences.
RisktoplayersintheNFLisdependentontwomajoraspects:likelihoodof
injuriesandperformancedecrease.Likelihoodofinjuryissimplygamesplayedbyviable
playersovertotalgamesavailable.Thismayunderestimateinjuryriskassomeplayers
developinjuriesbeforetheseasonbegins,makingthemnonviabledespitebeing
drafted.Ontheotherhandperformancedecrease,whichiscalculatedbycomparing
performancefromoneseasontothenext,mayeasilyoverestimaterisk.Assumingthe
previousseason’soutputisareasonablepredictorofperformanceinthenextseason,
bycalculatingthepercentageofplayersthatseeanydropinperformancefromthe
previousseason,wemayfindtheriskofunderperformingduringaflukyseason.That
valuefailstoincludeplayersoutperformingtheirexpectationsandimproving,thusthis
measureoverestimatesrisk.Thisoverestimationhelpstocompensatefor
underestimationfrominjuries.
Usingempiricaldata,Ifoundthattheaverageriskisquitesmall,onlyapplyingto
10%ofallplayers(Figure9Chakravarthy,2010).Meanwhile,fantasyownersappearto
drasticallyoverpaybenchplayers,thinkingthatsuchplayerswerelikelytocontributeto
theteamdespitethelowchancetheyareneeded(Figure10Chakravarthy,2010).By
assumingthatthegoalofeachowneristowinhisleague,Icouldconcludethatowners
wereoverestimatingthedangerofasuddendropinperformance.Whenateam
correctsforthatoverestimatedriskbyloweringthedegreeofinducedrisk‐aversion,itis
22
abletoallocatemoremoneytostartingplayersandthereforewintheauctionfortop
freeagents.Thisallowsamorerisk‐neutralteamtocollectbetterstartingplayersatthe
expenseofbenchplayers,althoughsuchateamwouldalsotakeonmorerisk.Whether
anowner’sinducedriskpreferenceswouldberisk‐aversedependswhollyonwhether
hewouldwanttowinhisleagueorsimplyavoidfinishingnearthebottom.Anowner
withagreatdesiretowinhisleaguewouldhavearisk‐lovingpreferencebecausetaking
onhigherriskgiveshimagreateraveragemeanperformance.Continuinginthesame
veinanddefiningathresholdforwinningaleague,11Iwasabletogenerateadirect
relationshipbetweenplayerperformanceandcost.IntheNFL,thattypeofrelationship
isfarmoredifficulttodobecauseteamscannotmerelysetathresholdforamountof
talentrequiredtowintheSuperBowl.However,theresultsfromthepreviousstudyare
notwithoutusefulnessinconsideringlivefootball.
Fantasyownersoftenappearinducedtohavepreferencesthatareveryrisk‐
averse,ascanbeseenbythecoefficientbetweenfantasyauctionpricesonfantasy
points.Aplayerisworthhisexpectedtotalcontributiontoateam,discountedbythe
probabilityhedoesnotcontributetothatpotential–theriskofthatplayer
gettinginjured.Theregressionshowedthatthediscountrateofstartingplayersisnearly
40%,fourtimeshigherthantheempiricalvalueIfoundforrisk(Figure10Chakravarthy,
2010).Bytestingplayervaluationswithalowerdiscountrateinasimulatedauction,I
foundthatsuchavaluationlendsitselftoadraftwithameanhigherexpectedfantasy
11BecauseIhadaccesstothedistributionoffantasyteamtotalscoresoveraseason,Iwasabletoconstructadistributionofscores.Teamsneedtoscoreinthetop10%oftheirleaguetowin–generatinganaveragethresholdofscores.
23
points,implyingahigherexpectedutility.However,lowrisk‐aversionalsoincreasesthe
standarddeviationofexpectedpointtotal,whichisdetrimentaltoutility,suggesting
thatrisk‐aversionmaynotbeirrational;rather,itisinducedbythepreferencesfacedby
theindividual.Italsoappearsthathavingstrongpositionalinfluences,aswellasavalue
baseddraftingstrategyisthebestwaytoobtainateamwithhighoutput.Theimpactof
thisstudyinprofessionalfootballseemstobeambiguous,butinrealityhasdirect,and
intuitivelyapparent,implicationsonhowtoapproachthefreeagentmarkets.
Thisstudyhassomelimitationsbutfoundclearevidencethatfantasyfootball
ownerswereoverestimatingtheprobabilitythatplayersunderperformedasaresultof
injuryorsimplyaflukyseason.Thiscouldbeconsideredinducedrisk‐aversionandit
mayberational–ownersdonotwanttolosetheirleaguesandwouldtakealower
meanexpectedpointtotalinexchangeforlowstandarddeviation.Therearemultiple
explanationsforthiswithdirectNFLimpact.Thefirstisthatownersdonotalwaysuse
empiricaldatawhenevaluatingplayers.Instead,theyrelyonotheraspectsoftheplayer
andgetutilityfromotheraspectsnotdirectlyrelatedtowinning.Popularitywouldbe
themostobviousfactorinfantasyfootball,butintheNFLitcouldbeanyformofnon‐
statisticalbenefit–leadership,teamwork,orotherformofself‐sacrifice.This
explanationisdifficulttoprove,butrunscountertoexpectationsbyfansoftheNFLand
ifsystematicallyevidentmightsparksimilarproteststotheoneinCincinnati.
Othervaluegainedfromthisstudyliesinhowbesttoevaluateplayers.
Understandingthepositionsthatneedthemosthelpwillprovideteamswithanother
24
factorwithwhichtoweighskillsanddeterminehowbesttoevaluateplayers.The
indirecteffectsofateamspendingmoremoneyoncertainplayerscouldalsogenerate
positiveexternalities–someveteransmayjoinsuccessfulteamsinthehopesofwinning
achampionshipbeforeretirement.Suchanexternalitywasobservedmostrecentlyin
theNewEnglandPatriots,whowereabletosignRandyMossandJuniorSeauinno
smallpartbecauseofahistoryofsuccessandahighprobabilityoffuture
championships.Beingwillingtospendahigherallocationofthesalarycaponstarting
playersinsteadofbenchplayersandhavelessrisk‐aversepreferencecouldalso
contributetohelpingateamgeneratetheleveloftalentnecessarytobesuccessful.
25
TheoryandTestableHypotheses
ThisanalysisteststwoquestionsintheNFL:whetherteamsallocatesalary
purelybasedonexpectationsoffutureperformanceandwhetherNFLOwnersexhibit
thesametypeofinducedrisk‐aversepreferencesshownintheirfantasyfootballpeers.
Theallocationofsalaryhasnotbeenplumbedbyresearchandconcernsthreemajor
aspects:whethersalaryispredictablebypastperformance,whetherperformanceinthe
pastcanpredictperformanceinthefuture,andhowsalaryandperformanceweightthe
past.Answeringthesequestionscanshedlightonthewayteamsevaluatetheirplayers
anddecidetoallocatesalarytodifferentplayers.Suchananalysiscouldevenprovide
waysforteamsinterestedinmaximizingon‐fieldtalentunderthesalarycaptodosoin
newways.
Inducedrisk‐aversionintheNFLishardtogaugebecauseitisimpactedbyapair
ofcompetingeffects.Thesalarycaplimitstheamountanownermayspendonhis
players,justasinfantasyfootball.Thiswouldleadsuchanownertoavoidcommittinga
hugeamounttooneplayer.However,allNFLcontractshavetheuniquesalaryescape
clause–cuttingplayers.Ateamcancutaplayerbeforetheseasonandavoidhavingto
paythatsalarybeyondtheguaranteedamount.Eventhatamountcouldbewaivedbya
teamifaplayerisgivenacontractbyanotherteam.Thisabilitytoreleaseplayersgives
ageneralmanagerorownermoreflexibilityinsigningcontracts.Theeffectsofbeing
abletoremoveacontractfromthebooksandbeingforcedtospendwithinthelimitsof
acap,makeitunclearwhicheffectwillbemoresignificantandwhetherNFLOwners
havespecificriskpreferencesinducedbytheirmarket.
26
ProblemI:PlayerSalaryandSalaryGrowth
Earlier,Imentionedthevalueofunderstandingwhyplayersgetpaidinacertain
manner–howpaymentisalignedwithexpectationsforthefuture.Ifaplayerispaid
exactlyaccordingtohowheispredictedtoperforminthefuture,clearlytheteamis
willingtotaketheriskofsomeinjuryorweakperformance.If,ontheotherhand,teams
arepayingdifferentplayersdifferentlywithregardtofutureexpectedperformance,I
hypothesizeitwouldindicateafearofinjuryorsomeothermotiveinallocatingcap
spaceasdiscussedearlier.Breakingdowntherelationshipbetweenpayandexpected
futureperformancecanlendinsightintohowteamsviewtheconflictingimpactsofthe
salarycapandabilitytocutplayers.Regressingpastperformanceoncurrentsalarycan
definethatrelationshipclearlyandsuccinctly.
Thequestionbeingconsideredis:Whatarethebestpredictorsofsalaryandare
theyconsistentovertime?ThequestionmustbeconsideredusingOLSregressionsof
previousseasonperformancemetricsonfuturecapvalue.Thiswouldbeaseriesofone
yearlaggedregressionsintheform:
𝑆𝑎𝑙𝑎𝑟𝑦 = 𝑎 + 𝐵! ∗ 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑌𝑒𝑎𝑟!𝑠 𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 1
𝐻!: 𝐵!!""# = 𝐵!!""# = 𝐵!!""# = 𝐵!!""# 2
Thenullhypothesisisthattherearecertainstrongpredictorsofsalaryandtheyhave
similarcoefficientsinalltheyearsconsideredbystepdownregressions.Alternatively,if
salariesdonothaveconsistentlystrongpredictors,asseeninthosestepdown
regressions,salaryisdeterminedbyrandomlychangingcharacteristicsor,morelikely,
27
salaryisnotdeterminedbyon‐fieldcharacteristicsandtherelationshipillustratedby
theregressionshaslittlesignificance.
28
ProblemII:PlayerPerformanceandPerformanceGrowth
Thevaluationofplayerscanhelptounderstandteamutility.Ifateamgives
playersahighsalaryforreasonsthatcannotbeexplainedonthefield,thatteamclearly
hasadifferentutilityfunctionthanateamthatpaysplayersindirectaccordancewith
expectedfutureperformance.Unfortunately,parsingthedifferencebetweenreasons
fordifferingutilityfunctionsisharderthanitlooks.Thedifferencebetweensystemsof
thetwoteamsmayhaveahugeimpactonsalariesoffered.Footballissuchasystem
specificsportthatsmalldisruptionsbetweensystemsmayrenderaplayerhighly
ineffective,aswasseenwithChadOchocincoduringthe2012season.Itisalsopossible
thatateamcaresagreatdealaboutmerchandisingandsignsplayersbasedonexpected
revenue,whichwouldhaveanadditionalimpactonsalaryandmaynotbedirectly
visibleindataanalysis.
