DeterminantsofNFLSpreadPricing:

IncorporationofGoogleSearchDataOvertheCourseoftheGamblingWeek

ShivS.GidumalandRolandD.Muench

Underthesupervisionof

Dr.EmmaB.Rasiel

Dr.MichelleP.Connolly

DepartmentofEconomics,DukeUniversity

Durham,NorthCarolina

2017

Shiv graduated with High Distinction in Economics and a minor in History in May 2017. Following graduation, he will be working in New York as an Associate Consultant at Bain & Company, a management-consulting group. He can be contacted at shiv.gidumal@gmail.com. Roland graduated with High Distinction in Economics and a minor in Mathematics in May 2017. Following graduation, he will be working in New York as an Analyst at Jefferies, an investment bank. He can be contacted at roland.d.muench@gmail.com.

2

TableofContents

Acknowledgements........................................................................................................................3

Abstract..........................................................................................................................................4

1.Introduction................................................................................................................................5

2.NFLWageringMarketStructure.................................................................................................7

3.LiteratureReview.....................................................................................................................13

4.TheoreticalFramework............................................................................................................16

4.1.OpeningSpreadDeterminants..........................................................................................17

4.2.IncorporationofNewInformationintoSpreadPrices......................................................18

4.3.DeterminantsofRealizedOutcomes................................................................................19

5.Data..........................................................................................................................................21

5.1.DependentVariables.........................................................................................................21

5.2.GoogleSearchLevelConstruction....................................................................................22

5.3.IndependentVariables......................................................................................................26

6.Results......................................................................................................................................31

6.1.Regression1:OpeningSpreadDeterminants...................................................................32

6.2.Regressions2and3:ClosingSpreadDeterminantsandOpeningSpreadEfficiency........33

6.3.Regressions4and5:TestingFactorsGamblersConsideronRealizedOutcomes............35

7.SummaryofResults..................................................................................................................37

8.SuggestionsforFurtherExploration.........................................................................................37

References....................................................................................................................................39

A.Appendix..................................................................................................................................41

A.1.Cross-CorrelationMatrix..................................................................................................41

A.2.TableofIndependentVariableDefinitions.......................................................................42

3

Acknowledgements

Wewouldliketothankourthesisadvisors,Dr.EmmaRasielandDr.MichelleConnolly,whohaveguidedusfromthebeginning.Wecouldnothavecompletedthisworkwithouttheiradvice,encouragement,andvaluablecriticismonearlierworks.Wealsowanttoexpressourutmostgratitudetoourpeersfromthethesisworkshop,whoengagedwithourideasevenwhentheymayhaveappearedconvolutedandcrazy.Withoutouradvisorsandpeersintheseminar,wewouldnothavebeenabletoshapeourideas.

4

Abstract

WeinvestigatethefactorsincorporatedbyLasVegasinsettingopeningspreadsforNFLmatchups.WeincludeanovelproxymeasureforgamblersentimentconstructedwithGooglesearchdata.WetheninvestigatewhetherchangesinthisproxyarereflectedintheclosingspreadsforNFLmatchupsandfindthattheyare.Wealsorevealbettors’preferencesforhighlyvisibleteamsandteamsperformingwellasoflate.Weshowthatthefactorsthatmatterintheactualoutcomeofagamearehomefieldadvantage,averagepointsscoredforandagainst,and,mostinterestingly,ourproxymeasureforgamblersentiment.

JELCodes:G14,G17

Keywords:marketefficiency,NFLPointspreadwagers,GoogleTrends,LasVegas

5

“Writing’slikegambling.Unpredictableandsporadicsuccessesmakeyoumoreaddicted,notless.”

-M.JohnHarrison,20121.Introduction

LasVegas’sportsbettingmarketconsistsofcasinosthateachofferamenuofdifferent

wagersforbettorstoplaceonoutcomesofNationalFootballLeague(NFL)games.Through

thesewagers,LasVegas’sportsbettingmarketalsopresentsaconvenientvenuetotestthe

EfficientMarketHypothesis.1Todate,manyarticleshavetestedwhetherstrategiesexistto

generatereproducibleprofitswithinvarioussportsbettingmarkets(Zuberetal.,1985;Thaler

andZiemba,1988;Saueretal.,1988;Camerer,1989;WoodlandandWoodland,1994;Grayand

Gray,1997;Gandaretal.,1988;Sinhaetal.,2013;Fodoretal.,2013).However,thefindings

havebeenmixedacrossdifferentsportsgamblingmarkets,withsomeresearchersidentifying

repeatable,profitablestrategies(Zuberetal.,1985;ThalerandZiemba,1988;Camerer,1989;

WoodlandandWoodland,1994;Gandaretal.,1988;Sinhaetal.,2013;Fodoretal.,2013)and

othersfailingtofindany(Saueretal.,1988;GrayandGray,1997).Furthermore,some

strategiesarefoundtobeprofitablewhenappliedinacertainsport’sgamblingmarket,yet

unprofitablewhenappliedinanother(ThalerandZiemba,1988;WoodlandandWoodland,

1994).Regardlessoftheirpositionontheefficiencyofthesportsgamblingmarket,thevast

majorityofthesestudiesexamineif,atadiscretemoment,themarketincorporatesall

availableinformationintobettingprices,thuseliminatingtheopportunitytoconsistently

generateabove-average,risk-adjustedreturns.

ThispaperfirstaimstoinvestigateexactlywhatinformationLasVegasincorporatesinto

theinitial,oropening,pricesitoffersonNFLwagers.LasVegasmustattempttodeterminethe

factorsthatbettorsconsiderwhenplacingwagersinordertoconstructpricesthatwillattract

relativelyequalbettingfromgamblersonbothsidesofawager.Therefore,thefactorswe

investigateareonesthatwebelievebettorsconsiderintheirchoicesofteamsandmatchupsto

wageron.Thesefactorsincludemeasurementsofteams’relativehistoricalandrecent

performance,homefieldadvantage,nationalvisibility,andpreparationtime.Lastly,we

1WeuseadefinitionforEfficientMarketHypothesistakenfromFama(1970)thata“marketinwhichsecuritypricesalways‘fullyreflect’allavailableinformationiscalled‘efficient.’”Animplicationofanefficientmarketisthatitisimpossibletodevelopastrategytoconsistentlybeatthatmarketandachieveabove-averagereturns.

6

attempttoincorporatethecurrentgamblersentimentoneachteam.Tocapturethecurrent

sentimentofthegamblingpublic,weuseGooglesearchfrequencydataleadinguptoLas

Vegas’releaseofopeningprices.

Wethenexpandonpastresearch,whichhaslookedatgamblingpricesonlyatdiscrete

pointsintime,byexaminingthemovementofpricesfromtheopeningprice,offeredatthe

beginningofthegamblingweek,totheclosingprice,offeredjustbeforethestartofamatchup.

Weaddameasurementofnewlyrevealedgamblingsentimenttothefactorsthatdetermine

openingpriceandtestifthischangeingamblersentimentispricedintotheclosingprice.We

againmeasuregamblersentimentthroughGooglesearchfrequencydata,inthiscasecaptured

fromthetimeperiodbetweentheopeningandclosingprices.Inthisway,weevaluatethe

EfficientMarketHypothesis’applicabilitytotheNFLwageringmarket;weverifywhether

publiclyavailableGooglesearchdataisincorporatedintoclosingprices.Further,weinvestigate

ifthefactorsusedbyLasVegastosettheopeningpriceareappropriatelypricedinatthe

beginningoftheweekoriftheymateriallyaffectthemovementofpricesoverthecourseofthe

week.TheEfficientMarketHypothesisstatesthatanyinformationavailableatthetimeopening

pricesarereleasedshouldnotaffectfuturepricemovements.

Next,wetestifthefactorsthatdeterminetheclosingpricesforwagerssignificantly

predicttherealizedoutcomesofNFLmatchups(andthustheoutcomesofwagersplaced).This

testallowsustodeterminethepredictiveefficacyoffactorsconsideredbygamblerswhenthey

placebets.Finally,usingourfindings,weattempttoconstructaprofitablebettingstrategyin

outofsampledata.Shouldastrategyexist,itwouldprovideevidencecontradictorytothe

EfficientMarketHypothesis,whichdoesnotallowforreproducible,profitablestrategies.

7

2.NFLWageringMarketStructure

WebeginwithadiscussionoftheNFLwageringmarketanditssimilaritiestoother

financialmarkets.TheAmericanNFLgamblingmarketexistslegallyonlywithinthestateof

Nevada.Forthisreason,itisreferredtoas“LasVegas”forthedurationofthispaper.

OneofthemostprominentsportswagersofferedbyLasVegasforNFLwageringisthe

“Pointspread.”InaPointspreadwager,oneoftheteamsinagameisassignedanumber,

namedthe“spread,”whichcanbepositiveornegative.Attheendofthegame,thisnumber

willbeaddedtothatteam’sscore.Bettorswageronwhichteamwillhavethehigherscore

afterthespreadistakenintoaccount.Ateamlistedwithanegativespreadisthefavorite,while

apositivespreaddenotestheunderdog.Thespreadcanbedefinedrelativetoeitherteam,and

theterm“teamofrecord”isusedtoidentifywhichteam’sspreadisbeingpresented(Grayand

Gray,1997).

Forexample,supposethereisanupcominggamebetweenArizonaandNewEngland,

andArizonaistheteamofrecordwitha-9pointspread.IfArizonawinsbymorethan9points,

theyaresaidtohavewon“relativetothespread”(RTS),whileanArizonawinbyfewerthan9

pointsoraNewEnglandvictorymeansthatNewEnglandwonRTS.IfArizonawinsbyexactly9

points,thegameiscalleda“push,”andallmoneyisreturnedtobettorsatnocosttothem.This

scenariocanequivalentlybewrittenwithNewEnglandastheteamofrecordwitha+9point

spread.TheseoutcomesrelativetothespreadareshowngraphicallyinFigure1.

Figure1.OutcomesRelativetotheSpreadofHypotheticalMatchup

BetweenNewEnglandandArizonaWhereArizonaHasaSpreadof-9

"NewEnglandWinsRTS" "Push" "ArizonaWinsRTS"

← -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 →

(Arizona'sPointTotal-NewEngland'sPointTotal)

ThePointspreadbetisan“even-oddsbet”,whereeachteamis,asassessedbythe

casinosthatcompriseLasVegas,expectedtowin50%ofthetimeafteradjustingforthe

spread.LasVegasachievesaprofitbyincorporatingafeethatforcesgamblerstowagerslightly

8

morethantheystandtowin.Theliteraturereferstothisamountbyseveralnames,suchas

“vigorish,”“vig,”“juice,”or“cut,”butwillbereferredtohenceforthas“vigorish.”LasVegas

quotesthevigorishalongsidethespread.Themostcommonvigorishis10%and,insuchcase,

gamblersmustwager10%morethanwhattheywouldstandtowin(i.e.$1.10forevery$1.00

theywouldwin).LasVegascansetthevigorishhigherorlowertoenticebettingoneitherside

ofthebet.Forinstance,ifitwereloweredto5%agamblerwouldonlyhavetorisk$1.05towin

$1.00,amoreattractiveoptionthanwagering$1.10.AgeneralizedPointspreadbetwillbe

denotedashavingaspreadof𝛼andavigorishof𝛽,where 𝛼isanintegeroraninteger+ !!and

𝛽isapercentagewith0 ≤ 𝛽 ≤ 1.2Agamblermustwager$(1+ 𝛽)towin$1.Thiscan

equivalentlybestatedintermsofa$1wagerwhereagamblerwins$ !!!!

foreachdollarbet.

