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ArpadElo,theinventoroftheEloratingsystem
EloratingsystemFromWikipedia,thefreeencyclopedia
TheEloratingsystemisamethodforcalculatingtherelativeskilllevelsofplayersincompetitorversuscompetitorgamessuchaschess.ItisnamedafteritscreatorArpadElo,aHungarianbornAmericanphysicsprofessor.
TheElosystemwasoriginallyinventedasanimprovedchessratingsystembutisalsousedasaratingsystemformultiplayercompetitioninanumberofvideogames,[1]associationfootball,gridironfootball,basketball,[2]MajorLeagueBaseball,competitiveprogramming,Magic:TheGathering,esports,andothergames.
Thedifferenceintheratingsbetweentwoplayersservesasapredictoroftheoutcomeofamatch.Twoplayerswithequalratingswhoplayagainsteachotherareexpectedtoscoreanequalnumberofwins.Aplayerwhoseratingis100pointsgreaterthantheiropponent'sisexpectedtoscore64%ifthedifferenceis200points,thentheexpectedscoreforthestrongerplayeris76%.
Aplayer'sEloratingisrepresentedbyanumberwhichincreasesordecreasesbasedupontheoutcomeofgamesbetweenratedplayers.Aftereverygame,thewinningplayertakespointsfromthelosingone.Thedifferencebetweentheratingsofthewinnerandloserdeterminesthetotalnumberofpointsgainedorlostafteragame.Inaseriesofgamesbetweenahighratedplayerandalowratedplayer,thehighratedplayerisexpectedtoscoremorewins.Ifthehighratedplayerwins,thenonlyafewratingpointswillbetakenfromthelowratedplayer.However,ifthelowerratedplayerscoresanupsetwin,manyratingpointswillbetransferred.Thelowerratedplayerwillalsogainafewpointsfromthehigherratedplayerintheeventofadraw.Thismeansthatthisratingsystemisselfcorrecting.Aplayerwhoseratingistoolowshould,inthelongrun,dobetterthantheratingsystempredicts,andthusgainratingpointsuntiltheratingreflectstheirtrueplayingstrength.
Contents
1History1.1ImplementingElo'sscheme
2Differentratingssystems2.1FIDEratings
2.1.1Performancerating2.1.2FIDEtournamentcategories
2.2Liveratings2.3UnitedStatesChessFederationratings
2.3.1TheKfactorusedbytheUSCF2.3.2Ratingfloors
2.4Ratingsofcomputers3Theory
3.1Mathematicaldetails
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3.1Mathematicaldetails3.2Mathematicalissues
3.2.1Mostaccuratedistributionmodel3.2.2MostaccurateKfactor
4Practicalissues4.1Gameactivityversusprotectingone'srating4.2Selectivepairing4.3Ratingsinflationanddeflation
4.3.1Combattingdeflation5Useoutsideofchess
5.1Useoutsideofgaming6Referencesinthemedia7References8Furtherreading9Externallinks
History
ArpadElowasamasterlevelchessplayerandanactiveparticipantintheUnitedStatesChessFederation(USCF)fromitsfoundingin1939.[3]TheUSCFusedanumericalratingssystem,devisedbyKennethHarkness,toallowmemberstotracktheirindividualprogressintermsotherthantournamentwinsandlosses.TheHarknesssystemwasreasonablyfair,butinsomecircumstancesgaverisetoratingswhichmanyobserversconsideredinaccurate.OnbehalfoftheUSCF,Elodevisedanewsystemwithamoresoundstatisticalbasis.
Elo'ssystemreplacedearliersystemsofcompetitiverewardswithasystembasedonstatisticalestimation.Ratingsystemsformanysportsawardpointsinaccordancewithsubjectiveevaluationsofthe'greatness'ofcertainachievements.Forexample,winninganimportantgolftournamentmightbeworthanarbitrarilychosenfivetimesasmanypointsaswinningalessertournament.
Astatisticalendeavor,bycontrast,usesamodelthatrelatesthegameresultstounderlyingvariablesrepresentingtheabilityofeachplayer.
Elo'scentralassumptionwasthatthechessperformanceofeachplayerineachgameisanormallydistributedrandomvariable.Althoughaplayermightperformsignificantlybetterorworsefromonegametothenext,Eloassumedthatthemeanvalueoftheperformancesofanygivenplayerchangesonlyslowlyovertime.Elothoughtofaplayer'strueskillasthemeanofthatplayer'sperformancerandomvariable.
Afurtherassumptionisnecessary,becausechessperformanceintheabovesenseisstillnotmeasurable.Onecannotlookatasequenceofmovesandsay,"Thatperformanceis2039."Performancecanonlybeinferredfromwins,drawsandlosses.Therefore,ifaplayerwinsagame,heisassumedtohaveperformedatahigherlevelthanhisopponentforthatgame.Converselyifheloses,heisassumedtohaveperformedatalowerlevel.Ifthegameisadraw,thetwoplayersareassumedtohaveperformedatnearlythesamelevel.