Thequestionbeingconsideredis:whichaspectsofplayerperformancedothe
mosteffectivejobofpredictingfutureperformanceandwhetherthoseaspectsare
consistent.Thisissimilartotheearlierquestionaskedregardingsalary,butthistime
focusesonwhetheritispossibletopredictperformance.Impliedbythequestionisthe
comparisonoftheseresultswiththeresultsfromthepreviousproblemtoconsider
whetherpredictionsofsalaryalignwithpredictorsofperformance.Thequestionwillbe
consideredbyaseriesofstepdownOLSregressionsofpreviousperformancemetricson
futurefantasypointtotals.
𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 = 𝑎 + 𝐵! ∗ 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑌𝑒𝑎𝑟′𝑠 𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 3
29
𝐻!: 𝐵!!""# = 𝐵!!""# = 𝐵!!""# = 𝐵!!""# 4
Thenullhypothesisisthatthepredictorsofperformanceareconsistent.Alternatively,
predictorsofperformancecouldbeinconsistent,meaningteamshavenogoodon‐field
performancemethodforpredictingfutureperformance.
Thisconclusion,inconjunctionwiththepreviousonecanshedlightonthe
movementofsalaryandwhetheritisinaccordancewithchangesinperformanceand
themostimportantquestionofProblemsIandII.
𝑆𝑎𝑙𝑎𝑟𝑦 = 𝑎 + 𝐵! ∗ 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑌𝑒𝑎𝑟!𝑠 𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 5
𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 = 𝑎 + 𝐵! ∗ 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑌𝑒𝑎𝑟!𝑠 𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 6
𝐻!: 𝐵! = 𝐵! 7
Ifwerejectthenullhypothesisweimplythatteamsprovidesalarynotaccordingto
futureperformancebutratherduetosomeothercharacteristicsthatcannotbe
measuredbyon‐fieldstatistics.Sucharesponsewouldsupporttheconclusionthat
salaryisnotgiveninaccordancewithexpectedfutureperformance,butaccordingto
someotherpreferences.Ifthenullhypothesisholds,however,salaryisallocatedwith
regardtofutureperformance.Thenullhypothesisiscomplicatedbythequestions
previouslydiscussed–whether𝐵! isconstantforpredictingfutureperformanceand𝐵!
constantforfuturesalary.Ifthosehypothesesdonothold,thenwecannotacceptthe
nullhypothesisandareforcedtoinferthatsalaryisnotgiveninaccordancewith
expectedfutureperformance,acruciallyimportantconclusionintryingtodefineOwner
preferences.
30
ProblemIII:LaggedValues
Theperformance–salaryrelationshipcanalsobedefinedbytherelativeweights
ofthepast.Studyinglaggedvalueswillbeanimportantportionofthisstudybecauseit
showshowpastperformancedictatesfutureperformanceandfuturepayment.The
relativeweightsofpastperformancecanlendinsightintothereasonsbehindpaying
players.Forexample,ifperformanceinyearthreeismostlystronglypredictedbya2:1
ratioofperformanceinyeartwotoperformanceinyearone,onewouldexpectthe
sameratioofperformanceinyearstwoandonetopredictsalaryinyearthree.Ifthat
ratiochangesdrastically,itcouldindicatethemotivesbehindpayingplayers–whether
itisindirectaccordancewithfutureon‐fieldperformance,orwhetheritisaresultof
somethingnotmovingwithexpectedfutureperformance.Payingplayersforprevious
workthatisunlikelytobereprisedsuggeststhatOwnersvaluecharacteristicsthatare
noton‐fieldperformance,likeleadershipormerchandisingrevenue.
Continuedtestingofthisdatacanprovideanswerstomajorquestionsregarding
NFLsalaries.Understandinghowplayersarepaidandwhetherthatisdifferentfromthe
wayplayersareevaluatedcangiveinformationregardingthewayteamshandle
contractsignings.FantasyfootballisanunderappreciatedtoolinNFLcircles,butcould
provideawayforateamtryingtomaximizetalentonthefieldandexpectedfuture
productionwhilestayingundertheNFL’shardsalarycap.Infantasyfootball,owners
haveahugepoolofplayerstochoosefrom,12meaningtheycanaffordtoberisk‐averse
12Anaveragefantasyfootballrosterincludesfewerthantwelveplayersatsixpositions.Fantasyownerscanchoosethoseplayersfromall32NFLteams’53playerrosters.Thus,atenteamleagueselects120ofthenearly1700playersavailable
31
andhopeforthepossibilityofaplayerwithlowexpectationsoutperformingthose
expectations.IntheNFL,however,theabilitytofindplayerswhocannotcompeteis
rare,andquitenoteworthy.VictorCruzoftheNewYorkGiantsisastrikingexample
joiningtheleagueasarelativeunknownquantityandsucceeding.Giventhenumberof
undraftedplayers,itisraretofindsuchatalentandgroomhimtocompeteonahigh
level.Andevenafterfindingthatplayer,hemustbepaidinaccordancewithhis
performanceinfutureyears,soholdinghimforthedurationofhiscareeratthesame
lowrateiseffectivelyimpossible.Thus,weseetheselectivepressuresoftheNFLand
fantasyfootball–intheNFL,beinghighlyrisk‐averseisafarmoredifficultstrategyto
justifybecauseofthescarcityoftoptierplayersmakesacquiringthoseplayersmore
importantandtheabilitytocutacontractallowsforanimmediateoutifthecontract
signingwastoogenerousfromateam’sperspective.
Thequestionofthelaggedvaluesofperformanceaspredictorsoffuture
performanceandfuturesalarycanclarifythemotivationsofallocatingsalaryandmay
helpdefinethewayplayersarepaid.Byregressinglaggedperformancevaluesonfuture
salaryandfutureperformance,wemaycomparetherelativeweightsofthepast
performancebyobservingtheratiobetweencoefficients.
𝑆𝑎𝑙𝑎𝑟𝑦 = 𝑎 + 𝐵!! ∗ 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑌𝑒𝑎𝑟!𝑠 𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 + 𝐵!!
∗ (𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 𝑇𝑤𝑜 𝑌𝑒𝑎𝑟𝑠 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 )
8
32
𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒
= 𝑎 + 𝐵!! ∗ 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑌𝑒𝑎𝑟!𝑠 𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 + 𝐵!!
∗ (𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒 𝑇𝑤𝑜 𝑌𝑒𝑎𝑟𝑠 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 )
9
𝐻!:𝐵!!
𝐵!!=𝐵!!
𝐵!!
10
Thenullhypothesisisthattherelativeweightsonthepastarethesame,asdetermined
bytheseriesofOLSregressions,meaningthatteamsallocatesalarybasedontheir
expectationsforfutureperformance.Alternatively,iftheweightsaredifferentfor
futuresalaryandfutureperformance,itwouldindicatethatfuturesalaryisnot
allocatedaccordingtoexpectedfutureperformance,implyingotherreasonsfor
allocatingfuturesalaries,perhapsincludingfuturepotentialasastarorcharacteristics
importanttotheteamliketeamwork.Itmayseemmorestraightforwardtocompare𝐵!!
directlyto 𝐵!!,andviceversa,butsuchacomparisonisdrasticallycomplicatedbythe
magnitudeofeachcoefficient.Suchatestwouldallowusinsightintohowexactlythis
ratiodiverges,butdoesnotaccountforrelativeweights.Ratherthanseeingtheexact
magnitudegiventoeachyear,themoreimportantquestioniswhethertheweightson
pastyearsareequal,becausethatwouldillustrateaconsistencyinsalaryallocationin
accordancewithperformancegrowthovertime.
33
ProblemIV:RiskPreferencesandCuttingPlayers
StudyingtheriskpreferencesofNFLteamsisanimportantquestionandit
mesheswithmypreviouswork.ThequestionofwhetherNFLteamsdisplayinduced
risk‐aversionisoftwoparts,anditreliesonthefantasypricinganalysisbefore.A
piecewiseOLSregressionofperformanceonfantasyprice,splitatstartingandbackup
playersillustratestheriskpreferenceoffantasyteamowners.Meanwhile,thesame
piecewiseregressionofperformanceonNFLcapvalueseparatedbystartingandbackup
playersillustratesanyrisk‐aversionofNFLOwners.Mypreviousresearchshowedthat
thereislittledifferencebetweenthestartersandbenchplayersinfantasypriceandthat
thepiecewiseregressionshavelittlechangeinslopebetweenthetwopoolsofplayers.13
Thisisthecasedespiteexpectedperformanceforafantasyteam.Althoughmostofthe
benchplayerswillearntheteamfew,ifany,points,theyarepaidasthoughtheywould,
seeminglyindicatingveryrisk‐aversepreferencesbyfantasyownerswhoseemto
assumethatthoseplayerswouldbenecessary.Unfortunately,NFLbackupsrarelyearn
anystatisticsatallbecause,unliketheirfantasycounterparts,theydonotoftentakethe
field.Thisisminorproblemwithmeasuringthevalueofbackups,butassumingthat
weightingofcertainstatisticsamongbackupsarenotdifferentfromthecorresponding
weightsofthosestatisticsamongstarters,theproblemoflimitedobservabilityisa
minorone.
ThedistinctionofNFLplayersbetweenfirst‐stringandsecond‐stringisacomplex
one,becauseviewingtheproblemafteraseasonpresentsamuchdifferentpicturethan
13Figure13illustratesthispoint.
34
beforetheseason.Thereisanargumenttobemadethatteamsmaythinkthatone
playerisastarteronlytofindouthalfwaythroughtheseasonthatanotherplayeris
better.Ifthiswerethecase,itwouldoverestimateanyoverpaymentoflowperforming
players.However,thisstudyshows,particularlyinProblemsIIandIII,thatthereare
manystrongindicatorsforfutureperformance,towhichallteamswouldhaveaccess.
Thus,thefactthatteamscouldstatisticallyinferfutureproductionmitigatestheexpost
biascausedbydefiningstartersandbenchplayersaftertheseasoniscomplete.
Thestrengthofthisanalysisrequiresunderstandingthebenefitoftargetasa
proxyforateam’sfaithinthequalityofaplayercombinedwithameasureoftalent.
Betterplayers,starters,wouldreceivemoretargetsthanbenchplayers.Forthiscase,
thedefinitionofstarterwillbeaplayerabovethemedianintargets–benchplayersare
thosewhoarebelowthemeanintargets.IntheResultssectionProblemII,a
breakdownofthevalidityofusingtargetsasaproxyfortalentwillbedescribedinfull,
sosplittingthegroupofwidereceiversintopoolsofstartersandbenchplayersbytheir
positionintargetsfollows.
𝐶𝑎𝑝 𝐻𝑖𝑡!"#$"%$ = 𝑎 + 𝐵!"#$"%$ ∗ (𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒) 11
𝐶𝑎𝑝 𝐻𝑖𝑡!"#$! = 𝑎 + 𝐵!"#$! ∗ (𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒) 12
𝐻!: 𝐵!"#$"%$ = 𝐵!"#$! 13
Thenullhypothesisisthatthepiecewiseregressionofstartersandbenchplayersin
performanceonNFLcapvaluewillexhibitthesamepatternasinfantasyfootball–very
similarslopes,indicatingthesamesortofriskpreferenceasamongfantasyowners.The
35
alternativehypothesisisthattheslopesaredifferentinthepiecewiseregression,
suggestingthattheriskpreferencepatternintheNFLisdistinctlydifferentthanthatof
thefantasymarket.Ifthedifferentslopesconsistofalowerslopeinamongbackupsand
ahigherslopeamongstarters,itwouldmostlikelyindicatethattheNFLplayermarket
induceslessrisk‐aversepreferencebecausethescarcityoftoplevelplayersintheNFL
limitstheabilityforteamstoberisk‐averseinsearchingfortoptierplayers.