Foragamblerwhowagers𝑛!dollarsonthefavorite,his/hercashflowsareshowninTable1.

Table1.CashFlowsforWagerof𝒏𝒇onFavorite

GameOutcomeCashFlowatTime

ofBet

CashFlowafter

OutcomeofGameNetCashFlow

Favoritewinsby

amountgreater

than𝛼

i.e.Favoritewins

relativetothe

spread(RTS)

−𝑛! 𝑛! + 𝑛!1

1+ 𝛽 𝑛!1

1+ 𝛽

Favoritewinsby𝛼

i.e.Push−𝑛! 𝑛! 0

Favoritelosesor

winsbyamountless

than𝛼

−𝑛! 0 −𝑛!

2Usingan𝛼thatisaninteger+ !

!allowsLasVegasto,ifitwishes,finetunethespreadtobebetweentwo

consecutiveintegers.Inthiscasethereisnopossibilityfora“push”tooccur,sincethedifferencebetweenthetwoteams’pointtotalswillalwaysbeaninteger.

9

i.e.Favoriteloses

RTS

Foragamblerwhowagers𝑛!dollarsontheunderdog,his/hercashflowsareshowninTable2.

Table2.CashFlowsforWager𝒏𝒖onUnderdog

GameOutcomeCashFlowatTime

ofBet

CashFlowafter

OutcomeofGameNetCashFlow

FavoritewinsRTS −𝑛! 0 −𝑛!

Push −𝑛! 𝑛! 0

FavoritelosesRTS −𝑛! 𝑛! + 𝑛!1

1+ 𝛽 𝑛!1

1+ 𝛽

The“houseadvantage”istheexpectedprofitforthecasinoasapercentageofthetotal

amountbet,i.e.theexpectedrateofreturntothecasinofromwagers.First,consideracasino’s

profitfunctionforagivenPointspreadbet

𝜋 =

𝑁! + 𝑁! − 𝑁! + 𝑁!!

!!! = −𝑁!

!!!!

+ 𝑁! 𝑤ℎ𝑒𝑛 𝐹𝑎𝑣𝑜𝑟𝑖𝑡𝑒 𝑤𝑖𝑛𝑠 𝑅𝑇𝑆

𝑁! + 𝑁! − 𝑁! + 𝑁! = 0 𝑤ℎ𝑒𝑛 𝑡ℎ𝑒 𝑟𝑒𝑠𝑢𝑙𝑡 𝑖𝑠 𝑎 𝑝𝑢𝑠ℎ𝑁! + 𝑁! − 𝑁! + 𝑁!

!!!!

= −𝑁!!

!!!+ 𝑁! 𝑤ℎ𝑒𝑛 𝑈𝑛𝑑𝑒𝑟𝑑𝑜𝑔 𝑤𝑖𝑛𝑠 𝑅𝑇𝑆

(1)

where𝑁! isthetotalamountwageredonthefavoriteand𝑁!isthetotalamountwageredon

theunderdog.𝑁! and𝑁!aredeterminedbythemarket’sresponsetothespreadofferedby

LasVegas.Thus,𝑁! and𝑁!arefunctionsof𝛼and𝛽,aswellasgamblersentiment,whichin

turndependsoninformationavailabletogamblers.Theexpectedvalueofthecasino’sprofit

functionis

𝔼 𝜋 =

−𝑁!!

!!!+ 𝑁! 𝑃 𝐹𝑎𝑣𝑜𝑟𝑖𝑡𝑒 𝑤𝑖𝑛𝑠 𝑅𝑇𝑆 +

−𝑁!!

!!!+ 𝑁! 𝑃 𝑈𝑛𝑑𝑒𝑟𝑑𝑜𝑔 𝑤𝑖𝑛𝑠 𝑅𝑇𝑆

(2)

10

Forillustration,supposethatLasVegascanperfectlysetthelinetoattractequalwageringon

bothsidesandgiveeachteama50%chanceofwinningRTS.Thiswouldresultin𝑁! = 𝑁!and

𝑃 𝐹𝑎𝑣𝑜𝑟𝑖𝑡𝑒 𝑤𝑖𝑛𝑠 𝑅𝑇𝑆 = 𝑃 𝑈𝑛𝑑𝑒𝑟𝑑𝑜𝑔 𝑤𝑖𝑛𝑠 𝑅𝑇𝑆 = !!.Expectedcasinoprofitbecomes

𝔼 𝜋 = −𝑁!1

1+ 𝛽 + 𝑁!12+ −𝑁!

11+ 𝛽 + 𝑁!

12 = 𝑁! 1−

11+ 𝛽 =

12𝑁

𝛽1+ 𝛽

where𝑁 = 𝑁! + 𝑁!,thetotalamountbet.Theexpectedhouseadvantageisthen

𝔼𝜋𝑁 =

𝔼 𝜋𝑁 =

𝛽2(1+ 𝛽)

Assumingthemostcommonvigorishof𝛽 = 10%,wegettoahouseadvantage

of !!!or4.55%.Therefore,ifacasinocan(andchoosesto)setthespreadsothatbothteams

havea50%chanceofwinningRTSandsothatequalwageringisplacedoneitherside,itwill

earn4.55centsforeachdollarwagered.Thisisessentiallythecasino’scommission,whichis

similartothecommissionearnedbybrokersinthefinancialworld.

Undertheabovetwoassumptions,itcanbeshownthat𝑉𝑎𝑟 !!

= 0,as

𝔼𝜋𝑁

!

=𝛽!

4(1+ 𝛽)! = 𝔼𝜋𝑁

!

Sincethevarianceofthereturnsiszero,thecasinowouldmakerisklessprofitifthese

twoassumptionshold.

Inreality,itisimpossibleforacasinotoperfectlysetthespreadinthismanner.First,it

cannotpredicttheprobabilitiesoftheoutcomesofthegamewithperfectaccuracyandthus

doesnotknowwhichspreadwillresultina50%chanceofeitherteamwinningRTS.Second,it

cannotperfectlyforecastthepreferencesofthewageringmarket,𝑁! and𝑁!,andthuscannot

guaranteethattherewillbeequalbettingonbothsidesofthespreadset.Further,evenifthe

casinowereabletodobothperfectly,itispossiblethatthespreadthatresultsina50%chance

ofwinningdiffersfromthespreadthatwouldattractequalbettingonbothsides.Oncethese

assumptionsarerelaxed,wenolongerknowforcertainwhat𝔼 !!

equalsand𝑉𝑎𝑟 !!

becomesgreaterthanzero.Inpractice,skilledprofessionalswithextensiveknowledgeofthe

industrysetopeningspreadsandthenactivelymanagethemoverthecourseoftheweek

leadinguptothegamewiththegoalofachievingthehighest𝔼 !!

andthelowest 𝑉𝑎𝑟 !!

.

(5)

(3)

(4)

11

DuetotheblackboxnatureofLasVegasitisimpossibletoknowwhethercasinostake

activepositionsintheoutcomesofgames.3Researchtodatehasfoundcontradictoryevidence,

withAveryandChevalier(1999)andPaulandWeinbach(2005)pointingtowardsactive

positionsandHumphreysetal.(2013)findingevidenceofneutralpositions.Regardlessof

whetheranactivepositionistakenbyacasino,spreadswillalwaysbeadjustedasgambler

sentiment,asrevealedthroughnewlyplacedwagers,shifts(Kreiger,2015).Ifahigherthan

anticipatedproportionisbetonthefavorite,LasVegaswillincreasethespread’smagnitudeto

provideanincentivetobetontheunderdog.Conversely,ifalowerthananticipatedproportion

isbetonthefavorite,bookmakerswilldecreasethespread’smagnitudetoprovideanincentive

tobetonthefavorite.

ThispapertakesadvantageofthefactthatLasVegasadjustsspreadsoverthecourseof

theweekasnewinformationisrevealedbythebettingpatternsofgamblers.When

determiningopeningspread,LasVegascanonlyuseinformationavailableatthatpointintime

alongwithitsbestestimateofgamblers’sentimentabouteachteam.Astheweekprogresses,

gamblersrevealtheirpreferencesforamatchup’stwoteamsthroughtheplacementofbets.If

LasVegas’estimateofgamblers’sentimentturnsouttobeinaccurate,LasVegasadjuststhe

spreadofferedaccordingly.UsingGooglesearchfrequencydataasaproxyforsentiment,we

testwhetherLasVegaspricesinthisgamblersentiment.WeexamineifGooglesearch

frequencydatatakenfromthedaybeforethereleaseoftheopeningspreadisincorporated

intothatspread.WethenseeifGooglesearchdatatakenoverthetimeperiodfromopening

spreadtoclosingspreadispricedintotheclosingspreadastheEfficientMarketHypothesis

wouldpredict.

Further,ifLasVegas’initialforecastofgamblersentimentisincorrect,abettorwhocan

betterpredictthatsentimentcouldforecastwhichdirectionthespreadwillmoveasLasVegas

adjusts.Becauseaplacedbetislockedinandsubsequentmovementsinthespreaddonot

3Anactivepositionisdefinedincomparisontoaneutralposition.Inaneutralposition,acasinowouldstandtomakethesameprofitregardlessofwhichteamwinsRTS.Thecasino’sreturnwouldhavenovarianceandwouldthusberisk-free.Incontrast,acasinowithanactivepositionwouldstandtomakemoreprofitifoneteamwinsRTSandlessprofit(orpotentiallyaloss)iftheotherteamwinsRTS.Althoughmaintaininganactivepositionexposesacasinotorisk,acasinocouldchoosetotakeanactivepositionifitbelievesitcanpredicttheeventualoutcomeofamatchupbetterthanthegamblingpublic.

12

affectitsstanding,thisabilitytopredictspreadmovementwouldallowthesavvybettorto

wageronagiventeamatthetimewhentheofferedspreadismostattractiveand,therefore,

winahigherpercentageofbets.Forbettorstoovercomethehouseadvantage,theymustbe

correctgreaterthan52.38%ofthetimetogenerateaprofitwhen𝛽 = 10%.4Thus,fora

Pointspreadstrategytobeeconomicallysignificantitmustsucceedmorethan52.38%ofthe

time.

