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

References

Armstrong,J.2011."2011DriveStats,"J.Armstron,DriveStats.FootballOutsiders,NFL

statisticsonaperdrivebasis.

Backman,S.E.2002."NflPlayersFightforTheirFreedom:TheHistoryofFreeAgencyin

theNfl."SportsLaw.J.,9,1.

Chakravarthy,P.2010."OptimizingDraftStrategiesinFantasyFootball."

Enterprises,NFL.2010."Year‐by‐YearSalaryCap,"Staff,NFLCommunications.New

York:NFL,Yearlylistingofmaximumteamsalary.

Garvey,E.1989."Forewordto"theScopeoftheLaborExemptioninProfessional

Sports":APerspectiveonCollectiveBargainingintheNfl."DukeLawJournal,1989(2),

328‐38.

Goodell,R.2011."OfficialPlayingRulesandCasebookoftheNationalFootballLeague,"

N.F.League,NewYork:NationalFootballLeague,113.

Heller,A.W.2000."CreatingaWin‐WinSituationthroughCollectiveBargaining:TheNfl

SalaryCap."SportsLaw.J.,7,375.

Kahn,L.M.2000."TheSportsBusinessasaLaborMarketLaboratory."TheJournalof

EconomicPerspectives,14(3),75‐94.

Larsen,A.;A.J.FennandE.L.Spenner.2006."TheImpactofFreeAgencyandtheSalary

CaponCompetitiveBalanceintheNationalFootballLeague."JournalofSports

Economics,7(4),374.

Leeds,M.A.andS.Kowalewski.2001."WinnerTakeAllintheNfl."JournalofSports

Economics,2(3),244‐56.

83

Massey,CadeandRichardThaler.2005."OverconfidenceVs.MarketEfficiencyinthe

NationalFootballLeague."NationalBureauofEconomicResearchWorking,No.11270.

Nissim,A.2004."TradingGame:NflFreeAgency,theSalaryCap,andaProposalfor

GreaterTradingFlexibility,The."SportsLaw.J.,11,257.

Redding,M.J.andD.R.Peterson.2009."ThirdandLong:TheIssuesFacingtheNfl

CollectiveBargainingAgreementNegotiationsandtheEffectsofanUncappedYear."

Marq.SportsL.Rev.,20,95,102.

Richard,B.2008."AllocationofScarceResources:InsightfromtheNflSalaryCap."

JournalofEconomicsandBusiness,60(6),536‐50.

Rösch,D.;R.Hodgson;L.Peterson;T.Graf‐Baumann;A.Junge;J.ChomiakandJ.

Dvorak.2000."AssessmentandEvaluationofFootballPerformance."TheAmerican

JournalofSportsMedicine,28(suppl5),S‐29.

Rosen,S.1981."TheEconomicsofSuperstars."TheAmericanEconomicReview,71(5),

845‐58.

Scully,G.W.2004."PlayerSalaryShareandtheDistributionofPlayerEarnings."

ManagerialandDecisionEconomics,25(2),77‐86.

Truelock,M.1993."FreeAgencyintheNfl:EvolutionorRevolution."SMULRev.,47,

1917.

Walder,S.2011."Evaluatingfantasyfootballadvancedstatistics."NYDailyNews

FantasyHuddle,September29,2011.

Zimbalist,A.2010."ReflectionsonSalarySharesandSalaryCaps."JournalofSports

Economics,11(1),17.