Alternatively,ifslopeishigheramongbackups,itindicatesevengreaterrisk‐averse
preferencesthaninfantasyfootballbecauseteamsareanxioustosecurebackup
players.
WhileunderstandingthemotivesofNFLownersmaybedifficult,thepossibility
offindingasalaryallocationsystemwiththegoalofwinninggamescouldstillbe
extremelyvaluableandtherearelessonsavailableinfantasyfootball.Thesystemtobe
consideredlaterinthispaperisoneofshortertermcontractswithhigher,incentivized
paymentstructuresandgreaterrelianceontheteam’sabilitytocutplayers.Sucha
systemwouldresultinaradicalchangeinthewaycontractnegotiationsareheld,butif
itweredoneacrosstheleagueratherthanjustbyoneortwoteamsitcouldleadtoa
moreopenmarketforplayers.Theremay,however,belargescalelimitationsforteams
treatingplayersassingle‐yearperformers.Thoselimitationswouldincludethe
reputationaleffectsofbeingateamaccusedofnotcaringaboutplayers.Suchalabel
mightstigmatizeateam,andcouldbesostrongthatthewaysalaryallocationand
contractlengthishandlednowmightberisk‐neutral.
36
Methods
Thisanalysisisseparatedintoseveralstepsdesignedtogenerateaproper
understandingofwhyNFLplayersarepaidingivenways.Inordertounderstandwhich
characteristicsofplayersaremostimportanttogeneratingsalary,onemustfirst
consideraplayer’scontribution.LeedsandKowalewski(2001)discussthe1993
CollectiveBargainingAgreementanditsimpactonskillpositionplayers.Theterm“skill
position”referstotheplayerswhowilltouchtheballmostonateam.Quarterbacks,
widereceivers,runningbacksandtightendsareallconsideredskillplayers.The
methodologicalfocusontheskillplayersistheresultofstatisticsregardingskillplayer
performancebeingwidelyavailableandisatacticImustreplicate.Widereceiversare
amongthemosttrackedplayers,withavarietyofstatisticalmetricsfortheir
performance,whichisthereasonthisstudyislookingmostlyatthatposition.Leedsand
Kowalewski(2001)alsofocusonplayersattheendsofthewagespectrum,meaning
thatgeneratingamodelforperformanceatanywagemayrequireapiecewise
breakdownofplayersbasedonwageorskill.
Iamstudyingwidereceiversbecausetheyhaveaplethoraofstatisticsand
despitethevarietyofroutestheyrun,theyfaceasingleeventmodelofperformance.
Thismeansthatalthoughwidereceiversfacemanytargetseverygame,eachofthese
targetsisroughlyindependent,particularlywhenconsideredoveranentireseason.A
“target”referstoapassinaplayer’sdirection.Thisservestoregulateanindividual’s
productionanddifferentiatebetweenplayersthatmayseemtobeequallyproductive
buthavedifferentdegreesofopportunity.Forexample,ifplayerAcatchesfourpasses
37
forfortyyardsandplayerBcatchesfourpassesforfortyyards,theymayappeartohave
beenequallyeffective.However,ifplayerAreceivessixtargetsandBreceivesten,Ais
themoreefficientplayer,accomplishingthesameamountofteambenefitinfewer
opportunities.Despitethebenefitofusingpointspertargetasavariable,targetsare
endogenouswithregardtotalentlevel–aplayerwhoreceivesfewertargetsmostlikely
haslessabilitythanhiscounterparts.Otherstatisticsthatareusedtodeterminethe
valueofawidereceiverareyardspercatch,whichplaceapremiumon“bigplay
ability,”animportantcharacteristicformanyteams,particularlythosewhooftenrun
insteadofpassingonoffense.Anotherbenefitfortheuseofwidereceiversisthatthey
rarelyhavetomakecrucialdecisions,unlikeaquarterbackoramiddlelinebacker,who
servesasacoachonthefield.Thismeansthattheamountofnon‐measurableabilities
ofsuchaplayerislimited.Ontheotherhand,certainplayersareassociatedwith
qualitiesthatareimportanttoteamsandsuchanassociationgivesthatplayerextra
weightinsalarynegotiations.Theconverseisalsotrue‐playersseenasa“cancer”to
theirteamarelessvaluedandtendtomakelessmoneythantheirpeerswhoareseen
aslessegotistical.14
First,todetectwhichaspectsofplayerperformancearemostrewarded,Imust
discoverwhichmetricsaremostimportantindeterminingpayscale.Thisstepinvolves
theThalerandMasseytechnique(2005)ofusingthesimplestindicatorsofperformance
14Therearemanyfamousexamplesofthistypeofplayer,butRandyMossisamongthemostsignificant.AHallofFamelevelplayerisrarelytradedorcutbecauseoftheirreproducibleperformancehebringsandtheassociatedinterestfromfans.Moss,however,wasreleasedthreeseparatetimesin2010aloneandiscurrentlyplanningacomebacktotheNFLthathasbeenviewednegativelybecauseheissuchadivisivecharacter.Itiscurrentlyunknownwhetherhewillbesignedbyanyteams.http://espn.go.com/nfl/story/_/id/7616262/report‐randy‐moss‐willing‐sign‐deal‐guarantee‐money
38
togenerateanideaofwhatplayersarepaidfordoing.Forexample,isagealarger
factorinsalarythanyards?Ifso,whichwaydoesthateffecttrend?Todothis,Imust
useavarietyoffactorstopredictthesalarycapportionofcontractbenefitsand
determinewhichismostimportant.Inidentifyingthis,Icanthendeterminetherelative
validityoftheseexplanatoryvariables.Forexample,iftouchdownsareastrong
predictorofwidereceiverpaygrades,andthedistributionoftouchdownsissomewhat
stochasticwhencomparedtoyardsorreceptions,knowingthatsalariescanbebasedon
inconsistentvariablesisimportantandsuggeststhatownersmaypayplayersforthings
otherthanexpectedperformanceonthefield.Alternatively,ifIfindthatpayrateis
linkedclosesttoafactorwithoutdirectimpactonproduction,likeage,thatmayalso
proveilluminating.Becausesalariesoftendonotchangebyalargefactor,measuring
whetherornotaplayerexperiencesradicalchangesinpayisimportant.Ifaplayer
experienceslargechangesinpay,whatcouldhavecausedsuchachange?Whichtypes
ofperformancesleadtochangesincapvalue?Howdotherawstatisticsgeneratefuture
salarygrowth?Thistypeofanalysiscanbefruitfulinstudyingthecreationofnew
contracts,butcanbeplaguedbysmallsamplesizesincesigningnewcontractsisrare.
Anothermajorinputtostudyissalarygrowth.Salary,orcapvalueinparticular,
canchangedependingonavarietyoffactors.Whatismostsignificantingenerating
increasesinsalary?AgedrivesupsalarybecauseoftheNFL’sCBA,butifthatistheonly
significantpredictorofsalarygrowth,theNFLallocationsystemmaybeweakbecause
ofaninabilitytopaybetterplayersmoremoney.Similartothepreviousportion,lagged
valuescanbeveryimportant.Howdoownerstreatthepastwhenallocatingsalary
39
changes?Tounderstandthis,Imuststudycurrentsalaryinconcertwithasimilarvariety
offactors,butfrompreviousNFLseasons.Thisanalysiswouldrevealifsalariesaremost
influencedbyrecentperformance,oriftheyareinfluencedmorebyperformancefrom
manyyearspast.Studyingthewaysalaryallocationisaffectedbypastperformanceis
notvaluablewithoutapointofcomparison.Performanceisalsopredictedbyprevious
performance,andiffutureperformanceispredictedbypastperformanceinthesame
mannerthatfuturesalaryispredictedbypastperformance,wecaninferthatsalaries
areallottedwithaneyetofutureperformance.Ontheotherhand,iftherelative
weightsofthepastdifferbetweenpredictingsalaryandperformance,understanding
thedifferencebetweensalaryallocationandwhatowners“should”becouldbe
illuminating.Unfortunately,thetendencyofmostNFLcontractstobemultipleyearsin
lengthcomplicatesthisanalysis,butostensiblyteamswouldbetryingtocompensate
playersinaccordancewiththeirexpectedperformanceinagivenyear.
Toanalyzeproduction,thisstudymakesuseofthefantasyfootballpointscheme
todetermineaplayer’svalue,whichcouldalsobecalledfantasypoints:
𝐹𝑎𝑛𝑡𝑎𝑠𝑦 𝑉𝑎𝑙𝑢𝑒 = 6 ∗ 𝑇𝑜𝑢𝑐ℎ𝑑𝑜𝑤𝑛𝑠 + 𝑌𝑎𝑟𝑑𝑠10 − 𝐹𝑢𝑚𝑏𝑙𝑒𝑠 14
Thisformulaisameasureofplayerproductionandisusedinfantasyfootballto
determinehowmanypointsaplayerearnsinagivengame.Betterplayersscoremore
points,worseplayersscorefewer.Thisformulabreaksperformanceintomultiplepieces
–scoringtouchdowns,gainingyards,andmaintainingpossessionofthefootballforthe
offensiveteam.Inafootballgame,scoringatouchdownearnsateamsixpoints,which
40
isthereasonfantasyfootballplayersgetsixpointspertouchdownscored.Theyardage
coefficientisbasedontheaverageNFLdrive,whichgainsapproximatelytwentyyards
andscoresapproximatelytwopoints(J.Armstrong,2011).Thus,coveringonehundred
yardsisworthapproximatelytenpoints,asshownbytheformulaabove.Similarly,
abouthalfoffumblesarelost,andalostfumbleendsadrive,correspondingtothelost
opportunityoftwopoints.It’simpossibletoknowwhichfumbleswillcauseachangein
possession,butonaverage,afumbleisanegativepointfortheteam.
Thereasonbehindusingthistypeofperformancemetricisthatallowsforfar
greatereaseinOLSregressions.Byusingoneresponsevariable,theregressionwillbe
fareasiertoanalyze.Unfortunately,fantasypointsarenotnormallydistributed,but
otherwiseitservesasanexcellentstatisticforacademicuse.Thefactthatitisright
skewsupportsmyearlierstatementregardingthescarcityoftoplevelplayers.This
scarcityexplainswhytopendplayersmakesomuchmoney.Thereareavarietyofother
metricsthatcanbeusedtomeasurewidereceiverperformance,likeDefense‐adjusted
YardsAboveReplacement(DYAR)andDefense‐adjustedValueOverAverage(DVOA).