4Whenabettorbets$1.10towin$1.00theymustbecorrecteleventimesforeverytentimestheyarewrongtobreakeven. 11 𝑤𝑖𝑛𝑠 $"##

!"#− 10 𝑙𝑜𝑠𝑠𝑒𝑠 $""#

!"##= 0.!!

!"= 52.38%i.e.theymustbecorrect52.38%ofthe

time.

13

3.LiteratureReview

Sportsbettinghasgainedacademicinterestinrecentdecades.Justasacademicshave

longsoughtreproduciblestrategiestogenerateprofitsinsecuritiesmarkets,sohavethey

searchedforexploitablepatternswithinsportswageringmarkets.ThalerandZiemba(1988)

findthatanaïvestrategyofwageringonfavoritesinracetrackbettinggeneratesprofitsinthe

longterm.Conversely,WoodlandandWoodland(1994)findtheoppositeholdsinbaseball,

wherebettingonunderdogsistheprofitablestrategy.Camerer(1989)findsthatifthemarket

perceivesthatateamis“hot”becauseofrecentwins,thespreadcanbecomebiasedandallow

forprofitablebettingstrategies.

ThefirstsignificantcontributiononNFLbettingmarketscomesfromZuberetal.(1985).

ZubertestsformarketefficiencyintheNFLbettingmarketbasedonthenotionthatthebest

unbiasedpredictoroftheactualpointspreadofanNFLgameshouldbethespreadofferedby

LasVegasdirectlybeforethegame.Thisisequivalenttothefinancialnotionthatforwardprices

arethebestunbiasedpredictorsoffuturespotprices.Usingaregressionthatincorporatesthe

closingspreadandteam-specificstatistics,Zuberisabletopredictwinningstrategieswitha

95%confidencelevel,aswellasdevisegamblingstrategiesthatreturnprofitsinexcessofthe

vigorish(Zuberetal.1985).Later,Saueretal.(1988)revisittheZuberstrategyanddetermine

thatlosseswouldoccurtobettorsusingthisstrategyifithadbeenextendedpast1985to1988.

Examiningtheperiodfrom1976to1994,GrayandGray(1997)findevidencethatLas

VegashashistoricallyoverpricedfavoritesanddiscountedhometeamsinNFLwagering

markets.Further,GrayandGrayfindthatteamsthatbeatthespreadinagivenseasontypically

continuebeatingspreadsinupcominggamesmoreoftenthanteamsthathadperformed

poorlyrelativetothespread.ThisphenomenondemonstratesthatLasVegasisslowto

incorporateateam’shistoricalperformanceintoprices.GrayandGrayalsodemonstratethat

LasVegasoverreactstoteams’recentperformance–overshootingwhensettinggambling

prices.Thisfindingsuggeststhatsportsbettorspossessashortmemoryandaretooquickto

discountateam’sperformanceearlierintheseason.Usingthispremise,GrayandGray

constructaneconomicallysignificantstrategythatinvolvesbettingongoodteamsthathave

notplayedwellasoflate.

14

Otherstudieshavefoundadditionalevidencesupportingtheexistenceofinefficiencies

withinthegamblingmarket.Fodoretal.(2013)findevidenceofhindsightbias,sincetoomuch

emphasisisputonteams’performanceoverthepreviousseasonwhenpricingforthefirst

weekofanewseason.Davisetal.(2015)expandsonthisbydemonstratingthattoomuch

emphasisisputonteams’performanceinthefirstweekofaseasonwhenpricingspreadsfor

thesecondweek.However,whilemanyofthesestudieshaveidentifiedinefficiencies5inthe

gamblingmarketusingbehavioralbiasesofbettors,fewresearchershaveexploredgambling

markets’incorporationofonecoreinformationalresource,theInternet.

Recently,academicshavestartedusingdatafromInternet-basedresourcesasproxies

forpopularsentiment.Sinhaetal.(2013)incorporatesTwitterdataintoapredictivemodelfor

NFLoutcomesandfindsthattheaggregated“wisdomofcrowds”representedbyTwitterdata

haspredictivepowerforNFLoutcomes.WhileSinhapresentsatestcaseofhowtoutilizesocial

mediatodirectlypredictdiscreteNFLoutcomes,neitherhenoranotheracademichastested

theimplicationsofchangingpopularsentimentongamblingpricemovementsoverthecourse

ofthegamblingweek.

InadditiontoTwitter,Googleandothersearchenginesarevaluableaggregatorsofthe

collectivepursuitofinformation.NumerousstudiesutilizeGoogleTrendsandGoogle

Categories,thetwopublicallyavailableformsofGoogle’ssearchquerydata,toforecastcertain

outcomes,includingelections(GayoAvelloetal.,2011),unemployment(Askitasand

Zimmermann,2009),thespreadofinfluenza(Ginsbergetal.,2009),andthestockmarket

(Bordinoetal.,2010).Thesestudieshaveprovenusefulinhighlightingthebestpracticesand

difficultiesassociatedwithusingGoogleTrendsandCategories.However,todatenostudies

haveexploredtheimpactofGoogle’ssearchquerydataonNFLgamblingmarkets.

Indeed,manystudieshaveidentifiedpossibleinefficienciesinthegamblingmarketby

isolatingpiecesofinformationthatbettorsdonotincorporateintotheirevaluationofawager

5Itisimportanttonotethatthepresenceofprofitablewageringstrategiesdoesnotnecessarilyimplyinefficiencyinthemarket.SinceLasVegasreactstobettorswhoexhibitcertainbiaseswhensettingspreads,thesebiasesbecomeincorporatedintotheprice.Thus,evenifLasVegasrationallyincorporatesthepreferencesofthemajorityofthegamblingpublic,asavvybettorcouldharnessknowledgeofthesebiasestogenerateprofitsbygoingagainsttheherd.

15

(Zuberetal.,1985;ThalerandZiemba,1988;Saueretal.,1988;Camerer,1989;Woodlandand

Woodland,1994;GrayandGray,1997;Gandaretal.,1988;Sinhaetal.,2013;Fodoretal.,

2013).OtherstudieshaveattemptedtousesocialmediaandInternetsearchenginesto

eliminateinefficienciesinpredictivemodelsforvariousoutcomes.Still,academicshaveyetto

examineLasVegas’incorporationoftheInternet’sinformationoverthecourseofthegambling

week.

Thispaperexpandsonthecurrentliteratureinthreeways.First,byusingGooglesearch

dataasaproxyforgamblersentiment,itinvestigatesthefactorsthatLasVegasusesinsetting

theopeningspreadforNFLmatchups.Second,againusingGooglesearchdata,itexamines

whethernewlyrevealedgamblersentimentbecomesincorporatedintotheclosingspreadas

theEfficientMarketHypothesispredicts.Third,itevaluatestheefficacyofgamblers’

incorporationofcertainfactorsintowageringchoicesandtheapplicationoftheEfficient

MarketHypothesistotheNFLwageringmarketbyattemptingtoconstructaprofitablebetting

strategy.

16

4.TheoreticalFramework

Thispaperteststhesemi-strongEfficientMarketHypothesis,whichassumesthatprices

instantaneouslyreflectallpubliclyavailableinformation(Fama,1970).IntheNFLwagering

market,LasVegas’spreadsareequivalenttopricesofwagersforbettorstopurchase.

Therefore,ifthesemi-strongEfficientMarketHypothesisholdsfortheNFLwageringmarket,

openingspreadsforagivenmatchupshouldincorporateallinformationpublicallyavailableat

themomenttheyarereleasedbyLasVegas.Additionally,anymoreinformationthatbecomes

availableoverthecourseoftheweekshouldbepricedin,becomingevidentintheclosing

spread.ToprovideclarityonthetimingofeventsthatoccurduringtheNFL’sgamblingweek

pleaseseeFigure2.

Figure2.IllustrationofTimingofEventsDuringNFLGamblingWeek

DuetothefactthatNFLgamesforagivenweekoccuronThursday,Saturday,Sunday,

andMonday,thereisnostandardweeklyformatforeachmatchup.Thespecificdaysofthe

1 2 3 4 5 6 7

PreviousWeek's

GameDay

GameDayPlus1

GamblingPeriod

CurrentWeek's

GameTakesPlace

Opening Closing RealizedSpread Spread Spread

Period1Period2

Period3

Period4

Period5

Period6Period7 Theactualoutcomeofthegame,"RealizedSpread,"isknown.

Daythatteamplayedthepreviousweek;"GameDay"Googledatatakenfromthisday.Dayaftherthedaytheteamplayedthepreviousweek;"GameDayPlus1"Googledatatakenfromthisday.OpeningSpreadissetbyLasVegasbasedoncurrentinformationavailableandanticipatedgamblersentiment.Gamblersplacebetsthroughoutthisperiodrevealinggamblersentiment;LasVegasreactsbyadjustingthespreadoffered;"Weekly"Googledatatakenfromthisperiod.GamblingPeriodendsrightbeforegamebeginswithfinalspreadofferedbeingtheClosingSpread;ClosingSpreadrepresentstheinterplaybetweentheOpeningSpreadandtheinformationrevealedbygamblersovertheGamblingPeriod.Gametakesplace.

17

weekthatdataarepulledfromvaryforeachmatchup,buttherulesfordefiningtheNFL

gamblingweekasoutlinedabovearefollowedforgatheringdataforeachindividualmatchup.

4.1.OpeningSpreadDeterminants

Tobeginouranalysis,weinvestigatewhatfactorsLasVegasconsiderswhenpricingthe

openingspread.TodothiswerunanOLSregressionoftheopeningspreadonavarietyof

factorsthatbettorswouldconsiderintheirwageringdecisions(Regression1)and,thus,that

LasVegaswouldconsiderinpricingtheopeningspread.6Intheseindependentvariableswe

includedummyvariablestocontrolforhomefieldadvantage,whetherateamplayeda

primetimegametheweekbefore(andthusexposuretoanationalaudience),andwhethera

teamhadabyetheweekbefore(andthusanextraweektopreparefortheiropponent).

Wealsoincludeavarietyofwinningpercentagestatisticstocontrolforateam’s

performancethatseason.Thesewinningpercentagesarebrokendownintotwocategories.

First,weuseateam’sgeneralwinningpercentage,i.e.consideringwhethertheteamwinsor

losesamatchup.Second,weincludeateam’swinningpercentagerelativetothespread,i.e.

consideringwhethertheteamwinsorlosesafterthespreadadjustmentistakenintoaccount.

WeincludethewinpercentageRTSduetothefindingsofGrayandGray(1997)thatteamswho

beatthespreadinthepasttendtobeatthespreadmoreofteninthefuturethanotherteams.

Sincethesefindingshavebeenpublicforsolong,itwouldmakesensethattheyhavebeen

incorporatedintobettingstrategiesofgamblersand,thus,couldbeofinteresttoLasVegas

whensettingopeningspreads.Wefurtherdelineatewithinthesewinningpercentagesby

splittingthemintowinningpercentagesoverthelastthreegamesplayedandwinning

percentagesovertheentireseasonexcludingthelastthreegames.Wedothissinceithasbeen

shownthatgamblersoveremphasizerecentperformanceintheirdecisionmaking(Grayand

Gray,1997).

