AbdullahAlsaeed,CamGibsonChesnutt StanfordUniversity,STATS50 May24,2016

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VALUINGGOALS,SAVESANDDUELSINSOCCER

INTRODUCTIONSoccerconstitutesthelargestmajorityinglobalmarketshareat43%,followedbyAmericanfootballat13%andbaseballat12%1.Thus,puttingdollaramountsoncertainactions in soccer isquiteuseful for investorsandgamblersalike.Inthisreport,wetrytovaluecertainactionsinsoccer.Someofthequestionswetrytoanswerare:Howmuchisscoringagoalworth?Howmuchissavingagoalworth?Howmuchiswinningaone-on-oneduelworth?Thesequestionsmayhelpteamsbettervaluecertainactionsandhenceamplifythosethatareworththemost.Toanswerthesequestions,weanalyzegamedataforthe2011-2012seasonofthePremierLeague,aswellaswagedata.WethengeneralizeourfindingsforacompletePremierLeagueseasontoanalyzethevalueofplayerperformanceinlaterseasons,aswellasinothercompetitions.

DATA Opta Sports, a London-based sports data company, produced thedatasetused in the analysis. ThedatasetcontainedOpta’sClassicDatafeedfromthe2011-2012EnglishPremierLeagueseason,andeachrowofthedatasetconsistsofanindividual’sstatisticsinasinglegame.Thedatasetcontains184columnsofdata,allowingforextensiveanalysisofallaspectsofasoccerplayer’sperformance2. OptaSportshasspecificeventdefinitionsthatcorrespondtothestatisticsseeninourdataset.Thefollowingeventswereusedinouranalysis:

GOALS:Goalswereusedtoassestheperformanceofstrikersinourdataset.Overallshotfrequency,ontargetandoff targetwasalsoused. Itwasassumedthatthesolepurposeofstrikers is toscoregoals,although inreality,theycouldhaveotherparallelrolessuchasplaymakingandwithdrawingdefenders.

DUELS:Aduelisa50-50contestbetweentwoplayersofopposingsidesinthematch.Foreveryduelwon,thereisacorrespondingduellostdependingontheoutcome.Wechoosethismetricfordefendersovertackles.Atackleisawardedifaplayerwinstheballfromanotherplayerwhoisinpossession.Wedecidedthatduelsareabettermetricfordefendersbecausesomegreatdefendersneverstealtheballfromtheopponents,butexcelbybeingingoodpositionsandwinningtheimportantduelstheymustwintopreventattacksfromresultingingoals.

SAVE:Agoalkeeperpreventingtheballfromenteringthegoalwithanypartofhisbody.Goalkeepershavethesmallestsubsetofstatisticsthatpertaintothemsosaveswereusedastheonlymetricforgoalkeepersintheanalysis.

Inadditiontothegamedata,allmonetaryvaluesusedaresourcedfromtransfermarkt.com.Throughouttheanalysis,marketvalueoftheplayer isusedtodetermineaplayer’smonetaryworth,specificallythemarketvalueofthegivenplayerinJune2012,attheendofthe2012EnglishPremierLeagueseason.

1https://www.atkearney.com/documents/10192/6f46b880-f8d1-4909-9960-cc605bb1ff342https://datahub.io/dataset/uk-premier-league-match-by-match-2011-2012

AbdullahAlsaeed,CamGibsonChesnutt StanfordUniversity,STATS50 May24,2016

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METHODSWhenevaluatingplayers,regressiontothemean(RTTM)wasusedtodetermineaplayer’struetalentcomparedto the observed statistic.When evaluating players as possible transfer acquisitions in a competitive soccerleague,webelieveitisimportanttoconsideratruetalentmetricthataccountsfortheobservedstatisticsofallsoccerplayers’intheEnglishPremierLeague.Sometimespureobservedpercentagecanbemisleading,andtoaccountforthis,wesubsetthedatatoincludeonlythemostactiveplayersateachpositionandfurthermore,regresstowardsthemeantodetermineaplayer’struetalentcomparedtotherestoftheplayersintheleagueatthesameposition.AllbasicanalysiswasdoneinR.

RESULTS Theresultofouranalysisisdecomposedbyposition.Keyactionsofstrikers,defendersandgoalkeeperswillbeassessedandcomparedtoeachotherintheirvalues.