Theproblemwiththosemetricsisthattheyrequireplaybyplayanalysisforeachplayer
beingstudied,datacurrentlyunavailableforeveryyearnecessary.Inanycase,these
statisticsarehighlycorrelatedwitheachotherandwithfantasypoints,meaningthatall
threeareapproximatelythesamemetricofsuccess(S.Walder,2011).Toconfirmthose
findings,IcomputedthecorrelationbetweenDYARandfantasypoints(.856)andthe
correlationbetweenDVOAandfantasypoints(.839).Thosecorrelationsaresufficiently
41
largetosuggestmyanalysiswouldprovidesimilarqualitative,ifnotnecessarily
quantitative,resultswithanyofthethreemetrics.
Similarlytotheanalysisofpayment,analyzingperformancegrowthcanalsobe
revealing.Generally,onewouldexpectperformancegrowthtobehighestinthefirst
yearsofaplayer’scareer,beforeheentershisprime.Ifperformancegrowthandsalary
growthmovetogether,wemayconcludethatplayersarepaidinadirectrelationshipto
performance.Thegrowthvariablesaremorecomplextoanalyzebecausesalarygrowth
ishamperedbythefactthatmanyNFLcontractsaremultipleyearsinlength.This
presentsacaveatonanyconclusionsgleanedfromananalysisonsalarygrowthbecause
teamsmaybetryingtopredictperformanceveryfarintothefuture,when
extrapolationsmaygrowincreasinglyhazy.Drawingtooheavilyontheseinferences,
then,wouldleadtoanoverestimationofanydifferencebetweenfutureexpected
performanceandfuturesalary.Thebenefitofusingdataendingin2009,though,allows
forcorrectionsinthecaseofteamsrestructuringcontractsandshowingthe
restructuredvalueratherthantheinitialvalue,whichmayhavebeenashortsighted
decision,andlowerstheeffectofhugeextrapolations.15Thislimitationaside,lookingat
growthbetweencontractsaswellastheeffectsofcuttingaplayermayprovidemore
informationonthedecisionsmadebyNFLteamswhenaplayerisupforanewcontract.
Generatingthesedummyvariablesreliesonfindingplayerswhoseeaverylargejumpin
expectedcapvalueorwhodidnotretirebutwerenotonateam’srosterduringa
15Teamsmaysigncontractsincludingthepossibilityofdeadmoney,inwhichaplayerisguaranteedmoneyandthencut.Thebenefitoftheolderdatasetisthatsuchmoneywouldbeincludedinaplayer’scaphitfortheseasonimmediatelybeforebeingcut,sothecosttotheteamofthatplayerisnotlost.
42
season.Thesepatternswouldsuggestthataplayersignedanewcontractorhadbeen
cut.Studyingtheeffectsofperformanceonnewcontractsandcutscanhelpdefinea
prescriptiveapproach
Theremainderofthisworkliesinidentifyingthepatternofrelationshipbetween
playerskillandplayersalarywhichcouldrevealtheriskpreferencesinducedbythe
NFL’ssalarycap.Definingsuchriskpreferencesmayenabletheformationofadirect,
prescriptivepolicyrecommendation.Identifyingrisk‐aversionseemsstraightforward–a
moreskilledplayershouldbepaidmorethanalessskilledplayer.Similarly,aplayer
withhighexpectationsoffuturegrowthshouldmakemoremoneythanapeerwitha
lowerpotentialforgrowth.Iftheserelationshipsfollownonlinearpatterns,thatmay
illuminateourunderstandingofspendingpatternsandinducedriskpreferences.If,for
example,aplayerwithaveryhighceilingispaidmorethanaplayercurrently
outperforminghimbutwithalowerceiling,itcouldsuggestthatownersandgeneral
managersareriskloving–placinggreatervalueonthepossibilityofhighfuture
performancethanonthecertaintyofmoderatecurrentperformance.Similarly,the
inversecouldbetrue.Inanycase,afocusedanalysisofsalaryandperformancefactors
isnecessarybeforemakinganyconclusionsandforminganyrecommendations.
43
Data
ThesalarydataforthisstudyiscominglargelyfromUSAToday’sNFLSalaries
Database.ItisthemostaccessibledatasourceforNationalFootballLeagueSalariesand
hasinformationasrecentas2009.ThisworkusesthefivemostrecentseasonsofNFL
salarydataavailable,from2005to2009,toensurethatallthesalaryfiguresusedare
fromthesameCBA,whichwassignedpriortothe2005NFLseason.USATodayprovides
theyearlybasesalary,signingbonus,capfigure,andtotalpaymentincludingbonusand
salaryforeachplayerintheNFLindollarfigures.Capfigurereferstotheamountthat
countsagainstateam’stotalsalarylimit.Becauseteamsareforcedtoallocatesalaries
tostaywithinacertainspendingbudgetandtheownersareverywealthy,thecap
allocationisthemostimportantaspectofaplayer’sincome.
Thus,ifateamispayingaplayer$11million,butthecapvalueisonly$6million,
thelatterfigureisofmoreinterestsincetheremaining$5millioniscomingdirectly
fromtheowner’spocketandthemarginalcostofthatremainingpaymentisessentially
inconsequential.Moreover,muchofthat$5millionfigurewillnotbepaidtotheplayer
asitincludesperformanceincentivebonusesthatareextremelyunlikelytobe
realized.16USATodaycollectsinformationforthisdatabasefromtheNFLPlayers
Association,playeragents,andtheirownresearch.Thedatabaseusestermsfrom
contractscompletedatthebeginningofaseason.Limitationsonsalaryliketherookie
capmayaccountforsomesalaryinefficiencies,butdummyvariablesfortherookie
16IntheremainderofthisarticleIwillusetheterms“salary”and“capvalue”interchangeablyassalaryandcapfigureareidenticalwhenbonusesarediscounted.Whenreferringtothetotalpaymentabove,Iwilluse“totalsalary.”
44
contractarenotavailable.Rarely,aplayermayextendorsignacontractduringthe
season.Suchacontractwouldnotbeincludedinthisdatabaseuntilthenextseason.Ifa
teamchangesthewaythemoneyisdistributedinacontract,suchachangewouldonly
beincludedindataforthenextseason,andcapvaluewouldaccountforanysuch
change.Theabilityofteamstorestructurecontractswouldtheoreticallyimprovethe
abilityofcapvaluetomovealongwithexpectedperformanceandunderestimateany
differencesinexpectedfutureperformanceandfuturesalary.
ProFootballReferenceisthesourceforrawon‐fielddatafrom2005to2009.
ThiswebsitegetsdatafromtheESPNFootballEncyclopediaandtracksstatsusingthe
ESPNstatisticscenter.ESPNalsoprovidesthedataforfantasyfootballauctionprices
andusage.ForwidereceiversProFootballReferenceprovidesmostofthedatatobe
studiedandincludesdataoneverywidereceiveronanNFLrosteratanypointduringa
season.Ifaplayerplayedinoneseason,butnotinthenext,heisnotincludedfor
multiyeargrowthstatistics,butaplayerwouldbeincludedforsingle‐yearstatistics,and
allregressionsusingonlysingle‐yearstatistics.Thisanalysisalsomakesuseofdatafrom
FantasyFootballToday,whichprovidesthevariable“targets.”FantasyFootballToday
givesstrongtargetinformationonlyforthe2007,2008and2009seasons.Beforethose
seasons,targetinformationisnotavailable.Inanefforttoconsideroffthefieldeffects,
likeplayerpopularitywiththegeneralpublic,IcontactedtheNFLshop–theofficial
sellerofNFLmerchandising–inordertofindtherankingsystemforNFLjerseysales.
Theshop,however,doesnotreleasethatdatasoincludingexternalvariablessuchas
45
popularityiscurrentlyimpossible.Findingtherelationshipbetweenpopularityandpay
wouldalsobehelpfulindefininganowner’sutilityfunctionbutisacurrentlimitation.
46
Results
Thefirstimportantproceduraleffectwascorrectionofthevariablesincluded.
Manyvariableswererightskew,includingthesalarycapfigure(“capvalue”)andplayer
fantasypoints.Fantasypoints17werecreatedaccordingtotheformulagivenaboveand
shownagainhere:
𝐹𝑎𝑛𝑡𝑎𝑠𝑦 𝑃𝑜𝑖𝑛𝑡𝑠 = 6 ∗ 𝑇𝑜𝑢𝑐ℎ𝑑𝑜𝑤𝑛𝑠 + 𝑌𝑎𝑟𝑑𝑠10 − 𝐹𝑢𝑚𝑏𝑙𝑒𝑠 14
Thisformulaisthecentralcharacteristictoallportionsoftheresultsthatdealwith
playervalueandmeritsadiscussionofstrengthsandweaknesses.Bycombiningmany
aspectsofperformanceintoasinglenumber,itallowsforagreatdealofeasein
regressions.Itattemptstobesomewhatintuitivebyconvertingallperformanceinto
expectedpointsaddedtoateam.Moreover,itisacommonlyusedsystemwiththe
continuedgrowthoffantasyfootball,asdescribedearlier.However,sucha
simplificationremainsjustthat–asimplification.Itignoressomestatisticsthatmaybe
important,liketargets.Thisformulacannotconsidertheabilityofaplayertoserveasa
leaderorbeagoodteammate,thoughcomprehensionofpersonalitycannotbehad
withoutextensiveinterviews.Inshort,thismetricisveryuseful,butdoeshavesome
flawsduetoalackofdetail.
Thetargetisavaluableexplanatoryvariablebecauseitcanserveasameasureof
ateam’sfaithinacertainplayer.Atargetisaballthrowninareceiver’sdirection.
Betterreceiversusuallyhavemoretargetsbecausetheteamwantstoutilizethetalent
17Valueandpointsareinterchangeabletermsintheformulaabove.
47
ofthatreceiver.Usually,receiverswiththemosttargetshavethemostproductionon
thefieldbecausetheyarethebestreceiversontheirteam,lendingsomeendogeneity
tothecomparisonbetweentargetsandperformance.However,becausetargets
measuretheteam’sfaithinaplayer,theyareausefulmethodfordividingplayers
betweenfirstandsecond‐string,asinPartIV.Figure7illustratesthevalidityofthat
statement.Thestrengthofthisrelationshipdecreaseswhentargetsareusedasa
predictivevariableforvalue,buttherelationshipisstillclearlypositive.Fantasypointsin
previousseasonsmayalsopredicttargets–Figure8isanexampleofthatrelationship.
Intuitively,thisisreasonable–thebetteraplayerisinthepreviousseason,themore
likelyheistobeutilizedbyhisteaminthefuture.Thesegraphsshowthestrengthof
targetsasaproxyforfantasypointsandhowsimilarthetwostatisticsare.Becausea
playerwhohasmorefaithwillgetmoretargets,thisfactisusefulinthecomparison
betweenaplayer’sfantasypointsandhissalary,astargetscanbeusedasametricfor
worthintheeyesofacoachingstaff.
48
PartI:PlayerSalaryandSalaryGrowth
Aregressionofpreviousperformanceindicatorsonsalaryshowspredictorsof
playercapvalueappeartobewidelyscattereddependentontheyear.Thevariables
shownasstrongpredictors(p<.05)ofthenaturallogofcapvalueappearsinTable1.