Next,weincludeteamstatisticvariablestomeasureateam’saverageperformanceover

thecourseofthecurrentseason.Inchoosingwhichteamstowageron,bettorstaketheirpast

performanceasindicativeoffutureperformance,soitwouldmakesenseforLasVegastotake

thesestatisticalmeasuresintoconsiderationwhenpricingopeningspreads.Weincludea6ThespecificsoftheseindependentvariablesandmethodologyfortheircalculationwillbecoveredindepthinSection5.

18

team’saveragepassingyardspergame,averagerushingyardspergame,averageyardsallowed

ondefensepergame,averagepointsscoredpergame,averagepointsallowedpergame,and

averageturnoveradvantagepergame.

Finally,weexpectLasVegastoattempttomeasuregamblersentimentabouteachteam

whenpricingopeningspreads.Ifthegamblingmarketasawholeweretohaveamore

favorableperceptionofateam,morebetswouldbeplacedonthatteamand,consequently,

LasVegaswouldattempttoadjusttheopeningspreadtoaccountforthatsentiment.To

incorporatesentiment,weuseavariableconstructedfromaggregatedGooglesearchdata,

called“RelativeGoogleSearchLevel”,asaproxyforgamblersentiment.Fortheopeningspread

weusetwosuchvariables,eachconstructedwithdatafromdifferenttimeperiodsinFigure2.

OnevariableisconstructedwithGooglesearchfrequencydataaggregatedfromthe“Game

Day”period(Period1)andtheotherisconstructedwithGooglesearchfrequencydata

aggregatedfromthe“GameDayPlus1”period(Period2).Thecoefficientofthe“GameDay”

variableultimatelyisnotstatisticallysignificantinanyregressions,suggestingthatitisnota

factorconsideredbyLasVegasinpricingopeningspreads.Ontheotherhand,the“GameDay

Plus1”datahasstatisticallysignificanteffects,soweincorporateitintoourregression.This

makesintuitivesense,sincethe“GameDayPlus1”dataistakenfromatimeperiodcloserto

thereleaseofopeningspreadsandLasVegaswouldusethemostup-to-dateinformation

available.Also,interestingly,despitebeingseparatedbyonly24hours,“GameDay”and“Game

DayPlus1”dataarehighlyuncorrelated,withacorrelationof-0.099(SeeAppendixA.1for

cross-correlationmatrix).

4.2.IncorporationofNewInformationintoSpreadPrices

AfteridentifyingwhatfactorsaffecttheopeningspreadsofferedbyLasVegas,we

investigatewhethernewinformationrevealedoverthecourseoftheweekisincorporatedinto

theclosingspreadofferedjustbeforethegame.TodothisweruntwoOLSregressions,oneof

theSpreadMovementoverthecourseofthegamblingperiod(Regression2)andoneofthe

ClosingSpread(Regression3).TheSpreadMovementissimplythedifferencebetweenthe

ClosingSpreadandtheOpeningSpread.Weincludethesameindependentvariablesusedin

Regression1andaddanadditionalvariabletoincorporatethenewinformationintroduced

19

overthecourseofthegamblingperiod.Again,weuseavariableconstructedfromaggregated

Googlesearchdata,called“RelativeGoogleSearchLevel,”asproxyforgamblersentiment.

However,thistime,itisconstructedfromGoogledataaggregatedfromthe“Weekly”gambling

period(period4inFigure2).

IfLasVegasproperlypricesinthefactorsthatinfluencedtheopeningspread,noneof

thesefactorsshouldhaveastatisticallysignificanteffectonthespreadmovementbecauseall

ofthefactorsareknownatopenanddonotchange.Therefore,intheregressionofthespread

movement,theEfficientMarketHypothesispredictsthattheonlyvariablethatcouldbe

statisticallysignificantisthe“WeeklyRelativeGoogleSearchLevel,”sinceitisinformationthat

wasnotknownatthetimetheopeningspreadwasset.Fortheregressionoftheclosing

spread,wewouldexpecttoseesimilareffectsasintheregressionoftheopeningspread.

Additionally,wewouldexpecttoseethenewlycapturedinformationrepresentedby“Weekly

RelativeGoogleSearchLevel”incorporatedintotheClosingSpreadprice.

4.3.DeterminantsofRealizedOutcomes

Finally,weexplorewhetherfactorscommonlyconsideredbygamblersactuallyaffect

theoutcomesofgamesandbets.TodothiswerunaregressionoftheRealizedSpreadon

dummyvariablesforhomefieldadvantage,whetherateamplayedaprimetimegametheweek

before,andwhetherateamhadabyetheweekbefore(Regression4).Wealsoincludethe

teamstatisticvariablesofaveragepassingyardspergame,averagerushingyardspergame,

averageyardsallowedondefensepergame,averagepointsscoredpergame,averagepoints

allowedpergame,andaverageturnoveradvantagepergametocontrolforthequalityofthe

teamsinamatchup.DuetothefactthatwefindourrelativeGooglesearchlevelvariablestobe

statisticallysignificantinthedeterminationofopeningandclosingspreads,wealsoincludethe

relativeGooglesearchlevelvariablesinthisregressiontotestiftheyhaveanypredictivepower

intheoutcomesofgamesandbets.Inthisregression,thestatisticalinsignificanceofa

variable’scoefficientwouldsuggestthatthevariabledoesnotimpactactualoutcomesand,

thus,shouldnotbeconsideredbygamblers.WethentestZuber’snotionthattheClosing

Spreadservesasthebestpredictorforactualoutcomesofgames.Todothisweslightlymodify

Regression4byincludingtheClosingSpreadasanadditionalindependentvariable(Regression

20

5).ForZuber’sclaimtohold,theClosingSpreadshouldhaveastatisticallysignificantcoefficient

closeto1.00.

21

5.Data

5.1.DependentVariables

Thedependentvariablesusedinregressionsaretheopeningspread,theclosingspread,

thespreadmovementoverthecourseoftheweek,andtherealizedspread.Forconsistency,

wedefineeachspreadwiththeinitiallyfavoredteamastheteamofrecord.Becausespreads

withthefavoriteasteamofrecordarenegativeorzero,theopeningspreadisalwayslessthan

orequaltozero.However,becausetheinitialfavoritedeterminestheteamofrecord,closing

spreadscanbenegativeifthefavoriteremainsfavoredbyclose,positiveiftheunderdog

becomesfavoritedbyclose,orzeroifbettingcloseswithnofavoriteorunderdog.

InRegression2,weconsiderthespreadmovement,definedas:

𝑆𝑝𝑟𝑒𝑎𝑑 𝑀𝑜𝑣𝑒𝑚𝑒𝑛𝑡 = 𝐶𝑙𝑜𝑠𝑖𝑛𝑔 𝑆𝑝𝑟𝑒𝑎𝑑 − 𝑂𝑝𝑒𝑛𝑖𝑛𝑔 𝑆𝑝𝑟𝑒𝑎𝑑

Spreadmovementslessthanzerosuggestthattheinitiallyfavoredteambecomesmore

favoredoverthecourseoftheweek,astheclosingspreadwasmorenegativethantheopening

spread.Conversely,positivespreadmovementssuggestthattheinitiallyfavoredteambecomes

lessfavoredoverthecourseoftheweek.Intuitively,spreadmovementsequaltozeroimplyno

change.

OurdependentvariableinRegressions4and5istherealizedspread,definedas:

𝑅𝑒𝑎𝑙𝑖𝑧𝑒𝑑 𝑆𝑝𝑟𝑒𝑎𝑑 = 𝑃𝑜𝑖𝑛𝑡𝑠 𝑆𝑐𝑜𝑟𝑒𝑑 𝑏𝑦 𝐹𝑎𝑣𝑜𝑟𝑖𝑡𝑒 − 𝑃𝑜𝑖𝑛𝑡𝑠 𝑆𝑐𝑜𝑟𝑒𝑑 𝑏𝑦 𝑈𝑛𝑑𝑒𝑟𝑑𝑜𝑔

Whiletheotherdependentvariablesaredeterminedbeforethegametakesplace,therealized

spreadcanbecalculatedonlyafterthegameends.Thisvariableequalsthespreadthatwould

haveresultedinapush.

AfinalpointisthatLasVegasasawholecanbethoughtofasofferingastandardprice

eventhoughitiscomprisedofmanydifferentcasinosthatindependentlyoffertheirown

spreads.Ifacasino’sspreaddifferstoomuchfromanother’s,itopensupanarbitrage

opportunity,whichisquicklycorrectedbymarketforces.Atanygivenpointintime,almostall

spreadsofferedbyLasVegascasinosarethesame,atthemostdifferingby0.5points.Thisnear

equalityofpricesallowsthespreadofanygivencasinotobetakenasrepresentativeofthe

spreadofLasVegasasawhole.Thisfactisofparticularrelevancesincethespreadsweuse

comefromonlyonecasino,Caesar’s.ItallowsustouseCaesar’sasarepresentativefirmfor

(7)

(6)

22

theNFLgamblingmarketinLasVegas.Figure3illustratesasamplespreadpricemovement

overthecourseofagamblingperiodforfourcasinos;notehowcloselythefourspreadsmove

together.

Figure3.SampleSpreadMovementoverGamblingPeriod

SpreadisquotedwithNewYorkJetsasteamofrecord

(Source:VegasInsider;April2,2017)

5.2.GoogleSearchLevelConstruction

Ideally,wecouldregressaperfectmeasureofgamblersentimentonLasVegas’NFL

gamblingspreadsandtheirmovementstounderstandtheextentofthebettingmarket’s

incorporationofgamblers’preferences.However,duetotheimpossibilityofexactly

quantifyingtheamorphousnatureofgamblersentiment,wemustcreateaproxyforthis

sentiment.SincethebookmakersinLasVegascannotperfectlymeasuregamblersentiment

either,theytoohavetousesomeproxy.

Thispaperusesanaïve,relativeapproachtoattempttocapturethemoodofthe

gamblingmarket.Specifically,weassumethatthefrequencyofGooglesearchqueriescan

capturethecurrentmoodoftheoverallgamblingmarket.Thisassumptionisbasedontheidea

thatGoogleuserswillsearchforateammorefrequentlyiftheyareinterestedintheteam.

AlthoughnoteveryGoogle-searcherisguaranteedtogamble,mostgamblerslikelyuseGoogle

-9

-8

-7

-6

-5

-4

-3

SpreadMovementfor2015Week6,NewYorkJetsvs.WashingtonRedskins

Atlanss Caesar's GoldenNugget Mirage-MGM

23

toresearchtheirbets,soincreasesinsearchqueriesshouldcorrelatewithincreasedinterestin

ateamandbettingonsuchteam.

