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PackageweloApril302021TitleWeightedandStandardEloRatesVersion010Descri


2bettingtennisprob6welo2t7wta20199Index11atp2019ATPmatchesin2019DescriptionTennisdataformalematchesplayedin2019Detailscanbefoundonhttp//wwwtennis-datacouk/notestxtUsagedataatp2019FormatAnobjectofclass

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1 Package`welo'April30,2021TitleWeightedan
Package`welo'April30,2021TitleWeightedandStandardEloRatesVersion0.1.0DescriptionEstimatesthestandardandweightedElo(WElo,An-gelinietal.,2021 oi:;.1;/;&#xj.ej;&#xor55;.2021.04.011)rates.Thecurrentversionpro-videstheseratesfortennis.Inthefuture,newsportswillbeadded.Thewelopackageof-fersaexibletooltoestimatetheWEloandElorates,accordingtodifferentsys-temsofweights(gamesorsets)andscalefactors(constant,proportionaltothenum-berofmatches,withmoreweightonGrandSlammatchesoronmatchesplayedonaspe-cicsurface).Moreover,thepackagegivesthepossibilityofestimatingthe(bootstrap)stan-darderrorsfortherates.Finally,thepackageincludesabettingfunctionwhichautomaticallyse-lectsthematchesonwhichplaceabet.LicenseGPL-3EncodingUTF-8LazyDatatrueRoxygenNote7.1.1RdMacrosRdpackDependsR oi:;.1;/;&#xj.ej;&#xor55;(=4.0.0),Importsxts oi:;.1;/;&#xj.ej;&#xor55;(=0.12.0),Rdpack oi:;.1;/;&#xj.ej;&#xor55;(=1.0.0),boot oi:;.1;/;&#xj.ej;&#xor55;(=1.3)Suggestsknitr,rmarkdownNeedsCompilationnoAuthorVincenzoCandila[aut,cre]MaintainerVincenzoCandilaÊnd;&#xilav;&#x@gma;&#xil.c;&#xo

2 m00;RepositoryCRANDate/Publication2021-0
m00;RepositoryCRANDate/Publication2021-04-3006:50:05UTCRtopicsdocumented:atp_2019..........................................2betting............................................2clean.............................................4random_betting.......................................51 2bettingtennis_prob.........................................6welot............................................7wta_2019..........................................9Index11 atp_2019ATPmatchesin2019 DescriptionTennisdataformalematchesplayedin2019.Detailscanbefoundonhttp://www.tennis-data.co.uk/notes.txtUsagedata(atp_2019)FormatAnobjectofclass"data.frame".SourceTennisarchivefromhttp://www.tennis-data.co.uk/Exampleshead(atp_2019)str(atp_2019) bettingBettingfunction DescriptionPlacesbetsusingtheWEloandEloprobabilities,onthebasisoftwothresholdsrandq,accordingtoAngelinietal.(2021).Bydefault,theamountof$1isplacedonthebestodds(thatis,thehighestoddsavailable)forplayeriforallthematcheswhereitholdsthat^Pi;j(t) qi;j(t)�r;where^Pi;j(t)istheestimatedprobability(comingfromtheWEloorElomodel)thatplayeriwinsthematchtagainstplayerjandqi;j(t)isitsimpliedpro

3 babilityobtainedastherecipricaloftheBet3
babilityobtainedastherecipricaloftheBet365odds.Theimpliedprobabilityqi;j(t)isassumedtobegreaterthanq.Ifq=0,alltheplayersareconsidered.Ifqincreases,heavylongshotplayersareexcluded.Ingeneral,higherthresholdsrandqimplylessbettingopportunities. betting3Usagebetting(x,r,q,model,bets="Best_odds",R=2000,alpha=0.1,start_oos=NULL,end_oos=NULL)ArgumentsxListincludingtheoddsandplayersiandjobtainedfromthewelofitfunctionrVectororscalaridentifyingthethresholdoftheratiobetweentheestimatedandtheimpliedprobability(seeabove)qScalarparameterusedtoexcludetheheavyunderdogssignalledbyBet365bookmaker.Nobetswillbeplacedonthosematcheswhereplayershaveim-pliedprobabilitiessmallerthanqmodelValidchoicesare:"WELO"and"ELO"betsoptionalParameteridentifyingonwhichtypeofoddsthebetisplaced.Defaultto"Best_odds".Validchoicesare:"Best_odds","Avg_odds"and"B365_odds"."Best_odds"arethehighestoddsavailable."Avg_odds"aretheaverageoddsforthatmatchand"B365_odds"aretheBet365oddsRoptionalNumberofbootstrapreplicatestocalculatethecondenceintervals.Defaultto2000alphaoptionalSignicancelevelfortheboostrapcondenceintervals.Defaultto0.1start_oosoptionalCharacterpar