Thisisaseriesofregressionsforthefouryearsbetween2006and2009.Eachofthe
variablesreferstothevariableintheyearbeforetheregression.Thus,inthe2006
coefficients,thegamesplayedvariablereferstogamesplayedin2005.
Table11819illustratesthegeneralinconsistencyindeterminingwhichvariables
aresignificantindeterminingsalary.Overthefourregressionsabove,ageistheonly
variablewhichisconsistentlysignificantalthougheachyearproducesafairlyhighR‐
squaredterm,forcingustorejectthenullhypothesisandaccepttheideathatsalaryis
notabletobepredicteddirectlyfromthepreviousyear’son‐fieldperformancesincethe
coefficientonAgedoesnotstaywithina95%confidenceintervalovertime.Despitethe
lackofprecisionofcomparingcoefficientsfromdifferentregressions,the
multicollinearityofagepreventsastrongertest,andthedifferenceinmagnitudeofthe
coefficientsseemstoprecludethenecessityofastrongertest.Inordertotestthe𝐵! in
PartIIoftheresults,oneneedstocalculatetheaveragevalueofeachpredictorto
comparetotheaveragevaluesfor𝐵!.Belowisthesumoftheaveragecoefficientfor
eachofthesevariablesforthefouryearperiod,illustratingtherelativestrengthofeach:
18Thistable,andmanyothers,showdifferentvariablesforeachregression.Thatisbecausetheonlyvariablesshownineachregressionaretheonessignificantatp=.05.Toseethecompleteregression,includingstatisticallyinsignificantvariables,seeTable2.19ThereasonforlistingFantasyPointsasasquarerootistocorrecttherightskew.
49
𝐸 𝑆𝑎𝑙𝑎𝑟𝑦 𝐶𝑎𝑝 𝐹𝑖𝑔𝑢𝑟𝑒 𝑡
= 𝑒 .!"∗!"#(!!!)!.!"∗!"#$% !"#$%&(!!!)!.!" ∗!"#"$%&'()(!!!)!.!"#∗ (!"#$%(!!!))
15
Wheretistheseasoninquestionandt‐1isthepreviousseason.Bybreakingdownthis
equation,wemayseeevensmallchangesineachofthesevariablescouldhaveamajor
effectontheestimatedsalarycapvalueforaplayerbecauseoftheexponentialnature
ofthefunctionabove.Giventhespecificationwithlogofsalarycapvalueasthe
dependentvariable,thepositivecoefficientonperformanceindicatesincreased
marginalreturntoimprovementsinperformance.20Thistypeofincreasedmarginal
returnsuggeststhebenefitsofbeinga“star.”Starpowerisafocusofallathletics
becausethefinancialbenefitsofhavingoneofthefewtopplayersataposition.The
analogyusedbysportswriters,“nevertradeadollarforfourquarters,”isanapt
descriptionoftheissuesfacedbyteamstryingtoacquirestarperformers.Thus,aplayer
movingfrombeingsimplygoodtobeingelitehashugerepercussionsforhisteamthat
gobeyondhelpinghisteamtowingames,supportingtheexponentialequationabove.
WhileTables1and2illustratetheinconsistenciesinfindingstrongpredictorsfor
salaryinagivenseason,usingsalarygrowthasaproxyforsalarydoesnotilluminatethe
situation.Measuringthesalarycapvalueinyeartwoasafractionofthathitinyearone
isonewaytomeasuresalarygrowth.Runningthesamestepwiseregressionsforsalary
growthinsteadofsalaryreiteratesthelackofconsistentpredictorsforsalary.Tables3
and4illustrateseveralstrikingresults,namelythaton‐fieldperformancemetricsdoa
20ThisstatementissupportedbytheresultsoftheregressioninTable1a,showingthecoefficientonthesquareroottermtobefarlesssignificantthanthecoefficientonthesquaredterm,𝑝 < 0.001
50
poorjobofpredictingsalarygrowthinthefutureandthattheyhaveawiderangeof
variablesthatmayhavebeenexpectedtobeimportantarenotconsistentlystatistically
significant.Thisinconsistencyreinforcesrejectionofthenullhypothesisthatfuture
salaryandexpectedperformancegrowthmovetogetherandmaybearesultofthefact
thatmostplayerssignmultiyearcontractsthatareheldforextendedperiodsoftime
despitechangesinplayerperformance.
However,combatingtheeffectsofmultiyearcontractsisdifficult.Whenlimiting
focustothoseplayerswhoexperiencelargechangesinsalarycapvalues–playerswho
signednewcontracts,samplesizedrasticallydrops,reinforcingthestatementsabove
thatpredictingfuturesalaryisimperfectandthatplayersoftensignmulti‐yearcontracts
insteadofshorttermcontractsthatwouldrequirethemtosignnewcontractsoften.For
example,therewerenosignificantpredictorsforsalarygrowthin2006or2008.In2007
and2009thesamplesizewastoolowtogenerateanyrealconclusions(N=34,17
respectively).Findingweakregressions,however,doesgiveusinsightintotheway
teamspayplayers.Teamsrarelygiveplayerslargechangesinsalary,evenwhenthere
arelargechangesinperformance.Howeverwhenachangedoesoccur,thereasonsfor
itdifferacrossindividuals.Theremaybemanyexplanationsforthis,butthemostlikely
onemightbetheopportunitycostofchangingaplayer’ssalary.Terminatingaplayer’s
contractandrenegotiatingasalaryiscertainlynoteasyandcouldbeapointof
frustrationforeveryoneinvolved.Thismightbeadrivingforcebehindthelimited
numberofcontractchangesseen.
51
PartII:PlayerValue
Predictorsofplayerperformance,unlikesalary,remainrelativelyconsistent,
thoughtheseregressionshaveweakerR‐squaredvalues.Table5,6and7bothshowthe
issueswithpredictingfuturesalary–althoughnoneoftheexplanatoryvariablesin
Table5appearinallfourregressionsitisclearthatfantasypointspergameisa
significantpredictoroffutureperformancebecausethemagnitudeisrelatively
constant.Inordertolookforstrongerpredictors,Table7isthesameanalysisasabove,
butextendedintothepasttofindbetterpredictorsandovertwoyearsinsteadofone.
Thuswecanseethatbecause𝐵!iswithina95%confidenceintervalovereachyear
testedforfantasypointspergamewecannotrejectthenullhypothesisthat𝐵!is
constantacrosstime.
Toconsidertheotherquestioninthisportionoftheanalysis,wemustcompare
𝐵! and𝐵!.Theaveragecoefficientsareshownintheequationbelow:
𝐸 (𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒(𝑡))
= [.465 ∗ 𝐹𝑎𝑛𝑡𝑎𝑠𝑦 𝑃𝑜𝑖𝑛𝑡𝑠 𝑝𝑒𝑟 𝐺𝑎𝑚𝑒(𝑡 − 1)+ .016
∗ 𝑅𝑒𝑐𝑒𝑝𝑡𝑖𝑜𝑛𝑠(𝑡 − 1)]!
16
Thisallowsustorejectthenullhypothesisthat𝐵! =𝐵! ,whichimpliesfuturesalary
growsindirectcompensationforexpectedfutureperformance,becausetheconsistent
predictorsaredifferentfromtheinconsistentpredictorsofsalary.Rejectingthenull
hypothesiscomplicatestheabilitytogenerateaconclusionregardingtheexactmotives
ofallocatingsalary,butdoeselucidatethepointthatsalarydoesnotmovewith
increasesinplayervalue.
52
Table6illustratesthedifficultyofpredictingfutureperformance.AlthoughR‐
squaredtermsappearreasonablyhighandthevariablefantasypointspergameisa
strongpredictor,theotherexplanatoryvariablesarenotsignificant.Appearinginmore
gameshasanegativecorrelationwithfutureperformance,asdoageandnumberof
gamesstarted.Itisunclearwhatexactlycausedthiseffect,butitmayhavebeenthe
resultofdecliningperformanceafteryearsofperforminginone’sprime.Thus,aging
seemstobemoresignificantasafactorinlostabilitythaningainedexperience.Thisis
aninterestingfindingthatcouldbeexploredinthefuturebyanotherstudy.
Anothermethodofmeasuringthestrengthofawidereceiverisconsideringhis
fantasypointspertarget.Ahighpointpertargetfiguremeansthatareceivermakesthe
mostofhisopportunities,whilealowpointpertargetfiguresuggestsweaker
productionwhencorrectedforopportunities.Thiswouldseemtobeastrong
explanatoryvariableforperformancebecausepresumablyaplayerwithhighmarginal
returnsperopportunityshouldseemoreopportunitiesinthefuture.Unfortunately,
usingpointspertargetasapredictivetoolislargelyineffective.InFigure9,onecansee
thatpointspertargetisn’tnearlyasusefulasaproxyforfantasypointsasnumberof
targets,whichisstronglycorrelatedbothwithcurrentproductionandfuture
production.Thisisamajordisconnectionbetweenpointspertargetanditsimpacton
performanceandonpayment.Figure10showsaverystrongpositivecorrelation
betweenpointspertargetandfutureperformance,butFigure11showsthatpointsper
targetisn’tnearlyasstronganexplanatoryvariableoffuturesalary.Thiseffectmaybe
53
confoundedbydefensesfocusingonbetterreceivers,makingtheirpointspertarget
lowerthantheirlessskilledpeers.
Anotherwaytothinkaboutpredictingperformanceisbyconsidering
performancegrowth.Whatpredictssharpincreasesinperformance?Tables8and9
showthatintheyears2007,2008and2009,changesinperformanceareverymuch
inconclusivewithlowR‐squaredvalues,despitethelargesamplesize.Thereisasample
biasinthoseregressionssinceperformancegrowthwillbeoverestimated.Playerscut
afteraseasonarenotincludedandonlyimprovingorhighlevelplayerswouldbepartof
thedataset,sotheindividualsexperiencingnegativeperformancegrowtharelesslikely
toremainintheleagueandwouldnotbeinthedataset.Surprisingly,eachstepdown
regressionreportedthatthegamesplayedvariablewassignificantwithanegative
coefficient.Thissuggeststhatthenumberofgamesplayedisimportantandnotjust
becauseitisnegativelycorrelatedwithastatisticevaluatedonapergamebasis.21That
is,playerswhoplayasurprisingamountofgamesinoneyearmaydosoasaflukeand
seetheirproductiondropbackdowntothenormasaregressiontothemean.
21Fantasypointspergamealsohaveanegativecoefficient,suggestingthatthereissomethingbeyondsimpleconfusionofexplanatoryvariables.
54
PartIII:LaggedValues
Table10includestheresultsoftwotime‐laggedregressionstopredict
performance.Eachusedthethreepreviousseasons’valuesaspredictors.Bothstep
downregressionseliminatedthemostdistantyearandcameupwithsimilarratiosof
yearsintothepasttopredictfutureperformance.Thisshowsthatpredicting
performancebasedonthepastcanuseasomewhatconsistentmodel.Table11shows
thatpredictingsalaryusinglaggedvaluesfromthepreviousthreeseasonsgenerates
similarresults,inthatthethirdseasonpastisimmediatelyremovedfromtheregression
assalarymaybepredictedusingthetwomostrecentseasonsonly.Whiletheseresults
doonlyincludethetwopreviousseasons,therelationshipinweightingthetwoprevious
seasonsisnotonlyinconsistent;itismarkedlydifferentfromtherelationshipbetween
weightingthetwopreviousseasonsseenearlier.