Optimally,wewouldclassifyeachindividualsearchrelatedtoagiventeamasnegative

orpositive.Forexample,ifateam’squarterbackisinjured,Googlesearchesforthatteammay

increasebecausebettorsareinterestedinwageringagainstthatteam.Conversely,ifateam’s

quarterbackisplayingexceptionallywell,Googlesearchesforthatteammayincreasebecause

bettorsareinterestedinwageringonthatteam.Unfortunately,wecannotidentifyindividual

searchesandevaluatewhethertheyarepositiveornegativebecauseGoogledoesnotprovide

suchgranularityinitspublicallyavailabledata.Further,itisimpossibletoidentifyevery

possiblesearchcombinationaboutaparticularteamthatcanbeinputintoGoogle.Asaresult,

ourmeasureforsearchinterestforagivenNFLteamissimplythesearchfrequencyofthat

team’sname.

Asdiscussedinexistingliterature(GayoAvelloetal,2011;AskitasandZimmermann,

2009;Ginsbergetal.,2009),Google’spublicallyavailablehistoricalsearchquerydataprovidesa

numberforeachsearchtermasapercentageofthesinglelargestsearchvolumeofallgiven

termsonanygivendayintheselectedperiod.Consequently,itisnotusefultocomparethe

numbersprovidedbyGoogleTrendsacrossdifferentperiodsunlesstheyarebasedonthesame

scale.Previousauthorshavethereforefoundusingabenchmarktermthebestwaytocompare

searchvolumesfordifferenttermsacrossdifferenttimeperiods.Weselecttheterm“Google

Website”asourbenchmarkbecauseitssearchfrequencyoverour5-yearperiodisrelatively

constantandremainsclosetothatoftheNFLteams’.

Figure4.“MiamiDolphins”vs.“GoogleWebsite”SearchLevel

24

(Source:GoogleTrends;March20,2017)

Figure4showsGoogleTrends’searchfrequencydataforthesearchterms“Miami

Dolphins,”representedbythesolidline,and“GoogleWebsite,”representedbythedashed

line,fromthebeginningofthe2011NFLseason,September8th2011,untiltheendofthe2016

NFLseason,January1st,2016.Asthegraphillustrates,thesearchterm“GoogleWebsite”

remainsrelativelyconstantandaroundtheaveragefrequencylevelfortheNFLteam

throughouttherelevantperiod,the2011through2016NFLseasons.

Thisconsistencyallowsustomitigatethepossibilityoffluctuationsinourbenchmark

term’ssearchfrequencyarbitrarilyaffectingtheNFLteams’searchlevels.BecauseanNFL

team’ssearchlevelmustbecomparedtothebenchmarkterm,fluctuationsinthebenchmark

termaltertherelativevaluesforeachNFLteam’ssearchfrequency.Thus,atermwithlow

varianceinsearchvolume,suchas“GoogleWebsite”isanidealbenchmark.

Furthermore,theproximityofthebenchmark’saveragesearchfrequencytothe

averagesearchfrequencylevelfortheNFLteamsallowsustocaptureasmuchoftheir

variationinsearchfrequencyaspossible.BecauseGoogleTrendsdoesnotprovidehistorical

searchfrequencylevelsforperiodssmallerthanaday,thegreatestgranularitywecanobtainis

thedailysearchfrequencylevelforeachterm.Oneachrelevantday,wesearchfortwosearch

frequencyvalues,onefor“Googlewebsite”andonefortheNFLteamname,thehigherof

whichGoogleassignsavalueof100andthelowerofwhichisscaledasapercentageofthat

0

20

40

60

80

100

miamidolphins:(Worldwide) googlewebsite:(Worldwide)

25

100.Sincethefrequencyof“GoogleWebsite”remainssimilartotheaverageofourNFLteams,

itprovidesadetailedscalewithwhichtomeasurethefluctuationsintheNFLteam’ssearch

frequencies.Ifthebenchmarktermwerevastlyhigherthantheteamsearchterm,the

observedvalueswouldalwaysbe100forthatbenchmarktermand0or1fortheteamsearch

term.Conversely,iftheteamsearchtermwerevastlygreaterthanthebenchmarkterm,the

observedvalueswouldalwaysbe100fortheteamsearchtermand0or1forthatbenchmark

term.Ineitherscenario,mostoftheteamsearchterm’svariationislostduetothechosen

scale.Thebestbenchmarkisthusonethatisonaverageatthesamesearchlevelastheteam

searchterm.

Weevaluateeachteam’ssearchfrequencylevelasamultipleofthebenchmark“Google

Website”onthedayaftertheyplayagameduringtheNFLseasonsfrom2010-2016.

Furthermore,weevaluateeachteam’saveragesearchfrequencyingamblingperiodbetween

openandcloseasshowninFigure2.ThesearecalledtheGooglesearchlevelsforteamiat

weekt,respectivelydenoted

𝐺𝑎𝑚𝑒 𝐷𝑎𝑦 + 1!,! =𝐷𝑎𝑖𝑙𝑦 𝑇𝑒𝑎𝑚 𝑆𝑒𝑎𝑟𝑐ℎ 𝐿𝑒𝑣𝑒𝑙!,!

𝐷𝑎𝑖𝑙𝑦 𝐺𝑜𝑜𝑔𝑙𝑒 𝑊𝑒𝑏𝑠𝑖𝑡𝑒 𝑆𝑒𝑎𝑟𝑐ℎ 𝐿𝑒𝑣𝑒𝑙!,!

𝑊𝑒𝑒𝑘𝑙𝑦!,! =!"#$%&'( !"#$%& !"#$%&# !"#$ !"#$%! !"#"!!,!

!"#$%&'( !"#$%& !"#$%&# !""#$% !"#$%&" !"#$%! !"#"!!,!

where𝐺𝑎𝑚𝑒 𝐷𝑎𝑦 + 1!,!representsthesearchfrequencylevelonthedayaftertheprevious

week’sgameand𝑊𝑒𝑒𝑘𝑙𝑦!,!representstheaveragesearchfrequencyduringthegambling

periodleadinguptothecurrentgame.Wehaveobservationsfor32teamsspanning119

weeks.SinceGoogleTrendsgivestherelativesearchlevelsasintegersbetween1and100,

𝐺𝑎𝑚𝑒 𝐷𝑎𝑦 + 1!,! and 𝑊𝑒𝑒𝑘𝑙𝑦!,!haveapossiblerangefrom !!""

to100.Ifteamidoesnotplay

weekj,weset𝐺𝑎𝑚𝑒 𝐷𝑎𝑦 + 1!,! and 𝑊𝑒𝑒𝑘𝑙𝑦!,! = 0,increasingtherangetobefrom0to100.

SometeamsaremorepopularthanothersandreceivemanymoredailyGoogle

searchesonaverage.Asaresult,wecompareeachteam’sGooglesearchlevelforaparticular

weektoitssearchlevelsfortheprevious17weeks,thelengthofafullNFLseason.For

example,wewouldcompare2013’sweek6totheaveragefrom2012’sweek6through2013’s

week5.Thisallowsustoseehowagivenweek’ssearchlevelcomparestotheteam’stypical

(8)(9)

26

searchleveloverthepastseason.TodothiswedivideGooglesearchlevelbytheaverage

Googlesearchlevelforthepast17weekstogetarelativeGooglesearchlevel,

𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐺𝑎𝑚𝑒 𝐷𝑎𝑦 + 1!,! =𝐺𝑎𝑚𝑒 𝐷𝑎𝑦 + 1!,!

1𝑋!,!

𝐺𝑎𝑚𝑒 𝐷𝑎𝑦 + 1!,!!!!!!!!!"

𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑊𝑒𝑒𝑘𝑙𝑦!,! =𝑊𝑒𝑒𝑘𝑙𝑦!,!

1𝑋!,!

𝑊𝑒𝑒𝑘𝑙𝑦!,!!!!!!!!!"

where𝑋!,!isarandomvariablethatcountsthenumberofgamesplayedbyteamiin

weeks(t-17)to(t-1).7WeusethisconstructedrelativeGooglesearchleveltocompare

Googlesearchactivitybetweendifferentteams.Webelievethatthedifferencebetweenthe

RelativeGoogleSearchLevelsfortheinitialfavoriteandunderdogshouldcapturebettors’

relativelevelsofinterestinthetwoteams.Aseitherteam’srelativeGooglesearchlevel

variableincreases,webelievethatbettors’interestinthatteamincreases.Whileimperfect,we

believethisservesasareasonableproxytomeasuregamblersentiment.

Thevariableweultimatelyuseinourregressionsistheinitialfavorite’srelativeGoogle

searchlevelminustheinitialunderdog’srelativeGooglesearchlevel

𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐺𝑜𝑜𝑔𝑙𝑒 𝑆𝑒𝑎𝑟𝑐ℎ 𝐿𝑒𝑣𝑒𝑙 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙

= 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐺𝑜𝑜𝑔𝑙𝑒 𝑆𝑒𝑎𝑟𝑐ℎ 𝐿𝑒𝑣𝑒𝑙!"!#!$% !"#$%&'(

− 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐺𝑜𝑜𝑔𝑙𝑒 𝑆𝑒𝑎𝑟𝑐ℎ 𝐿𝑒𝑣𝑒𝑙!"!#!$% !"#$%#&'

WhenthisvariabletakesapositivevalueitindicatesmoreGooglesearchesfortheinitially

favoredteam.AnegativevalueindicatesmoreGooglesearchesfortheinitialunderdog.

5.3.IndependentVariables

Foreachmatchup,therearetwoteams,aninitialfavoriteandaninitialunderdog.Inthe

fifteencasesinourdatasetwheretheopeningspreadis0,werandomlyassigninitial

favorite/underdogdesignationstotheteamsinthesematchups.Therandomnessofthe

designationsshouldmitigateanynoisecontributedbythesematchups.Sinceallofourspreads

arequotedwiththeinitialfavoriteastheteamofrecord,inourregressionsofopeningand

closingspread(Regressions1and3),anegativecoefficientwouldmeanthatincreasesinthe

correspondingvariableleadtotheinitialfavoritebecomingmorefavored,ceterisparibus.7Thisistoadjustforbyeweeks,whichresultinassignedgooglesearchlevelsof0.

(10)

(11)

(12)

27

Similarly,inourregressionsoftherealizedspread(Regressions4and5),anegativecoefficient

wouldmeanthatincreasesinthecorrespondingvariableleadtotheinitialfavoritescoring

morepoints,ceterisparibus.Ourhypothesisfortheregressionofspreadmovement

(Regression2)isthatallindependentvariablesknownatthetimeoftheopeningspreadwillbe

statisticallysignificant.ThisleavesusonlyexpectingtheweeklyrelativeGooglesearchlevel

variabletobestatisticallysignificant,sinceitrepresentsnewinformationlearnedfromopento

close.Astatisticallysignificanctcoefficientforanyoftheotherindependentvariableswould

suggestthatLasVegasdoesnotfullypriceinthegamblingmarket’spreferenceforthatvariable

initsopeningspread.Ourhypothesesfortheregressionsonopening,closing,andrealized

spread(Regressions1,3,and4)arediscussedinrelationtoeachindividualvariablebelow.