STRIKERSFromatop-downapproach,theaimofanyteaminasoccermatchistowin,andateammaynotwinunlesstheyscoreatleastonegoal.Thus,itisevidenttoputavalueongoals,assomestrikercontractsinvolveclausesforanextrabonusforeachgoalscored.Sincemostgoalsarescoredbystrikers,onlyplayersinsuchpositionwereconsideredinthisanalysiswiththeobjectivetoputavalueonanygoalscored.However,anotherthesisistocorrelateplayerwageswiththeirshotaccuracy.Whenweplotthemarketvalueofthestrikerswithmorethan30shotsintheseasonversustheirgoalcountandshotaccuracy,wegetthefollowinggraphs:

From the graphs above,we calculated a correlation of 0.128 betweenmarket value and shot accuracy, orconversionrate,butobtainedacorrelationof0.677betweenmarketvalueandgoalsscoredperseason.Onemayarguethatplayersthatarehighlypaidaremorelikelytobeinbetterteamsthathavebetterplaymakers,andhencefinditeasiertoscoregoals.However,thisisasecondaryfactorinthecorrelationbetweenwages

AbdullahAlsaeed,CamGibsonChesnutt StanfordUniversity,STATS50 May24,2016

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andgoalsscored,asthemostdirectfactoristheinherentaddedvalueofscoringgoals.Sincegoalsscoredwasestablishedasabetterpredictorofmarketvalue,weplottedtheamountofmoneyinmarketvaluepergoalscored,andobtainedthefollowingprofile:

Themarketvalueofagoal inthePremierLeagueseasonof2011-2012wasfoundtobe1.562meuros.Thisfigurewasclosetootherestimatesintheliterature.Onestudydividedeachclub’sannualincomebythenumberofgoalstheclubscoredasameasureofthevalueofonegoal.Theaveragefigurereportedforthe2011-2012PremierLeagueseasonwas1.182meuros,whichisintherangeofourestimatehere3.

GOALKEEPERSOntheothersideofthepostlaygoalkeepers.Unlikestrikers,goalkeepershavemoredefinedroles,andasinglepurpose:Tonotletgoalsgoin.Toassesstheirbestperformanceindicator,wetestedthecorrelationbetweenthemarketvalueofgoalkeepersthathaveplayedmorethan180minutesandafewmetrics,whichareoutlinedinthetablebelow:

Performanceindicator Correlationtomarketvalue

Savesperseason 0.301

Savepercentage 0.183

SaveTalent4 0.257

3 http://www.sportingintelligence.com/2014/02/24/premier-league-goals-worth-915k-each-last-season-and-1-5m-now-240201/4 Calculated using the RTTM method outlined in the methods section

Helguson

Kev

in D

avie

sHolt

Saha

Graham

Morison

Yakubu

Bellamy

Fletcher

Di S

anto

Odemwingie

Long

Crouch

Zamora

Walters

Defoe Ba

Bendtner

Drogba

Doyle

Hernandez

Sturridge

Cisse

Adebayor

van

Per

sie

Welbeck

Dzeko

Aguero

Bent

Rodallega

Agbonlahor

Rooney

Balotelli

Suarez

Gervinho

Carroll

Torres

Mata

Million Euros in market value per goals scored

0

1

2

3

4

5

6

AbdullahAlsaeed,CamGibsonChesnutt StanfordUniversity,STATS50 May24,2016

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Thebestmetrictocorrelatewithgoalkeeperwageswastheirsavesperseason,outoftheonestested,althoughthecorrelationisprettylow.Giventhisinformation,wealsoassessthevalueofasaveusingthesamemethodasbefore.Wethenobtainthefollowingdistributionforthesubsetofgoalkeepersconsidered:

Fromthedistributionabove,wenoticeaninterestingdistinctionbetweengoalkeepersofthe“BigFive”inthepremierleague,andothers.Removinggoalkeepersofthe“BigFive5”,weobtainthefollowingcorrelations:

Performanceindicator

Correlationtomarketvalue

Correlationtomarketvaluewithout“BigFive”goalkeepers

Savesperseason 0.301 0.678

Savepercentage 0.183 0.183

SaveTalent 0.257 0.209

Aswecansee,thecorrelationtothevalueofsavesperseasonismuchbetterwhenweremovegoalkeepersofthe“BigFive.”Using thedistributionabove,weobtainameanmarketvalueper saveof212,000euros forgoalkeepers of the “Big Five”, and amean of 47,000 euros for goalkeepers of other teams,with standarddeviationsof46,000eurosand24,000eurosrespectively.Theestimatemakesscoringagoalworthabout15timessavingagoal,whichisanindicationoftheinherentfavorabilityofstrikersovergoalkeepersinsoccer.