𝐸 𝑃𝑒𝑟𝑓𝑜𝑟𝑚𝑎𝑛𝑐𝑒
= 8.585 ∗ 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑌𝑒𝑎𝑟!𝑠 𝐹𝑎𝑛𝑡𝑎𝑠𝑦 𝑉𝑎𝑙𝑢𝑒 + 3.967
∗ 𝐹𝑎𝑛𝑡𝑎𝑠𝑦 𝑉𝑎𝑙𝑢𝑒 𝑇𝑤𝑜 𝑌𝑒𝑎𝑟𝑠 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠
17
𝐸 (𝐶𝑎𝑝 𝐻𝑖𝑡) = 281388.5 ∗ 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑌𝑒𝑎𝑟!𝑠 𝐹𝑎𝑛𝑡𝑎𝑠𝑦 𝑉𝑎𝑙𝑢𝑒 + 308856
∗ 𝐹𝑎𝑛𝑡𝑎𝑠𝑦 𝑉𝑎𝑙𝑢𝑒 𝑇𝑤𝑜 𝑌𝑒𝑎𝑟𝑠 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠)
18
𝐵!!
𝐵!!= 2.161
19
𝐵!!
𝐵!!= 0.912
20
55
ThefactthattherationoflaggedindicatorsforPerformanceisnotwithina95%
ConfidenceIntervalofthesameratioforSalaryrequireswerejectthenullhypothesis
(Tables11and12).Thisindicatesthatweightingofthepast,asdonebyNFLGeneral
ManagersandOwnersindeterminingsalaryisdifferentfromtheweightingofthepast
inpredictingperformance–ahugelyimportantconclusionbecausethismeansthat
playersaredecidedlynotbeingpaidinaccordancewithwhattheirfutureperformance
isexpectedtobe.Thesefindingsallowustorejectthenullhypothesisandembracethe
alternativehypothesisandclarifytheinferencesfromProblemII.Becauselaggedvalues
ofperformanceonsalaryandperformancedonotlineup,clearlyfuturesalaryisnot
allocatedonthebasisofexpectedfutureperformance.Thisexplainstheconclusion
earlierthatsalarygrowthdoesnotoccurinconjunctionwithperformancegrowthby
showingthatfuturesalaryisnotmeantascompensationforfutureperformance.
56
PartIV:RiskPreferencesandCuttingPlayers
TherelationshipbetweenfantasyfootballandtheNFLisaninterestingone
becausebotharedependentonessentiallythesamegroupofpeople,butfantasy
footballsituatesplayersasiftheywereallononeyearcontracts.Thissimplifiesa
player’spricetoequatewithexpectedperformance.Essentially,ifIexpectaplayerto
giveme500yardsandfourtouchdowns,I’llpayhimdirectlyinaccordancewiththat
performanceunlessIalreadyhavefourwidereceivers,inwhichcasethemarginal
benefitofaddingafifthissmallbecauseIonlyhavealimitednumberofspotsfor
playerstobeonthefield.
Estimatinginducedrisk‐aversioninfantasyfootballisafairlystraightforward
problem.Whilebetterplayersaregoingtoreceivermore“payment”thantheirworse
counterparts,therelationshipbetweenthetwogroups22isimportant.Worseplayers
arelesslikelytoplaythantheirpeersandbringverylittlemarginalbenefittotheir
ownerbecauseateamcanveryeasilylimitstartingplayerstotheirbetterplayers.
Therefore,whilestartersshouldbepaidaccordingtoperformance,andbenchplayers
shouldbepaidaccordingtoperformance,therelationshipbetweenratesofpayment
forperformancediffersbetweenthetwopoolsdependingontheutilityfunctionofthe
owner.Anownerwithahighlevelofrisk‐aversionwouldhavesimilarrelationship
betweenperformanceandpaymentinthetwopoolsofplayers.Anownerwhoisrisk
22Thetwogroupsaresplitaccordingto“targets.”Playersabovethemediannumberoftargetsare“starters”intheNFLbecauseteamshaveroughlythesamenumberofstartersandbenchplayersatthewidereceiverposition.Playersbelowthemedianare“bench”players.
57
lovingwouldhaveaveryhighslopeinanOLSregressionofperformanceonpaymentin
thestartingpoolandaverylowslopeinthesameregressioninthebenchpool.
Infantasyfootball,weseethattheslopesoftheOLSregressioninthetwopools
arealmostidentical–reiteratingthefindingofhighrisk‐aversionmentionedearlier.
Figure5andFigure6illustratethesimilaritiesofthetwoOLSregressions.Whilethis
analysismayseemunclear,viewingthedifferencebetweenbenchplayersandstarting
playersintheNFLinperformanceregressedonNFLcapvalueclarifiesthedistinction
(Figure12,Figure13,andFigure13a).23TheslopesoftheOLSregressionsofthetwo
poolsaresimilarinfantasyfootball,butaredrasticallydifferentintheNFL.24This
supportsmyearlierhypothesisthatteamsintheNFLviewplayersverydifferentlythan
dotheirfantasycounterparts,perhapsasaresultofthescarcityoftopendtalent.This
issimilartothepredictionoftheefficiencywagetheory,perhapsasaresultofadverse
selection–teamspaythebestplayersmorebecauseplayersdifferfromeachotherin
termsoftalentandtalentisthebestindicatorofperformance.
Fantasyfootballmakesuseofoneyearcontractsforplayersinexchangeforan
Englishauction.TheNFLdoesnotoperateinthesamewaybecause,althoughit’s
certainlypossible,teamssignplayerstoextendedcontractsandrarelycutprominent
players.Teamsdocutplayersalthoughthelogicwithwhichtheydosodoesnotalways
23Interestingly,thereismuchgreaterspreadintheNFLregressionsthaninthefantasyversion.ThismaybearesultofothercharacteristicsOwnersfindvaluable,likeschematicfitorpersonality.24TheparabolicregressioninFigure13andFigure13aisofparticularinterestbecauseitseemstoindicatefurtherconclusionsaboutthewayOwnerspaytheirplayers.Theplayersmakinghighamountsofmoneyinthebackuppoolareallolderplayers,asevidencedbyFigure14.Theseplayersmayhavebeengivenlucrativecontractsbeforeexperiencingadecreaseinperformancebutforsomereasonhavenotbeencut.
58
follow.Figure15detailsthefantasypointsandproductionofplayerscutin2009.For
someplayers,thereasonforcutsseemsobvious–poorproductionandveryhighsalary.
Ontheotherhand,thereareseveralplayerswhoseemtoproduceatahighlevelbut
getcutanyway.OnewouldexpectFigure15tolookverydifferent.Performanceisa
majorfactor,butoftenplayerswhoarecutarenotgivenopportunities(Figure16).
Breakingdownproductionperdollarshouldlendmorelightonthesituation,butthatis
notthecase.Playerswhoprovidealargeamountofvalueatalowcostcanstillbecut
(Figure17).Furtheranalysisseemstoindicatethattheplayersmostlikelytogetcutare
thosewhoreceivefewtargetsorconvertfewertargetsintoreceptionsthandotheir
peers.Figure18illustratesthateffectingraphicform,inwhichveryfewcutplayersare
abovetheaverage.
TheapparentconclusionfromthisinformationisthatNFLownerscouldtakea
pagefromthebooksoffantasyfootballgurusandstartcuttingplayersmore
aggressively.Therearemanyplayerswhoclearlydonothavehighcatchrates(Figure
18)butarenotcut.Therearealsoolderplayerswhoarepaidinaccordancewiththeir
statureratherthanwithperformance(Figure13a,Figure14).Cuttingmoreaggressively
wouldallowthoseplayerstobesignedagaininconcertwiththeiron‐fieldproduction.
Obviouslythereareotherfactorstoconsider–namelyinterpersonalrelationships
crucialtoteamchemistry–buttherelevanceoffantasyfootballandtheusefulnessof
single‐yearcontractscannotbedenied.
59
Limitations
Themostapparentlimitationofthisstudyisthepositionbeingstudied:wide
receivers.Becauseotherpositionshavenotbeenlookedat,itseemslikeamajor
weakness.However,theconclusionsfoundforwidereceiversshouldholdforany
position,eveniffindingstatisticalevidenceishardtodo.Thesourceofthismispricingis
notwidereceiverspecific,ratheritistheresultofadministratorsweightingthepast
differentlythanperformancetrackrecordwouldrecommend.Linemen,forexample,
aremostlikelyalsomispricedwithrespecttofutureperformance,butbecausethedata
trackedforlinemenisverylimited,sharpeningthoseconclusionsisnearlyimpossible.
Weightingofthepastwouldnotbedifferentdependingonposition,andinaposition
wherestatisticaldataisdifficulttofindpricingmaybemoreambiguous.
Additionally,thereareissueswiththepursuitofdirectpolicyrecommendations
becauseitisimpossibletofullyunderstandthereputationaleffectsofthose
recommendations.Itisquitepossible,forexample,thatateamhasconsideredthe
positionofonlyofferingshorttermcontracts,butthatsuchapositionwouldbe
untenableinthefreeagentmarketandplayerswouldneversignwithsuchateam.This
issuehurtsmyabilitytomakeastrongrecommendation.Similarly,judgingateam’srisk‐
aversionisnotparticularlyeasygiventhedifficultiesofknowingwhetherateamhas
consideredanalternativeapproachandgiventhatunderstandingthegoalsofateamis
anebuloustaskatbest.Thoseweaknessesaside,thereisthecapacitytoelucidatesome
conclusionsandseehowanOwnerunderstandingtheseconclusionsmightbeableto
affecthismanagementstyleinthefuture.
60
Conclusion
Themostimportantfindingsinthisresearcharethefollowing:NFLteamsdonot
payplayersinaccordancetofutureexpectedperformanceandtheydisplayformofrisk
preferenceswithregardtobackupplayersdistinctlydifferentfromthoseoftheir
fantasycounterparts.Insteadofpayingdirectlyforfutureperformance,theyweightthe
pastinadistinctlydifferentmannerthanwouldseemcorrectifonlypayingfor
performance,asevidencedbytheresultsinProblemsIIandIII,whenthepredictorsof
salaryandperformanceweredifferent,aswerethelaggedpredictorsofeach.Themost
reasonableinference,therefore,isthatteamsvalueaspectsotherthanfuture
performanceandarewillingtopayforthoseaspects.Anexamplewouldincludethe
capacityfor“starpower.”InPartIoftheresultssectionIdiscussedtheincreased
marginalreturnsofsalarytoanincreaseinvalue,reinforcingtheideathatteamscare
aboutthingsotherthanfutureperformanceandthatstarpowerisoneofthem,
becausemoretalentedplayersaremorerecognizedandcapableofsellingmore
merchandise.CapacityforbecomingastarisnotsomethingaffordedtoeveryNFL
playerandtheonesthatdohavesuchprecocioustalentarescarce.Teamsseize
opportunitiestogetstarsperhapsbecausestarsbringtheorganizationahugeamount
ofrevenue.