4 ameterdenotingthestartingyearforthebets.
ameterdenotingthestartingyearforthebets.Ifincluded(defaulttoNULL),thenthebetswillbeplacedonmatchesstartinginthatyear.Ithastobeformattedas"yyyy"end_oosoptionalCharacterparameterdenotingtheendingyearforthebets.Ifincluded(defaulttoNULL),thenthebetswillbeplacedonmatchesincludedintheperiod"start_oos/end_oos".Ithastobeformattedas"yyyy"ValueAmatrixincludingthenumberofbetsplaced,theReturn-on-Investiment(ROI),expressedinper-centage,anditsboostrapcondenceinterval,calculatedusingRreplicatesandthesignicancelevel .Examplesdata(atp_2019) 4cleandb_clean()db_est()bets(())bets cleanCleaningfunction DescriptionCleansthedatasetinordertocreateasuitabledata.framereadytobeusedinthewelofitfunction.Usageclean(x,MNM=10,MRANK=500)ArgumentsxDatatobecleaned.Itmustbeadata.framecomingfromhttp://www.tennis-data.co.uk/.MNMoptionalMinimumnumberofmatchesplayedbyeachplayertoincludeinthecleaneddataset.Defaultto10.Thismeansthateachplayerhastoplayatleast10matchesMRANKoptionalMaximumrankoftheplayerstoconsider.Defaultto500.Thismeansthatallthematcheswithplayerswithranksgreaterthan500aredroppedDetailsThecleaningoperationsare:1.Removealltheuncompletedma

5 tches;2.RemovealltheNAsfromB365odds;3.Re
tches;2.RemovealltheNAsfromB365odds;3.RemovealltheNAsfromthevariable"ranking";4.RemovealltheNAsfromthevariable"games";5.RemovealltheNAsfromthevariable"sets";6.RemoveallthematcheswheretheB365oddsareequal;7.Deneplayersiandjandtheiroutcomes(YiandYj);8.RemoveallthematchesofplayerswhoplayedlessthanMNMmatches;9.RemoveallthematchesofplayerswithrankgreaterthanMRANK;10.Sortthematchesbydate.ValueData.framecleaned random_betting5Examplesdata(atp_2019)db_clean()str(db_clean) random_bettingRandombettingfunction DescriptionPlacesbetsonplayersiandjrandomlychosen,amongallthematchesselectedbythefollowingstrategy:bydefault,theamountof$1isplacedonthebestodds(thatis,thehighestoddsavailable)forplayeriforallthematcheswhereitholdsthat^Pi;j(t) qi;j(t)�r;where^Pi;j(t)istheestimatedprobability(comingfromtheWEloorElomodel)thatplayeriwinsthematchtagainstplayerjandqi;j(t)isitsimpliedprobabilityobtainedastherecipricaloftheBet365odds.Theimpliedprobabilityqi;j(t)isassumedtobegreaterthanq.Ifq=0,alltheplayersareconsidered.Ifqincreases,heavylongshotplayersareexcluded.Oncegotthenumberofmatchessatisfyingthepreviouslydescribedstrategy,eachplayer(ian

6 dj)onwhichplaceabetisrandomlyselected.Th
dj)onwhichplaceabetisrandomlyselected.ThentheROIofthisstrategyisstored.Finally,themeanoftheROIobtainedfromrepeatingthisoperationBtimesisreported.Usagerandom_betting(x,r,q,model,bets="Best_odds",B=10000,start_oos=NULL,end_oos=NULL,values="NO")ArgumentsxListincludingthebestoddsandtheplayersiandjobtainedfromthewelofitfunctionrVectororscalaridentifyingthethresholdoftheratiobetweentheestimatedandtheimpliedprobability(seeabove) 6tennis_probqScalarparameterusedtoexcludetheheavyunderdogssignalledbyB365book-maker.NobetswillbeplacedonthosematcheswhereplayershaveoddssmallerthanqmodelValidchoicesare:"WELO"and"ELO"betsoptionalParameteridentifyingonwhichtypeofoddsthebetisplaced.Defaultto"Best_odds".Validchoicesare:"Best_odds","Avg_odds"and"B365_odds"."Best_odds"arethehighestoddsavailable."Avg_odds"aretheaverageoddsand"B365_odds"aretheBet365oddsBoptionalNumberofreplicatestocalculatetheoverallmeanROI.Defaultto10000start_oosoptionalCharacterparameterdenotingthestartingyearforthebets.Ifincluded(defaulttoNULL),thenthebetswillbeplacedonmatchesstartinginthatyear.Ithastobeformattedas"yyyy"end_oosoptionalCharacterparameterdenotingtheendingyearfo