5 Man United, Man City, Liverpool, Arsenal, Chelsea

Friedel

Kenny

Schwarzer

Cerny

Given

Ruddy

Hennessey

Foster

Al-Habsi

Howard

Begovic

Mignolet

Westwood

Vorm

Doni

de V

ries

Krul

Bunn

Stockdale

Guzan

Szczesny

De

Gea

Reina

Hart

Lindegaard

Cech

Euros in market value per goals saved

0

50000

100000

150000

200000

250000

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Althoughassessinggoalkeepers’performanceusing their savecountmayseemreasonable, severalanalystshave actually challengedusing thismetric. Someanalysis quantified the contributionof the quality of shotreceivedtohavethemostimpactonsavepercentage,andgoalkeeperperformance6.

DEFENDERSWhenevaluatingdefenders,multiplemetricscouldbeusedtorateadefenderasOptadatagivesfanstackles,duels,passes,andblocksamongotherstatisticsfordefenders.However,throughexperimentationwiththesevariousmetrics,itwasdeterminedthattheduelwinpercentage,calculatedby(duelswon/totalduels)gavetheclearestseparationinratingthetopdefenders.

Theabovegraphshowsmarketvalueversusgoalsforthemostactivedefendersinthe2011-2012EPLseason,thatis,defenderswhoplayedin12gamesandwonover125duels.Whenlookingatdefendersintheanalysisthatarevaluedinthetransfermarketatover15,000,000,onenoticesthatoftheseplayers:Ivanovic,Skrtel,Terry,Koscielny,Sagna,Vermaelen,Jones,Richards,Walker,Clichy,Evra,Kaboul,onlyYounesKabouldoesnotcomefromthetraditional“BigFive”clubsinEnglishFootball(Arsenal,Liverpool,ManchesterCity,ManchesterUnited,andChelsea).Thisdemonstratesthatthe“BigFive”clubs inEnglishFootballarewillingtopay large

6http://11tegen11.net/2014/02/03/never-judge-a-goal-keeper-by-his-saves/

0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68

510

1520

Defender Talent vs. Market Value

Duel Win Percentage Talent

Mar

ket V

alue

(Mill

ions

of E

uros

)

Huth

Warnock

Evra

Hangeland

Hutton

Vermaelen

Terry

Clichy

Dunne

BerraWilliams

McAuley

Richards

Jos_ Enrique

Skrtel

Assou-Ekotto

Wilson

Figueroa

Kaboul

Sagna

Cole

Jonas Olsson

John Arne Riise

Ivanovic

Rangel

Taylor

Naughton

Koscielny

Walker

Jones

Jagielka

Coloccini

Johnson

Collins

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amounts for themostactivedefenders in the leagueandholdwhomostmajorclubsdeemtobethemostvaluabledefenders.

However,theregressiontothemeananalysisdemonstratesthathigh-paiddefendersarenotnecessarilythemosteffectiveortalentedinoneononeduelsbecauseonlyfiveofthetenhighestpaiddefendersfallaspartofthe top ten talented defenders in the analysis. The bottom-right quadrant of the graph reveals high valuedefendersbecausethesedefendersare,accordingtoourmodel,activebecausetheyhavewonahighnumberofduels,talentedbasedonthepercentageofduelswon,andcostafractionoftheamountinsalaryassomeofthehighestpaiddefenders.Themodeldemonstratesthatthefollowingfiveplayersarethemosthigh-valueddefendersinthe2011-2012EPLseason:McAuley,Jagielka,Figueroa,Hangeland,andRobertHuth.Thisanalysiscouldbeusedbymid-tableclubswhomaywanttospendmoneyonatopdefender,butarenotwillingtospendasmuchmoneyasthe“BigFive”clubsdoinEngland.

In professional soccer, particularlywith defenders, themedia plays a large role in rating players since thepositionhasveryfewavailablestatisticalmethodsforplayerevaluations.ArecentarticleintheLiverpoolechoentitled,“PhilJagielkaandthestatsthatprovehe’sEngland’smostvaluabledefender,”claimsthatinthe2015-2016 season, Jagielka ranked top two in four of the five key areas of defending (tackles, interceptions,clearances,blocks,andduels).AlthoughJagielkawasarelativelylow-profiledefenderinthe2011-2012season,usingthisanalysisafterthe2011-2012seasonwouldhaveresultedinsigningPhilJagielka,aplayerwhohasdevelopedintooneofthebestandmostconsistentdefendersintheEnglishPlayerLeague.