InRegression5,weincludetheClosingspreadintheregressionofrealizedspreadand

expectittobehighlystatisticallysignificantasfoundbyZuberetal.(1985).Sincemanyofour

independentvariablesareincorporatedintotheformationoftheClosingspread,weexpectits

inclusiontoreducethestatisticalsignificanceofthevariables’coefficientsasfoundin

Regression4.

5.3.1.DummyVariables

Thefirstdummyvariableisequalto1iftheinitialfavoriteisthehometeam.Weexpect

thisvariabletohaveanegativecoefficientinregressionsoftheopeningandclosingspreads

(Regressions1and3)sinceLasVegasmostlikelypricesinhomefieldadvantage.Wealso

anticipateanegativecoefficientinthefirstregressionofrealizedspread(Regression4)since

playingathomeisadvantageoustoNFLteams.

Theseconddummyvariableisequalto1iftheinitialfavoriteplayedinaprimetime

gametheweekbeforethecurrentmatchup.8Weanticipatethatthisvariablewillhavea

negativecoefficientintheregressionsoftheopeningandclosingspreads(Regressions1and3).

WebelievethatLasVegasrecognizesthatprimetimegameshavemoreviewersandpricesin

bettors’preferenceforwageringonteamswithwhichtheyarefamiliar.Thethirddummy

variableequals1iftheinitialunderdogplayedinaprimetimegametheweekbefore.Similarly,

weexpectthatthisvariablewillhaveapositivecoefficient.Weexpectastatistically8Wedefineaprimetimegametobeanygamebeginningafter8:00PMESTonaSundayorMonday,asthesearethegamesthatdrawthehighestnationalaudience.

28

insignificantcoefficientforbothprimetimevariablesintheregressionoftherealizedspread

(Regression4).AlthoughLasVegasmayattempttocapitalizeonbettors’irrationalpreferences,

wefindnoevidencetosuggest,noristherealogicalreason,thatplayinginaprimetimegame

theweekpriorshouldimproveorworsenperformanceinagame.

Thefourthandfifthdummyvariablesareequalto1ifthefavoriteandunderdog,

respectively,hadabyeweektheweekpriortoamatchup.9Weexpectthatthatthedummyfor

thefavoritewillhaveanegativecoefficientandthedummyfortheunderdogwillhavea

positivecoefficientintheregressionsoftheopeningandclosingspreads(Regressions1and3).

WehypothesizethatLasVegasanticipatesthatbettorswilldisproportionatelybetonteams

afterabyeweekbecausetheteamhashadanextraweekofrestandanextraweektoprepare

forthegame.Thus,weexpectteamswithabyetobemorefavoredintheopeningandclosing

spreads.Weexpectsimilarresultsintheregressionoftherealizedspread(Regression4),since

teamswithanextraweektoprepareandrestshouldperformbetter.

5.3.2.WinningPercentageVariables

SincesomeNFLgamesresultinatie,wecalculateWinningPercentageaccordingto

equation13.

𝑊𝑖𝑛𝑛𝑖𝑛𝑔 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 =!"#$!!"#$!

!"#$% !"#$%&

Then,weconstructourwinningpercentagevariablesasadifferencebetweentheinitial

favorite’swinningpercentageandtheinitialunderdog’s.

𝑊𝑖𝑛𝑛𝑖𝑛𝑔 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙

=𝑊𝑖𝑛𝑛𝑖𝑛𝑔 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒!"!#!$% !"#$%&'( −𝑊𝑖𝑛𝑛𝑖𝑛𝑔 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒!"!#!$% !"#$%#&'

Ourfirsttwovariablesjustusetraditionalwinningpercentage,whetherateamwonor

lost.Thesetwovariablesevaluatetwodifferentsegmentsoftheseason,inordertoidentify

preferencesinrecentversuspastperformance.Thefirstmeasuresthewinningpercentageinall

gamesexcludingthemostrecentthree.Thesecondvariablemeasurestheteam’swinning

percentageinthelastthreegames.10

9A“bye”weekisaweekofrestduringwhichanNFLteamdoesnotplayagame.EachNFLteamisgrantedonebyeweekperseason.10DuetotheconstructionofthesevariableswemustdropmatchupsinWeeks1-4ofeachseasonfromourdataset.

(13)

(14)

29

WeexpectLasVegas’spreadstofavorateammoreasitswinningpercentageincreases.

Asaresult,weexpectthatthecoefficientsofbothdifferentialstobenegativeinthe

regressionsoftheopeningandclosingspread(Regressions1and3).However,weexpectthe

absolutevalueofthecoefficientsofthewinningpercentageoverthelastthreegamestobe

largerthantheabsolutevalueofthecoefficientsofthewinningpercentageexcludingthelast

threegames.ThishypothesisstemsfromthefindingsofGrayandGray(1997),asdiscussedin

Section3,thatbettorshaveashortmemoryandaretooquicktodiscountearlyseason

performance.BecauseLasVegasknowsbettorsfocusonrecentperformance,theymostlikely

incorporaterecentwinningpercentageintotheirpricingofspreadsmorethanthewinning

percentageovertherestoftheseason.

Ourthirdandfourthwinningpercentagevariablesarecalculatedthesameway,except

withwinsandlossescalculatedrelativetothespread.Asaresult,theydeterminethe

percentageofspreadbetsthatabettorwouldhavewoniftheyhadplacedbetsonthisteam.

WeincludethemsinceGrayandGray(1997)findthatteamswhohadperformedwellagainst

thespreadearlierinaseasontendtocontinuetoperformwell.Wedonot,however,expect

thesetwowinningpercentagevariablestobestatisticallysignificantintheregressionsof

openingandclosingspread(Regressions1and3)sinceactualwinningpercentagesdoabetter

jobofcapturingthequalityofagiventeam.

5.3.3.TeamStatisticVariables

Weincludesixdifferentteamstatisticvariables.Eachvariableiscalculatedasthe

differencebetweentheinitialfavorite’saveragepergamestatisticandtheinitialunderdog’s

averagepergamestatistic.Therefore,eachvariabletakesapositivevalueiftheinitialfavorite’s

averagepergamestatisticisgreaterthantheinitialunderdog’saveragepergamestatistic,and

viceversa.Wecalculateallofthevaluesusingeachgameplayedthatseasonupto,butnot

including,thecurrentweek.Thesixstatisticsusedareaveragepassingyardspergame,average

rushingyardspergame,averageyardsallowedondefensepergame,averagepointsscored,

averagepointsgivenup,andaverageturnoveradvantagepergame.11

11Averageturnoveradvantageisthepergameamountofturnoverswonbyateamminusthepergameamountofturnoverslost.

30

Wehavethesameexpectationforalloftheteamstatisticvariables’coefficients;we

expecttheteamwiththesuperiorstatisticsineachcategorytobemorefavoredinopeningand

closinglines.Passingyards,rushingyards,pointsscored,andturnoveradvantagearestatistics

thatteamswanttomaximize.Therefore,weexpectthat,asthedifferentialsinpassingyards,

rushingyards,pointsscored,andturnoveradvantageincrease,LasVegasfavorsthefavorite

more.Asaresult,thesevariablesshouldhavenegativecoefficientsintheregressionsofthe

openingandclosingspreads.Similarly,weexpectthesevariablestohavenegativecoefficients

intheregressionofrealizedspreadsbecausethesemetricsshouldbepredictiveofateam’s

futureperformance.

Meanwhile,yardsallowedandpointsagainstarestatisticsthatteamswanttominimize,

soweexpectthatLasVegasfavorsthefavoritelessasthesevariablesincrease.Asaresult,we

expectpositivecoefficientsintheregressionsoftheopening,closing,andrealizedspreads.

31

6.Results

Table3.OLSRegressionsonOpeningSpread,SpreadMovement,andClosing

Spread

NumberofObservations 966 774 774Prob>F 0.0000 0.0000 0.0000R-squared 0.6034 0.1057 0.5743AdjR-squared 0.5967 0.0856 0.5647RootMSE 2.1702 1.4957 2.4407FavoriteisHomeTeam -3.4648 *** 0.0686 -3.3952 ***

(0.1608) (0.1251) (0.2041)FavoritePlayedPrimetimeLastWeek -0.8002 *** 0.2485 -0.5650 *

(0.2145) (0.1746) (0.2849)UnderdogPlayedPrimetimeLastWeek 0.6874 ** 0.0070 1.0348 **

(0.2494) (0.2031) (0.3315)FavoriteHadByeLastWeek -0.1863 -0.3930 -0.6014

(0.2619) (0.2062) (0.3365)UnderdogHadByeLastWeek 0.3534 0.6513 *** 0.8193 **

(0.2531) (0.1936) (0.3160)WinningPercentageNotIncludingLastThree -0.7503 ** 0.5792 ** -0.0518GamesDifferential(Favorite-Underdog) (0.2656) (0.2014) (0.3287)WinningPercentageLastThreeGames -1.1032 *** 0.3936 ** -0.4428Differential(Favorite-Underdog) (0.2069) (0.1632) (0.2664)WinningPercentageRTSNotIncludingLast -0.1223 0.1499 -0.0866ThreeGamesDifferential(Favorite-Underdog) (0.2134) (0.1653) (0.2697)WinningPercentageRTSLastThree 0.1037 0.1153 0.1188GamesDifferential(Favorite-Underdog) (0.1701) (0.1341) (0.2189)AverageOffensivePassingYardsPerGame -0.0081 *** -0.0047 ** -0.0083 **Differential(Favorite-Underdog) (0.0022) (0.0018) (0.0029)AverageOffensiveRushingYardsPerGame -0.0075 ** -0.0065 ** -0.0113 ***Differential(Favorite-Underdog) (0.0027) (0.0021) (0.0035)AverageYardsAllowedonDefensePerGame 0.0036 0.0042 ** 0.0108 ***Differential(Favorite-Underdog) (0.0020) (0.0016) (0.0025)AveragePointsScoredPerGame -0.3254 *** -0.0357 -0.4009 ***Differential(Favorite-Underdog) (0.0231) (0.0184) (0.0300)AveragePointsAllowedPerGame 0.2428 *** 0.0451 ** 0.2736 ***Differential(Favorite-Underdog) (0.0232) (0.0176) (0.0287)AverageTurnoverAdvantagePerGame 0.4005 *** -0.1175 0.2228Differential(Favorite-Underdog) (0.1023) (0.0785) (0.1282)GameDayPlus1RelativeGoogleSearch 0.1949 ** -0.0920 0.0333LevelDifferential(Favorite-Underdog) (0.0638) (0.0512) (0.0835)WeeklyRelativeGoogleSearch -- 0.1000 0.5224 **LevelDifferential(Favorite-Underdog) -- (0.1107) (0.1807)Constant -0.6826 *** 0.2062 -0.4758 *

(0.1671) (0.1304) (0.2127)***p<0.001,**p<0.01,*p<0.05 2011through2015NFLSeasons,notincludingweeks1through4forRegression1standarderrorsinparentheses 2012through2015NFLSeasons,notincludingweeks1through4forRegressions2&3

OLSRegression2SpreadMovement

OLSRegression3ClosingSpread

DummyVa

riables

Winning

Percentage

Varia

bles

Team

StatisticVariables

Google

Search

Levels

OLSRegression1OpeningSpread

32

6.1.Regression1:OpeningSpreadDeterminants

InRegression1,wefindthatLasVegasincorporatesmanyofthefactorswehypothesize

tobedeterminantsoftheopeningspread.Furthermore,forthemostpart,thesignsofeachof

thesefactorsalignwithourinitialhypotheses.