7 rthebets.Ifincluded(defaulttoNULL),thent
rthebets.Ifincluded(defaulttoNULL),thenthebetswillbeplacedonmatchesincludedintheperiod"start_oos/end_oos".Ithastobeformattedas"yyyy"valuesoptionalIfitis"YES",thenrandom_bettingreturnstheROIforeachreplicateB.Otherwise,itreturnstheaverage.Defaultto"NO"ValueBydefault,themeanoftheROI(inpercentage)acrosstheBvalues.Alternately,itreturnstheROIforeachBreplicate(settingparameter'values'to'YES')Examplesdata(atp_2019)db_clean()db_est()rand_bets(())rand_bets tennis_probProbabilityofwinning DescriptionCalculatestheprobabilitythatplayeriwinsoverplayerjformatchattimet+1usingtheWEloorEloratesattimet.Formally:^pi;j(t+1)=1 1+10(Ej(t)�Ei(t))=400;whereEi(t)andEj(t)aretheWEloorEloratesattimet. welot7Usagetennis_prob(i,j)ArgumentsiWEloorEloratesforplayerijWEloorEloratesforplayerjValueProbabilitythatplayeriwinsthematchagainstplayerjExamplestennis_prob(2000,2000)tennis_prob(2500,2000) welofitCalculatestheWEloandElorates DescriptionCalculatestheWEloandEloratesaccordingtoAngelinietal.(2021).Inparticular,theEloupdatingsystemdenestherates(forplayeri)as:Ei(t+1)=Ei(t)+Ki(t)[Wi(t)�^pi;j(t)];whereEi(t)istheElorateattimet,Wi(t)istheoutcome(1

8 or0)forplayeriinthematchattimet,Ki(t)isa
or0)forplayeriinthematchattimet,Ki(t)isascalefactor,and^pi;j(t)istheprobabilityofwinningformatchattimet,calculatedusingtennis_prob.ThescalefactorKi(t)determineshowmuchtherateschangeovertime.Bydefault,accordingtoKovalchik(2016),itisdenedasKi(t)=250=(Ni(t)+5)0:4;whereNi(t)isthenumberofmatchesdisputedbyplayeriuptotimet.Alternately,Ki(t)canbemultipliedby1.1ifthematchattimetisaGrandSlammatchorisplayedonagivensurface.Finally,itcanbexedtoaconstantvalue.TheWEloratingsystemisdenedas:Ei(t+1)=Ei(t)+Ki(t)Wi(t)�^pi;j(t)f(Wi;j(t));whereEi(t+1)denotestheWElorateforplayeri,^pi;j(t)theprobabilityofwinningusingtennis_probandtheWElorates,andf(Wi;j(t))representsafunctionwhosevaluesdependonthegames(bydefault)orsetswoninthepreviousmatch.Inparticular,whenparameter'W'issetto"GAMES",f(Wi;j(t))isdenedas:f(Wi;j(t))f(Gi;j(t))=(NGi(t) NGi(t)+NGj(t)ifplayerihaswonmatcht;NGj(t) NGi(t)+NGj(t)ifplayerihaslostmatcht; 8welotwhereNGi(t)andNGj(t)representthenumberofgameswonbyplayeriandplayerjinmatcht,respectively.Whenparameter'W'issetto"SET",f(Wi;j(t))is:f(Wi;j(t))f(Si;j(t))=(NSi(t) NSi(t)+NSj(t)ifp