DespitetheappearancethatteamsintheNFLcaremostforwinning,thissports
league,likeallothers,isdrivenfirstandforemostbyexperiencingfinancialsuccess.
Withoutthatfinancialsuccess,theleaguewouldhavetofold.OwnersintheNFLtoday
haveawildlypopularproductthatprovidesareturnoninvestmentevenduringthe
61
worstseasons.AsaresultofthefinancialsecurityofowninganNFLteam,manyfans
believeteamsmusttrytowinregardlessoffinancialsacrifices.However,theNFL’s
treatmentofsalaryincomparisonwithexpectedperformance,asinProblemIII,
suggeststhatthereareothermotivesatplayintheselectionofplayersandsomeof
thosemotivescouldwellbefinancial.ThisrendersmyinitialassumptionthatOwners
obtainutilityonlyfromwinningandallocateplayersalaryinaccordancewithutility
function.
Asmentionedearlier,itisdifficulttojudgetheinducedriskpreferencesof
Ownersbecauseknowingtheirexactutilityfunctionisimpossible.Instead,thispaper
showsthattheutilityfunctionofOwnersisdistinctlydifferentfromtheexpectationfans
haveoftheirOwners–animportantpieceofknowledge.Moreover,ownersarenot
risk‐averseinthesamewaythatfantasyfootballownersarerisk‐averse,evidencedby
thedifferenceinslopesseeninProblemIV.Fantasyownerspaybackupplayershigher
thanexpectedvaluesincaseofinjurieswhereasNFLOwnerspaycertainbackupsvery
littleandotherbackupsquitealot.Itisimpossibletosaywhetherthischoiceof
paymentis,infact,anydifferentthantherisk‐aversioninfantasyfootball.Fantasy
footballhasthelimitingfactorofsingleseasoncontractsandNFLteamsdonothavethe
luxuryofonlyhavingtosignsingle‐yearcontracts.Therefore,Ownersmaypaycertain
backupsinaveryrisk‐aversemanner–overpayingonthepossibilityofaplayer
becomingastaroronthechancesuchaplayerwillstayonateamthroughouthis
prime.Onewaytoavoidthispossibleloweredmarginalbenefitperdollarwouldbeto
cutplayersmorefrequentlyandsignshortercontracts,asinfantasyfootball,andpay
62
playersaccordingtoimmediatefutureperformance,somethingmucheasiertopredict
thanperformanceseveralyearsintothefuture.
RoschandHodgson(2000)useamedicalperspectivetodetermineafootball
player’sphysicalqualifications.Thistypeofanalysisrequirestheabilitytoworkdirectly
withtheplayerandhaveindividualsparticipatingintests.Theoptionfordirectplayer
contactbringstomindusingsimilardatatocomparetosalariesandingame
performance.Wouldcoachesandgeneralmanagersoverestimatethevaluesof
conventionalperformancetestsinevaluatingplayersandwritingcontracts?
MarketforcesintheNFLarecomplex,particularlyintheadventofstatistical
analysisinsports.Manyteamsareawareofthevalueofusingstatisticstopredictfuture
performanceandmayhaveindividualswhouseallstatisticaltoolsavailable.Thisfact
mayindicatetherationalityofNFLteams–evenwhileavoidingsomeofthestrategies
mentionedinthispaper,teamsarewillingtoadoptdifferentpayscalesinaneffortto
generaterevenuebycapitalizingonwellknownplayers.Thispresentsautilityfunction
differentfromtheonefansexpectfromOwners–onebasedonaspectsnot
encompassedbyon‐fieldperformance.
Alternatively,iftherewasateaminterestedinwinningregardlessoffinancial
motivesorotherpersonalmotives,thereappearstobeawayforwardthroughthe
benefitoftheNFL’sallowancesregarding“cutting”ofplayers.Signingshortercontracts
wouldallowteamstobebetter,albeitwithahighershorttermcost.Payingpurelyfor
expectedfutureperformanceinsteadofthehopesthataplayerremainsonateamfora
63
longtimewouldbeanotherwayforteamstogainanon‐fieldcompetitiveadvantage.
Thereareseveralwaysthatateamcouldbecomemoretalentedthantheircompetitors,
evenwhilestayingwithinthesalarycap,thatarecurrentlybeingunderutilized.Perhaps
thereasonforthisisthatteamsdon’trecognizetheseotherstrategies,butmorelikely,
mostOwnersgetmoreutilityfromincreasedfinancialbenefitthanfromhigher
probabilityofvictoryonthefield.
64
Tables
Table1:SummaryoftheSignificant(𝑝 < 0.05)ExplanatoryVariablesofFutureSalaryOLSRegression(Author’sCalculationsUsing:USATodayNFLSalaryDatabase;ESPN;FantasyFootballToday)
Variable 2006Coeff 2007Coeff 2008Coeff 2009Coeff AverageCoefficient
Age 0.042(.009)
0.078(.019)
0.098(.019)
0.100(.023)
.080
FantasyPointsPerGame
0.109(.029)
0.174(.021)
.071
Receptions 0.021(.002)
.005
SquareRootofPoints
0.177(.024)
.044
N 117 112 122 119R‐Squared .542 .559 .607 .611
Table1a:ConfirmationofIncreasingMarginalReturnsofSkillonFutureSalary(Author’sCalculationsUsing:USATodayNFLSalaryDatabase;ESPN)
Variable 2009CoeffSquareRootofFantasyPoints
‐213545.29(197847)
FantasyPoints 44988.55***(12940)
N 117R‐Squared .479
∗∗∗ 𝑝 < 0.001
65
Table2:AllExplanatoryVariablesofFutureSalaryOLSRegression(Author’sCalculationsUsing:USATodayNFLSalaryDatabase;ESPN;FantasyFootballToday)
Variable 2006Coeff 2007Coeff 2008Coeff 2009Coeff
Age .043*(.021)
.070***(.020)
.094***(.021)
.095***(.024)
GamesPlayed ‐0.007(.035)
‐0.008(.036)
‐0.016(.049)
‐0.003(.034)
GamesStarted .062**(.021)
0.028(.018)
‐0.019(.028)
0.006(.026)
Receptions 0.013(.010)
0.014(.009)
‐0.018(.012)
‐0.013(.013)
Yards 0.0007(.001)
0.0003(.001)
0.001(.001)
0.001(.001)
Fumbles ‐0.033(.053)
0.066(.072)
0.013(.058)
‐0.071(.071)
FantasyPoints ‐0.006(.008)
‐0.002(.009)
‐.022*(.008)
‐0.002(.010)
Targets 0.012(.008)
0.006(.008)
SquareRootofPoints
‐0.127(.108)
‐0.034(.095)
0.186(.127)
‐0.029(.110)
FantasyPointsperGame
0.154(.082)
0.046(.635)
0.210(.118)
.150*(.072)
N 117 112 122 119R‐Squared .569 .574 .667 .625
∗ 𝑝 < 0.05; ∗∗ 𝑝 < 0.01; ∗∗∗ 𝑝 < 0.001
66
Table3:SummaryoftheSignificant(𝑝 < 0.05)ExplanatoryVariablesofSalaryGrowthOLSRegression(Author’sCalculationsUsing:USATodayNFLSalaryDatabase;ESPN;FantasyFootballToday)
Variable 2006Coefficient Variable 2007CoefficientAgein2005 0.061
(.027)GamesStartedin
2006‐0.043(.014)
Receptionsin2005 0.021(.008)
FantasyPointsperGamein2006
‐.248(.072)
Pointsin2005 ‐0.009(.004)
R‐squared=.137 N=92 R‐Squared=.106 N=112
Variable 2008Coefficient Variable 2009CoefficientSquareRootofFantasyPoints
2007
0.112(.042)
Agein2008 ‐0.092(.045)
GamesStartedin2007
‐0.065(.024)
Yardsin2008 0.003(.001)
GamesStartedin2008
‐0.099(.048)
R‐squared=.096 N=78 R‐squared=.172 N=86
67
Table4:AllExplanatoryVariablesofFutureSalaryGrowthOLSRegression(Author’sCalculationsUsing:USATodayNFLSalaryDatabase;ESPN;FantasyFootballToday)
Variable 2006Coeff 2007Coeff 2008Coeff 2009CoeffAge 0.052
(.028)‐0.031(.0267)
‐0.001(.025)
‐.101*(.048)
GamesPlayed ‐0.044(.042)
‐0.005(.047)
0.019(.057)
0.033(.068)
GamesStarted 0.006(.025)
‐.068**(.023)
‐0.053(.033)
‐0.086(.053)
Receptions .023*(.011)
0.023(.012)
0.003(.014)
0.002(.025)
Yards ‐0.0005(.001)
‐0.001(.001)
0.0003(.001)
0.002(.003)
Fumbles ‐0.068(.019)
0.030(.094)
0.035(.069)
‐0.129(.139)
FantasyPoints ‐0.011(.009)
0.0006(.013)
‐0.011(.009)
0.002(.020)
Targets ‐0.009(.009)
‐0.009(.017)
SquareRootofPoints
0.146(.126)
.253*(.125)
.323*(.149)
‐0.015(.017)
FantasyPointsperGame
‐0.064(..092)
‐0.227(.172)
0.003(.138)
0.060(.141)
N 92 112 78 86R‐Squared .190 .194 .168 .194
∗ 𝑝 < 0.05; ∗∗ 𝑝 < 0.01; ∗∗∗ 𝑝 < 0.001
Table5:SummaryoftheSignificant(𝑝 < 0.05)ExplanatoryVariablesofFuturePerformanceOLSRegression(Author’sCalculationsUsing:ESPN;FantasyFootballToday)
Variable 2006Coefficient
2007Coefficient
2008Coefficient
2009Coefficient
AverageCoefficient
FantasyPointsperGame
0.637(.075)
0.512(.082)
0.712(.088)
0.465
Receptions 0.066(.010)
0.016
N 117 114 125 117R‐Squared .388 .281 .336 .444
68
Table6:AllExplanatoryVariablesofFuturePerformanceOLSRegression(Author’sCalculationsUsing:ESPN;FantasyFootballToday)
Variable 2006Coeff 2007Coeff 2008Coeff 2009CoeffAge ‐0.131
(.081)‐0.080(.087)
‐0.165(.100)
‐0.117(.108)
GamesPlayed ‐0.086(.103)
‐0.143(.113)
‐0.244(.162)
0.078(.131)
GamesStarted ‐0.0002(.081)
‐0.094(.079)
0.141(.126)
‐0.021(.118)
Receptions ‐0.016(.039)
.0889*(.041)
0.076(.057)
‐0.046(.053)
Yards 0.002(.003)
‐0.001(.004)
0.004(.0005)
0.003(.004)
Fumbles 0.300(.198)
0.355(.321)
‐0.106(.277)
0.094(.289)
Targets ‐0.068(.038)