Twoofourvariables,however,demonstratesurprisingresults.First,ourbyevariables

havenostatisticallysignificanteffectsontheopeningspread.Thesecondsurprisingresult

relatestoourGooglesearchvariable.Contrarytoourexpectationofanegativecoefficient,

whichwouldimplythatLasVegasfavorsteamswithhigherGooglesearchfrequencies,the

coefficientisstatisticallysignificantandpositive.Weproposethreepossibleexplanationsfor

thisunexpectedresult.

Explanation1:ItispossiblethatLasVegasincorporatesadifferentmeasureofgambler

sentimentthatisnegativelycorrelatedwithourGooglesearchvariable.Inthisway,LasVegas’

settingofopeningspreadsdependsonthisalternatemeasureanditsnegativecorrelationwith

theGoogleSearchvariableleadstoapositivecoefficient.

Explanation2:OurconstructedGooglesearchvariableisflawedandactuallycaptures

bettors’negativeopinionsofteams.Inthisscenario,asateamissearchedformore,bettors

wanttobetagainstthisteam,soLasVegasfavorstheteamlessinitsspreadpricing.

Explanation3:TheGooglesearchvariabledoesnotcapturegamblersentimentatall,

butrathercapturessomeotherfactorthat,whenincreased,causesLasVegastofavorfavorites

lessandunderdogsmore.

InRegression1,weidentifycertainfactorsthatLasVegasincorporatesintotheirsetting

ofopeningspreads.AswemovetoRegression2,wedetermineifaddingourmeasurementof

revealedgamblersentimenttothesefactorshaspredictivepowerforthespreadmovement

overthecourseoftheweek.Regression3showsuswhetherLasVegasincorporatesnew

information,revealedoverthecourseoftheweek,intotheirclosingspreadsandifanyofthe

factorsthatinfluencedtheopeningspreadhaveadifferenteffectontheclosingspread.Using

theregressionstogether,weevaluatewhetherLasVegasaccuratelygaugesbettors’

preferencesforeachofthesefactors.

33

6.2.Regressions2and3:ClosingSpreadDeterminantsandOpeningSpreadEfficiency

InRegression2,asweexpect,manyofthevariables’coefficientsdemonstrateno

statisticalsignificance.ThisfindingsuggeststhatLasVegassufficientlyincorporatesthese

variablesintotheirsettingofopeningspreads.

However,LasVegascannotsetthespreadsperfectlybecausetheycannotperfectly

forecastgamblers’preferences.Consequently,insomecases,LasVegasmisjudgesgamblers’

preferencesforcertainstatistics.IncontrastwiththecorrespondingcoefficientsinRegression

1,thegeneralwinningpercentagestatistics’coefficientsarepositiveinRegression2.Although

Regression1demonstratesthatLasVegaspriceswinningpercentagesintotheopeningspread,

thisfindingsuggeststhatLasVegasoverestimatesbettors’preferencesforhigherwinning

percentageswhentheysetopeningspreads.Furthermore,thevariables’statistical

insignificanceinRegression3suggeststhatbettors’placingofbetsoverthecourseoftheweek

eliminatesLasVegas’overestimationbytheclosingspread.

Similarly,inRegression2,thestatisticallysignificantcoefficientsoffouroftheteam

statisticvariablessuggestthatLasVegasdoesnotaccuratelyincorporategamblers’preferences

forthesestatisticsintotheopeningspread.However,thesecoefficientsinthespread

movementregressionaresmallinmagnitude.Further,whencomparingthecoefficientsonthe

samevariablesbetweentheopeningspreadandclosingspreadregressions,theyareall

relativelysimilar.Thissuggeststhat,althoughnotperfect,LasVegas’estimationofgamblers’

preferencesfortheseteamstatisticvariablesisrelativelyaccurateatthetimeoftheopening

spread.Thesmallchange,asevidencedbythestatisticallysignificantcoefficientsinthespread

movementregression,canbeexplainedbytheimpossibilityofknowinggamblers’exact

preferencesaheadoftimeanddoesnotnecessarilyimplythattheopeningspreadswereset

inefficientlybyLasVegas.

Asmentionedin6.1,thestatisticalinsignificanceoftheunderdogbyedummy’s

coefficientsuggeststhatLasVegasdoesnotincorporatethisinformationintotheiropening

spreads.However,thevariablehasastatisticallysignificantandpositivecoefficientin

Regressions2and3,implyingthatbettorshaveapreferenceforunderdogsthathadabyethe

34

previousweek.Consequently,wecontendthattheopeningspreadsofferedbyLasVegasdo

notefficientlyincorporatebettors’preferencesforunderdogswhohadabyetheweekbefore.

Lastly,ourGameDay+1Googlesearchvariabledoesnothaveastatisticallysignificant

coefficientinRegressions2or3.WeinterpretthisfindingtomeanthatLasVegasfully

incorporatesbettors’preferencesforGooglesearchesintotheiropeningspreads,whetheritis

duetoExplanation1,Explanation2,orExplanation3fromSection6.1.Furthermore,our

WeeklyGooglesearchvariablehasastatisticallysignificantcoefficientinRegression3,meaning

LasVegasincorporatesthenewinformationrevealedoverthecourseoftheweekintotheir

closingspreads.

35

6.3.Regressions4and5:TestingFactorsGamblersConsidertoPredictOutcomes

Table4.OLSRegressionsonRealizedSpread

NumberofObservations 774 774Prob>F 0.0000 0.0000R-squared 0.0589 0.0937AdjR-squared 0.0428 0.077RootMSE 13.757 13.509FavoriteisHomeTeam -3.0548 ** 0.5948

(1.1462) (1.3132)FavoritePlayedPrimetimeLastWeek 0.7810 1.3524

(1.5957) (1.5705)UnderdogPlayedPrimetimeLastWeek 1.9492 0.8692

(1.8588) (1.8363)FavoriteHadByeLastWeek 0.0550 0.6608

(1.8918) (1.8612)UnderdogHadByeLastWeek 1.0301 0.1208

(1.7788) (1.7549)AverageOffensivePassingYardsPerGame 0.0192 0.0282Differential(Favorite-Underdog) (0.0162) (0.0159)AverageOffensiveRushingYardsPerGame 0.0137 0.0259Differential(Favorite-Underdog) (0.0196) (0.0194)AverageYardsAllowedonDefensePerGame 0.0091 -0.0028Differential(Favorite-Underdog) (0.0142) (0.0142)AveragePointsScoredPerGame -0.5274 *** -0.0802Differential(Favorite-Underdog) (0.1567) (0.1748)AveragePointsAllowedPerGame 0.2910 * -0.0164Differential(Favorite-Underdog) (0.1472) (0.1554)AverageTurnoverAdvantagePerGame -0.3128 -0.5395Differential(Favorite-Underdog) (0.7192) (0.7076)GameDayPlus1RelativeGoogleSearch 1.2522 ** 1.2329 **LevelDifferential(Favorite-Underdog) (0.4680) (0.4596)WeeklyRelativeGoogleSearch -0.6857 -1.2261LevelDifferential(Favorite-Underdog) (1.0094) (0.9963)ClosingSpread -- (1.0836) ***

-- (0.2009)Constant -1.5821 -1.0266

(1.1882) (1.1713)***p<0.001,**p<0.01,*p<0.05standarderrorsinparentheses2012through2015NFLSeasons,notincludingweeks1through4forRegressions4&5

DummyVa

riables

Team

StatisticVariables

Google

Search

Levels

OLSRegression4RealizedSpread

OLSRegression5RealizedSpread

36

InRegression4,wefindmostvariables’coefficientstobestatisticallyinsignificant.This

findingsuggeststhatbettorshavenoreasontoconsidermanyofthefactorsthatthey

incorporateintotheirgamblingdecisions.Below,wediscusssomeofthemoreinteresting

findings.

Thehometeamdummyistheonlystatisticallysignificantdummyvariable.

Unsurprisingly,wefindabasisforhomefieldadvantage’sexistenceandestimatethatit

equatestoapproximately3marginalpointsscored.Whencomparingthisvaluetovariable’s

coefficientintheregressionsoftheopeningandclosingspreads(Regression1and3)to

evaluatewhetherLasVegasaccuratelyincorporateshomefieldadvantage,weseethatLas

Vegasgiveshometeamsslightlymoreofanadvantage,closerto3.5marginalpointsscored.

Notunexpectedly,wefindthecoefficientsoftheprimetimedummyvariablestobestatistically

insignificant,andconcludethatplayingprimetimetheweekbeforeconfersnoadvantagetoa

team.Wealso,somewhatunexpectedly,findthebyedummyvariables’coefficientstohaveno

statisticalsignificance.Thisresultimpliesthatthereisnomerittotheclaimthatteamswill

performbetterwhentheyhavetwoweekstoprepareforgames.

Onecouldargueforteamcoefficientstobestatisticallysignificantbecausetheyare

indicativeofateam’shistoricalperformanceand,therefore,predictiveoffutureperformance.

However,onlyaveragepointsscoredandaveragepointsallowedhavestatisticallysignificant

coefficients.Webelievethatthepointsscoredandallowedstatisticsalreadyreflectthe

informationconveyedbytheremainingoffensiveanddefensiveteamstatistics,respectively.

Further,theotherstatisticsdonotnecessarilyconvertdirectlyintopointsputuponthe

scoreboardbyateamand,therefore,therealizedspread.Pointsscoredandpointsallowed,

however,do(bydefinition).Consequently,wearenotsurprisedthatonlythesetwovariables

havepredictivepowerforoutcomes.

Lastly,ourmostinterestingfindingisthatourGameDay+1Googlesearchvaluehasa

statisticallysignificant,positivecoefficientontherealizedspread.Ifwereturntoourthree

ExplanationsfromSection6.1,webelievethisfindingprovidesmoreevidenceforExplanation

3.TheunknownfactorthatGooglesearchvaluescapturecouldalsohaveanimpactonthe

37

outcomesofgames.WehypothesizethatLasVegashasidentifiedthisfactor,recognizedits

impactonrealizedspreads,andincorporateditintoopeningandclosingspreads.