9 layerihaswonmatcht;NSj(t) NSi(t)+NSj(t)i
layerihaswonmatcht;NSj(t) NSi(t)+NSj(t)ifplayerihaslostmatcht;whereNSi(t)andNSj(t)representthenumberofsetswonbyplayeriandplayerjinmatcht,respectively.ThescalefactorKi(t)isthesameastheElomodel.Usagewelofit(x,W="GAMES",SP=1500,K="Kovalchik",CI=FALSE,alpha=0.05,B=1000,new_data=NULL)ArgumentsxDatacleanedthroughthefunctioncleanor,iftheparameter'new_data'ispresent,aformerestimatedlistcomingfromthewelofitfunctionWoptionalWeightstousefortheWEloratingsystem.Validchoicesare:"GAMES"(bydefault)and"SETS"SPoptionalStartingpointsforcalculatingtherates.1500bydefaultKoptionalScalefactordetermininghowmuchtheWEloandElorateschangeovertime.Validchoicesare:"Kovalchik"(bydefault),"Grand_Slam","Sur-face_Hard","Surface_Grass","Surface_Clay"and,nally,aconstantvalueK.Therstoption("Kovalchik")isequaltowhatwassuggestedbyKovalchik(2016),PuttingKto"Grand_Slam"letsthescalefactorequaltotherstop-tion,withthedifferencethateachGrandSlammatchismultipliedby1.1.Sim-ilarly,thechoices"Surface_Hard","Surface_Grass"and"Surface_Clay"makethescalefactorequaltotherstoptionbut,incaseofamatchdisputedonhard,grassorclay,respectively,thescalefactorincreasesb

10 y1.1.Finally,itcanbeanyscalarvalueK.Inth
y1.1.Finally,itcanbeanyscalarvalueK.Inthiscase,thescalefactorisconstant,indipendentlyofthenumberofmatchesplayedbeforethematchtCIoptionalCondenceintervalsfortheWEloandElorates.DefaulttoFALSE.If'CI'issetto"TRUE",thenthecondenceintervalsarecalculated,accordingtotheprocedureexplainedbyAngelinietal.(2021)alphaoptionalSignicancelevelofthecondenceinterval.Defaultto0.05BoptionalNumberofbootstrapsamplesusedtocalculatethecondenceinter-vals.Defaultto1000new_dataoptionalNewdata,cleanedthroughthefunctionclean,toappendtoanalreadyestimatedsetofmatches(includedintheparameter'x') wta_20199Valuewelofitreturnsanlistcontainingthefollowingcomponents:•results:Thedata.frameincludingavarietyofvariables,amongwhichtherearetheestimatedWEloandElorates('WElo_i','WElo_j','Elo_i'and'Elo_j',respectively),theirloweranduppercondenceintervals(ifCI=TRUE),labelledas'_lb'and'_ub',respectively,andtheprobabilityofwinningthematchforplayeri(labelledas'WElo_pi_hat'and'Elo_pi_hat',respectively,fortheWEloandElomodels).•matches:Thenumberofmatchesanalyzed.•period:Thesampleperiodconsidered.•loss:TheBrierscore(Brier1950)andlog-

11 loss(usedbyKovalchik(2016),amongothers)a
loss(usedbyKovalchik(2016),amongothers)averages,calculatedconsideringthedistancewithrespecttotheoutcomeofthematch.•highest_welo:TheplayerwiththehighestWElorateandtherelativedate.•highest_elo:TheplayerwiththehighestElorateandtherelativedate.•dataset:ThedatasetusedfortheestimationoftheWEloandElorates.ReferencesAngeliniG,CandilaV,DeAngelisL(2021).“WeightedEloratingfortennismatchpredictions.”EuropeanJournalofOperationalResearch.BrierGW(1950).“Vericationofforecastsexpressedintermsofprobability.”Monthlyweatherreview,78(1),1–3.KovalchikSA(2016).“SearchingfortheGOAToftenniswinprediction.”JournalofQuantitativeAnalysisinSports,12(3),127–138.Examplesdata(atp_2019)db_clean()res() wta_2019WTAmatchesin2019 DescriptionTennisdataforfemalematchesplayedin2019.Detailscanbefoundonhttp://www.tennis-data.co.uk/notes.txtUsagedata(wta_2019) 10wta_2019FormatAnobjectofclass"data.frame".SourceTennisarchivefromhttp://www.tennis-data.co.uk/Exampleshead(wta_2019)str(wta_2019) Indexdatasetsatp_2019,2wta_2019,9atp_2019,2betting,2clean,4,8random_betting,5tennis_prob,6,7welofit,3–5,7,8wta_