Thevalueofwinningaduelinthe2011-2012seasonpaidtothemostactivedefenderswas70,000euroswithastandarddeviationof43,000euros.Again,thelargestandarddeviationrelativetothemeandollaramountpaidtothemostactivedefendersinEnglishFootballdemonstratesthatagainandmoresothanthepreviousgraph,thehighsalariespaidbythe“BigFive”clubsinEnglishFootballcreatesahugediscrepancyinthewage

McAuley

Dunne

Figueroa

Warnock

Jona

s O

lsso

nRangel

Naughton

Berra

Williams

John

Arn

e R

iise

Wilson

Collins

Hutton

Taylor

Hangeland

Huth

Coloccini

Evra

Kaboul

Johnson

Jos_

Enr

ique

Walker

Assou-Ekotto

Jagielka

Cole

Koscielny

Clichy

Skrtel

Jones

Richards

Terry

Vermaelen

Sagna

Ivanovic

Euros Paid per Duel

Val

ue (E

uros

in T

hous

ands

)

0

50

100

150

AbdullahAlsaeed,CamGibsonChesnutt StanfordUniversity,STATS50 May24,2016

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data.Forexample,whenlookingatthedollaramountpaidforduelswon,thetop9playersinthismetricallcomefrom“BigFive”clubs,againsupportingtheideathatthe“BigFive”clubsarewillingtospendmoremoneythan other clubs for these important metrics. However, this analysis demonstrates that people are notnecessarilypayingforthebestdefendersbecauserelativelytwocheapdefenders,McAuleyandJagielka,rankhighestinouranalysisoftalent.

CONCLUSIONS The “Big Five” clubs in English Football arewilling to spend andoften overspendon themajormetrics forforwards,defenders,andgoalkeepersthatweidentifiedinourstudy.Thehighestsalariesarepaidbythese“BigFive”clubs,however,whenexaminingmetricssuchastalentvs.wageandthedollaramountpaidperacertainstatistic,onenoticesthatoftenthehighestpaidplayersdonotprovidethemostvalueforteams.Whilethe“BigFive”clubsinEnglishFootballarelikelytocontinuespendinginordinateamountonsalaries,smallerclubscanusetalentandwageanalysistoidentifytalentedplayerswhoareunderpaidandcantargettheseplayersinthetransfermarketwhenlookingforhigh-valuedplayers.

Evaluatingplayerspendinginthelast5yearsbyteamsintheEnglishPremierLeagueoverwhelminglysupportsourhypothesisthattheseBigFiveteamsarewillingtooutspendotherclubsonindividualstatistics.ThechartbelowshowsthespendingbyclubsinEnglishFootball.Noticethedrop-offafterthe5thteam.Arsenal(the5thteaminNetSpending)spendsmorethandoublewhatthesixthteamintheleaguehasspentonplayersoverthelast5years.

# Team MoneySpentonPlayerPurchasesLast5Years

1 ManchesterCity £472,800,000.00

2 ManchesterUnited £432,700,000.00

3 Chelsea £475,959,000.00

4 Liverpool £354,100,000.00

5 Arsenal £258,625,000.00

6 WestHam £120,600,000.00

Ouranalysisshowsthatagoalis18timesmorevaluablethanasaveandagoalis21timesmorevaluablethanadefenderduel.Asdescribedinthestrikersandgoalkeeperssectionofthepaper,actioncountcorrelatesbetterwithmarketvaluethanskilllevelforbothgoal-scoringandgoal-saving.However,withwinningduelsweseeverylowcorrelation(0.2)withmarketvalueversusplayertalentandanevenlowercorrelationwhenconsideringaction count. This makes sense when considering the description of the positions.While goalkeepers andforwardsareprimarily taskedwith savingand scoringgoals respectively,defendersareasked towinduels,tackle,completepasses,andforoutsidebacks,getforwardintotheattack.Sinceweareconsideringoutsidebacksandcenterbackswithinthedefenderscategory,thelowcorrelationisnotsurprisingduetothevarianceandrangeoftaskrequiredbytheposition.