0.019(.035)
FantasyPointsperGame
0.587**(.222)
0.265(.302)
0.242(.270)
.495*(.241)
N 117 114 78 86R‐Squared .424 .325 .401 .489
∗ 𝑝 < 0.05; ∗∗ 𝑝 < 0.01; ∗∗∗ 𝑝 < 0.001
Table7:SummaryoftheSignificant(𝑝 < 0.05)ExplanatoryVariablesofFuturePerformanceoverTwoSeasonsOLSRegression(Author’sCalculationsUsing:ESPN;FantasyFootballToday)
Variable 2007Coefficient
2008Coefficient
2009Coefficient
AverageCoefficient
Yards(t‐1) 0.004(.001)
0.005(.001)
0.003
Yards(t‐2) 0.003(.001)
0.001
Receptions(t‐1) 0.069(.018)
0.023
Receptions(t‐2) 0.036(.011)
0.012
GamesStarted(t‐1)
‐0.209(.082)
‐0.069
N 93 94 90R‐Squared .319 .465 .554
NB:“(t‐1)”referstothepreviousseason,while“(t‐2)”referstotwoseasonsprevious
69
Table8:SummaryoftheSignificant(𝑝 < 0.05)ExplanatoryVariablesofPerformanceGrowthOLSRegression(Author’sCalculationsUsing:ESPN;FantasyFootballToday)
Variable 2007Coefficient
2008Coefficient
2009Coefficient
AverageCoefficient
Games ‐0.153(.033)
‐0.145(.045)
‐0.075(.035)
‐0.121
FantasyPointspergame
‐0.134(.031)
‐0.045
N 114 79 84R‐Squared .333 .119 .054
Table9:AllExplanatoryVariablesofFuturePerformanceGrowthOLSRegression(Author’sCalculationsUsing:ESPN;FantasyFootballToday)
Variable 2007Coeff 2008Coeff 2009CoeffAge ‐0.025
(.033)‐0.030(.037)
‐0.041(.043)
GamesPlayed ‐.1479***(.039)
‐.119*(.051)
‐0.071(.042)
GamesStarted ‐0.050(.030)
0.002(.046)
‐0.004(.048)
Receptions 0.023(.015)
0.023(.021)
‐0.004(.022)
Yards ‐0.02(.001)
0.0003(.001)
0.001(.001)
Fumbles 0.0800(.117)
‐0.037(.099)
0.067(.117)
Targets ‐0.019(.013)
‐0.002(.014)
N 114 78 86R‐Squared .362 .168 .108
∗ 𝑝 < 0.05; ∗∗ 𝑝 < 0.01; ∗∗∗ 𝑝 < 0.001
70
Table10:LaggedPerformanceonFuturePerformanceOLSRegression(Author’sCalculationsUsing:ESPN;FantasyFootballToday)
Variable 2008Coefficient 2009Coefficient AverageCoefficient
SquarerootofPoints(t‐1)
8.373***(1.482)
8.796***(1.568)
8.585
SquarerootofPoints(t‐2)
3.817**(1.289)
4.116**(1.493)
3.967
RatioofCoefficients
2.194 2.137
N 94 90R‐Squared .462 .494
∗ 𝑝 < 0.05; ∗∗ 𝑝 < 0.01; ∗∗∗ 𝑝 < 0.001
Table11:LaggedPerformanceonFutureSalaryOLSRegression(Author’sCalculationsUsing:USATodayNFLSalaryDatabase;ESPN;FantasyFootballToday)
Variable 2008Coefficient 2009Coefficient AverageCoefficient
SquarerootofPoints(t‐1)
293794***(73174)
268983***(67610)
281388.5
SquarerootofPoints(t‐2)
289550***(63667)
328162***(64346)
308856
RatioofCoefficients
1.0147 .8197
N 94 90R‐Squared .4517 .528
∗ 𝑝 < 0.05; ∗∗ 𝑝 < 0.01; ∗∗∗ 𝑝 < 0.001
Table12:LaggedPerformanceonFutureFantasyPriceOLSRegression(Author’sCalculationsUsing:ESPN;FantasyFootballToday)ExtensionfromChakravarthy(2010)
Variable 2009CoefficientSquarerootofPoints(t‐1)
0.068(.019)
SquarerootofPoints(t‐2)
0.045(.014)
RatioofCoefficients
1.51
N 40R‐Squared .530
71
Figures
Figure1:FantasyPercentStartedin2011vs.AverageFantasyPointspergamein2011(Source:ESPN)
Figure2:FantasyRankin2011vs.FantasyPercentStartedin2011(Source:ESPN)
020
4060
8010
0
Per
cent
Sta
rted
0 5 10 15Average Points Per Game
020
4060
8010
0R
ank
0 20 40 60 80 100Percent Started
72
Figure3:FantasyPercentStartedin2010vs.TotalFantasyPointsScoredin2010(Source:ESPN)
Figure4:EffectiveFantasyPointsin2009vs.FantasyPointsin2009(Author’sCalculationsUsing:ESPN),ExtensionfromChakravarthy(2010)
• TheredlineistheOLSregressionforbenchplayers.• ThegreenlineistheOLSregressionforstartingplayers.𝑝 < 0.001• Slopesofredandgreenlinearesignificantlydifferent.
020
4060
80
Perc
ent S
tarte
d
50 100 150 200Fantasy Points Scored
050
0010
000
1500
020
000
2500
0
50 100 150 200 250Points
Effective Points Fitted valuesFitted values
73
Figure5:FantasyPricein2009vs.FantasyPointsin2009(Author’sCalculationsUsing:ESPN),25ExtensionfromChakravarthy(2010)
• TheredlineistheOLSregressionforbenchplayers.𝑝 < 0.001• ThegreenlineistheOLSregressionforstartingplayers.𝑝 < 0.001• Slopesofredandgreenlinearenotsignificantlydifferent.
25ThereasonFigure5andFigure6arelimitedtoN=60isthelackoffantasypricingdatafurtherthanthatpoint.
1015
2025
30
50 100 150 200Fantasy Points in 2009
Fantasy Price 2009 Fitted valuesFitted values
74
Figure6:FantasyPricein2008vs.FantasyPointsin2008(Author’sCalculationsUsing:ESPN),ExtensionfromChakravarthy(2010)
• TheredlineistheOLSregressionforbenchplayers.𝑝 < 0.001• ThegreenlineistheOLSregressionforstartingplayers.𝑝 < 0.001• Slopesofredandgreenlinearenotsignificantlydifferent.
Figure7:FantasyPointsin2009vs.Targetsin2009,𝑝 < 0.001(Author’sCalculationsUsing:ESPN;FantasyFootballToday)
1015
2025
30
50 100 150 200 250Fantasy Points 2008
Fantasy Price in 2008 Fitted valuesFitted values
050
100
150
200
0 50 100 150 200Targets in 2009
Fantasy Points 2009 Fitted values
75
Figure8:FantasyPointsin2009vs.Targetsin2008,𝑝 < 0.01(Author’sCalculationsUsing:ESPN;FantasyFootballToday)
Figure9:FantasyPointsperTargetin2009vs.FantasyPointsin2009(Author’sCalculationsUsing:ESPN;FantasyFootballToday)
050
100
150
200
0 50 100 150 200Targets in 2008
Fantasy Points 2009 Fitted values
-10
12
3
Fant
asy
Poi
nts
per T
arge
t 200
9
0 50 100 150 200Fantasy Points 2009
76
Figure10:FantasyPointsin2009vs.FantasyPointsperTargetin2008,𝑝 < 0.001(Author’sCalculationsUsing:ESPN;FantasyFootballToday)
Figure11:CapHitin2009vs.FantasyPointspertargetin2008,𝑝 < 0.05(Author’sCalculationsUsing:ESPN;FantasyFootballToday;USATodayNFLSalaryDatabase)
050
100
150
200
0 .5 1 1.5 2 2.5Fantasy Points per Target in 2008
Fantasy Points 2009 Fitted values
020
0000
0400
0000
6000
0008
0000
00100
0000
0
0 .5 1 1.5 2 2.5Fantasy Points per Target in 2008
Cap Value 2009 Fitted values
77
Figure12:CapHitin2009vs.FantasyPointsin2009(Author’sCalculationsUsing:ESPN;FantasyFootballToday;USATodayNFLSalaryDatabase)
• TheredlineistheOLSregressionforbenchplayers.𝑝 < 0.001• ThegreenlineistheOLSregressionforstartingplayers.𝑝 < 0.001• Slopesofredandgreenlinearesignificantlydifferent.
020
0000
04000
00060
0000
08000
00010
0000
00
0 50 100 150 200Fantasy Points 2009
Cap Value 2009 Fitted valuesFitted values
78
Figure13:CapHitin2008vs.FantasyPointsin2008(Author’sCalculationsUsing:ESPN;FantasyFootballToday;USATodayNFLSalaryDatabase)
• TheredlineisthequadraticregressionforbenchplayersofCapHitin2008vs.FantasyPointsin2008.𝑝 < 0.001
• ThegreenlineistheOLSregressionforstartingplayers.𝑝 < 0.001• Slopesofredandgreenlinearesignificantlydifferent.
Figure13a:Insetofbenchplayersfromchartabove, 𝑝 < 0.001
050
0000
010
0000
0015
0000
00
0 50 100 150 200Fantasy Points 2008
Cap Value 2008 Fitted valuesFitted values
010
0000
020
0000
030
0000
040
0000
0
0 20 40 60 80Fantasy Points 2008
Cap Value 2008 Fitted values
79
Figure14:CapValuein2008vs.Agein2008amongBenchPlayers, 𝑝 < 0.001(Author’sCalculationsUsing:ESPN;FantasyFootballToday;USATodayNFLSalaryDatabase)26
Figure15:CapHitin2008vs.FantasyPointsin2008amongPlayersCutin2009(Author’sCalculationsUsing:ESPN;USATodayNFLSalaryDatabase)
26N=64,despiteappearancesitmaybesmaller.
010
0000
0200
0000
3000
0004
0000
0050
0000
0
20 25 30 35 40Age in 2008
Cap Value 2008 Fitted values
010
0000
020
0000
030
0000
040
0000
050
0000
0
Cap
Val
ue 2
008
0 20 40 60Fantasy Points 2008
80
Figure16:Targetsin2008amongPlayersCutin2009(Source:ESPN;FantasyFootballToday;USATodayNFLSalaryDatabase)
Figure17:FantasyPointsperDollarin2008amongPlayersCutin2009(Author’sCalculationsUsing:ESPN;USATodayNFLSalaryDatabase)
0.0
05.0
1.0
15.0
2.0
25D
ensi
ty
0 20 40 60 80Targets in 2008
050
001.
0e+0
41.
5e+0
42.
0e+0
4D
ensi
ty
0 .0001 .0002 .0003Fantasy Points per Dollar 2008
81
Figure18:Receptionsin2008vs.Targetsin2008(Source:ESPN;FantasyFootballToday;USATodayNFLSalaryDatabase)
• Redpointsdenoteplayerswhowerecut.• Bluepointsdenoteplayerswhowerenotcut.
050
100
150
Rec
eptio
ns in
200
8
0 50 100 150 200Targets in 2008
Receptions in 2008 Receptions in 2008
82
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