InRegression5,wefindthattheinclusionoftheclosingspreadintheregressionof

realizedspreadpushesallvariables’coefficientstostatisticalinsignificance,exceptthe

coefficientoftheGameDay+1Googlesearchvalue.Asexpected,thesevariables,allofwhich

weprovetobeincorporatedintoclosingspreadsinRegression3,areoveridentifiedin

Regression5and,consequently,havenostatisticallysignificanteffect.However,weshowin

Regression3thattheGameDay+1Googlesearchvariableisnotincorporatedintoclosing

spreads.Therefore,wearenotsurprisedtofindthatitremainsstatisticallysignificantand

positiveinRegression5.ThisfinalfindingprovidesfurtherevidencethatLasVegasincorporates

theGameDay+1Googlesearchvariableintoopeningspreadsbecauseitcapturessome

unexpectedfactorthathasanimpactonoutcomes.Indeed,whilewerecognizetheflawsinour

hypothesis,webelievethisexplanationtobethemostlikely.

Forfun,weattempttousethisinformationtoconstructaprofitablebettingstrategyin

outofsampledatacollectedoverthecourseofthe2016NFLseason.Weattempttoharness

thepredictivepoweroftheGameDay+1Googlesearchdatatochoosewhichteamstowager

on.Althoughmanyvariationsofstrategiesaredevised,wefailtofindanystrategythat

consistentlyoutperformsthehurdlerateof52.38%inawaythatcannotbeattributedto

chance.TheabsenceofareproducibleprofitablestrategyaddsfurtherevidencethattheNFL

wageringmarketisefficient.

7.SummaryofResults

Throughourfiveregressions,weanswerseveralofouroverarchingquestions.First,we

findthatLasVegasincorporatesmanyfactorsintoitsopeningspreads,includingGooglesearch

frequencydata.Second,werecognizethatLasVegasincorporatesnewinformationrevealed

overthecourseoftheweekintoitsclosingprices.Third,weidentifythepertinentfactorsthat

affectactualoutcomes,butrealizethattheconstructionofaprofitablebettingstrategyisnot

possibleusingthisfactors.Overall,wefindlittleevidencetorefutethattheEfficientMarket

HypothesisholdsinLasVegas’NFLwageringmarket.

8.SuggestionsforFurtherExploration

38

WebelievethatthestatisticalsignificanceofGameDay+1Googlesearchvariable’s

coefficientintheregressionofrealizedspreadmeritsfurtherinvestigation.Studiescouldbe

conductedtoidentifythemystery“factor”withwhichthedataiscorrelatedinorderto

understandtheimplicationsofourfindings.Forexample,aconcurrentanalysisofspread

movementsoversmallertimeintervalsandliveGoogleTrendsdatacouldshedlightonthe

potentialfactorsthatthedatacaptures.

Furthermore,webelieveanysubsequentstudiesshouldattempttoutilizemore

granularsearchdata.DuetothelimitationsofhistoricalGoogleTrendsdata,wecouldnot

obtainsearchvaluesfortimeperiodssmallerthanoneday.Thereplacementofourdailyand

weeklysearchvalueswithhourlydataordataforsmallertimeintervalscouldyieldenlightening

results.OnecouldalsofurtherattempttobreakdowntheGooglesearchdataintermsofhow

positiveornegativeitistowardsaparticularteamthroughsemanticanalysis.This,however,is

difficulttododuetothelimitationsinthedatathatarereleasedpubliclybyGoogle.

39

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41

A.Appendix

A.1.Cross-CorrelationMatrix

Cross-CorrelationMatrix

FavoriteisHomeTeam(Dummy)

FavoritePlayedPrimetimeLastWeek(Dummy)

UnderdogPlayedPrimetimeLastWeek(Dummy)

FavoriteHadByeLastWeek(Dummy)

UnderdogHadByeLastWeek(Dummy)

WinningPercentageNotIncludingLastThreeGamesDifferential

WinningPercentageLastThreeGamesDifferential

WinningPercentageRTSNotIncludingLastThreeGamesDifferential

WinningPercentageRTSLastThreeGamesDifferential

AverageOffensivePassingYardsPerGameDifferential

AverageOffensiveRushingYardsPerGameDifferential

AverageYardsAllowedonDefensePerGameDifferential

AveragePointsScoredPerGameDifferential

AveragePointsAllowedPerGameDifferential

AverageTurnoverAdvantagePerGameDifferential

PriorWeek'sGameDay+1RGSLDifferential

WeeklyRGSLDifferential

FavoriteisHomeTeam

(Dummy)

1.000FavoritePlayedPrim

etimeLastW

eek(Dummy)

0.0411.000

UnderdogPlayedPrimetim

eLastWeek(Dum

my)

-0.027-0.044

1.000FavoriteHadByeLastW

eek(Dummy)

0.007-0.122

-0.0091.000

UnderdogHadByeLastWeek(Dum

my)

0.091-0.004

-0.1090.081

1.000WinningPercentageN

otIncludingLastThreeGamesDifferential

-0.190-0.028

-0.035-0.024

-0.0121.000

WinningPercentageLastThreeGam

esDifferential-0.237

0.017-0.010

-0.088-0.054

0.0511.000

WinningPercentageRTSN

otIncludingLastThreeGamesDifferential

0.0010.052

-0.074-0.015

0.031-0.035

0.0351.000

WinningPercentageRTSLastThreeGam

esDifferential0.015

0.0430.012

0.002-0.001

-0.040-0.034

0.0141.000

AverageOffensivePassingYardsPerGam

eDifferential-0.114

0.025-0.066

-0.061-0.011

0.0180.055

0.070-0.040

1.000AverageO

ffensiveRushingYardsPerGameDifferential

-0.1120.037

-0.029-0.037

-0.0230.169

0.0960.073

0.008-0.390

1.000AverageYardsAllow

edonDefensePerGameDifferential

0.101-0.037

0.0210.036

-0.063-0.201

-0.130-0.051

-0.0350.237

-0.1751.000

AveragePointsScoredPerGameDifferential

-0.2980.062

-0.035-0.053

-0.0640.361

0.3440.046

-0.0790.514

0.1810.204

1.000AveragePointsAllow

edPerGameDifferential

0.2030.047

0.0250.027

-0.024-0.456

-0.3480.031

0.0120.315

-0.1570.587

0.0061.000

AverageTurnoverAdvantagePerGameDifferential

-0.152-0.020

0.003-0.004

-0.0400.369

0.319-0.022

-0.064-0.186

0.1120.080

0.369-0.453

1.000PriorW

eek'sGameDay+1RGSLDifferential

-0.0260.373

-0.4020.006

0.0780.058

0.1500.040

0.003-0.031

0.033-0.028

0.063-0.085

0.0881.000

WeeklyRGSLDifferential

0.0400.391

-0.426-0.104

0.0680.126

0.1590.046

0.031-0.044

0.103-0.048

0.105-0.110

0.1050.550

1.000

42

A.2.TableofIndependentVariableDefinitions

DummyVariables

VariableName Description

𝐻𝑜𝑚𝑒!,! 1iftheinitialfavoriteisthehometeam

𝑃𝑟𝑖𝑚𝑒𝑡𝑖𝑚𝑒!,!!! 1iftheinitialfavoriteplayedaprimetimegamethe

previousweek

𝑃𝑟𝑖𝑚𝑒𝑡𝑖𝑚𝑒!,!!! 1iftheinitialunderdogplayedaprimetimegame

thepreviousweek

𝐵𝑦𝑒!,!!! 1iftheinitialfavoritehadabyethepreviousweek

𝐵𝑦𝑒!,!!! 1iftheinitialunderdoghadabyethepreviousweek

WinningPercentageVariables

VariableName Description

𝑊𝑃_𝑁𝑜𝑡𝐼𝑛𝑐𝑙𝑢𝑑𝑖𝑛𝑔_𝐿3!,! InitialFavorite’sseasonwinningpercentage,not

includingthepastthreegamesminusInitial

Underdog’sseasonwinningpercentage,not

includingthepastthreegames

𝑊𝑃_𝐿3!,! InitialFavorite’swinningpercentageonlyincluding

thelastthreegamesminusinitialUnderdog’s

winningpercentageonlyincludingthelastthree

games

𝑊𝑃_𝑅𝑇𝑆_𝑁𝑜𝑡𝐼𝑛𝑐𝑙𝑢𝑑𝑖𝑛𝑔_𝐿3!,! InitialFavorite’sseasonwinningpercentagerelative

tothespread,notincludingthepastthreegames

minusinitialUnderdog’sseasonwinningpercentage

relativetothespread,notincludingthepastthree

games

𝑊𝑃_𝑅𝑇𝑆_𝐿3!,! InitialFavorite’swinningpercentagerelativetothe

spreadonlyincludingthelastthreegamesminus

initialUnderdog’swinningpercentagerelativetothe

43

spreadonlyincludingthelastthreegames

TeamStatisticVariables

VariableName Description

𝑃𝑎𝑠𝑠𝑖𝑛𝑔𝑌𝑎𝑟𝑑𝑠!,! Averagepassingyardspergameforinitialfavorite

minusthatoftheinitialunderdog

𝑅𝑢𝑠ℎ𝑖𝑛𝑔𝑌𝑎𝑟𝑑𝑠!,! Averagerushingyardspergameforinitialfavorite

minusthatoftheinitialunderdog

𝑌𝑎𝑟𝑑𝑠𝐴𝑙𝑙𝑜𝑤𝑒𝑑!,! Averageyardsallowedondefensepergamefor

initialfavoriteminusthatoftheinitialunderdog

𝑃𝑜𝑖𝑛𝑡𝑠𝐹𝑜𝑟!,! Averagepointsscoredpergamebytheinitial

favoriteminusthatoftheinitialunderdog

𝑃𝑜𝑖𝑛𝑡𝑠𝐴𝑔𝑎𝑖𝑛𝑠𝑡!,! Averagepointsgivenuppergamebytheinitial

favoriteminusthatoftheinitialunderdog

𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙!,! Averageturnoverdifferentialpergamefortheinitial

favoriteminusthatoftheinitialunderdog

GamblerSentimentVariables

VariableName Description

(𝐺𝑎𝑚𝑒 𝐷𝑎𝑦_1!,!!!− 𝐺𝑎𝑚𝑒 𝐷𝑎𝑦_1!,!!!)

RelativeGoogleSearchLeveloftheinitialfavorite

minusthatoftheunderdogmeasuredontheday

afterthepreviousweek’sgameday

(𝑊𝑒𝑒𝑘𝑙𝑦!,!!! −𝑊𝑒𝑒𝑘𝑙𝑦!,!!!) RelativeGoogleSearchLeveloftheinitialfavorite

minusthatoftheunderdogmeasuredontheday

afterthepreviousweek’sgameday