Elodidnotspecifyexactlyhowclosetwoperformancesoughttobetoresultinadrawasopposedtoawinorloss.Andwhilehethoughtitislikelythateachplayermighthaveadifferentstandarddeviationtohisperformance,hemadeasimplifyingassumptiontothecontrary.
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Tosimplifycomputationevenfurther,Eloproposedastraightforwardmethodofestimatingthevariablesinhismodel(i.e.thetrueskillofeachplayer).Onecouldcalculaterelativelyeasily,fromtables,howmanygamesaplayerwouldbeexpectedtowinbasedonacomparisonofhisratingtotheratingsofhisopponents.Ifaplayerwonmoregamesthanexpected,hisratingwouldbeadjustedupward,whileifhewonfewerthanexpectedhisratingwouldbeadjusteddownward.Moreover,thatadjustmentwastobeinexactlinearproportiontothenumberofwinsbywhichtheplayerhadexceededorfallenshortofhisexpectednumber.
Fromamodernperspective,Elo'ssimplifyingassumptionsarenotnecessarybecausecomputingpowerisinexpensiveandwidelyavailable.Moreover,evenwithinthesimplifiedmodel,moreefficientestimationtechniquesarewellknown.Severalpeople,mostnotablyMarkGlickman,haveproposedusingmoresophisticatedstatisticalmachinerytoestimatethesamevariables.Ontheotherhand,thecomputationalsimplicityoftheElosystemhasproventobeoneofitsgreatestassets.Withtheaidofapocketcalculator,aninformedchesscompetitorcancalculatetowithinonepointwhathisnextofficiallypublishedratingwillbe,whichhelpspromoteaperceptionthattheratingsarefair.
ImplementingElo'sscheme
TheUSCFimplementedElo'ssuggestionsin1960,[4]andthesystemquicklygainedrecognitionasbeingbothmorefairandaccuratethantheHarknessratingsystem.Elo'ssystemwasadoptedbytheWorldChessFederation(FIDE)in1970.ElodescribedhisworkinsomedetailinthebookTheRatingofChessplayers,PastandPresent,publishedin1978.
Subsequentstatisticaltestshavesuggestedthatchessperformanceisalmostcertainlynotdistributedasanormaldistribution,asweakerplayershavegreaterwinningchancesthanElo'smodelpredicts."Whatistheelosystem"(http://tellyousomething.com/index.php/2015/07/08/whatistheelosystem/).Therefore,theUSCFandsomechesssitesuseaformulabasedonthelogisticdistribution.Significantstatisticalanomalieshavealsobeenfoundwhenusingthelogisticdistributioninchess.[5]FIDEcontinuestousetheratingdifferencetableasproposedbyElo.ThetableiscalculatedwithExpectation0,andstandarddeviation2000/7.
Thenormalandlogisticdistributionpointsare,inaway,arbitrarypointsinaspectrumofdistributionswhichwouldworkwell.Inpractice,bothofthesedistributionsworkverywellforanumberofdifferentgames.
Differentratingssystems
Thephrase"Elorating"isoftenusedtomeanaplayer'schessratingascalculatedbyFIDE.However,thisusageisconfusingandmisleading,becauseElo'sgeneralideashavebeenadoptedbymanyorganizations,includingtheUSCF(beforeFIDE),theInternetChessClub(ICC),FreeInternetChessServer(FICS),Yahoo!Games,andthenowdefunctProfessionalChessAssociation(PCA).Eachorganizationhasauniqueimplementation,andnoneofthemfollowsElo'soriginalsuggestionsprecisely.ItwouldbemoreaccuratetorefertoalloftheaboveratingsasEloratings,andnoneofthemastheElorating.
Insteadonemayrefertotheorganizationgrantingtherating,e.g."AsofAugust2002,GregoryKaidanovhadaFIDEratingof2638andaUSCFratingof2742."ItshouldbenotedthattheEloratingsofthesevariousorganizationsarenotalwaysdirectlycomparable.Forexample,someonewithaFIDEratingof
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2500willgenerallyhaveaUSCFratingnear2600andanICCratingintherangeof2500to3100.OnFICS,thecommand"tellsurveybotratingsfideestimate"givesaFIDEratingestimatebasedontheuser'sFICSrating.
FIDEratings
Seealso:FIDEWorldRankings
Fortopplayers,themostimportantratingistheirFIDErating.SinceJuly2012,FIDEissuesaratingslistonceeverymonth.
ThefollowinganalysisoftheJuly2015FIDEratinglistgivesaroughimpressionofwhatagivenFIDEratingmeans:
5323playershadanactiveratingintherange2200to2299,whichisusuallyassociatedwiththeCandidateMastertitle.2869playershadanactiveratingintherange2300to2399,whichisusuallyassociatedwiththeFIDEMastertitle.1420playershadanactiveratingbetween2400and2499,mostofwhomhadeithertheInternationalMasterortheInternationalGrandmastertitle.542playershadanactiveratingbetween2500and2599,mostofwhomhadtheInternationalGrandmastertitle.187playershadanactiveratingbetween2600and2699,allofwhomhadtheInternationalGrandmastertitle.40playershadanactiveratingbetween2700and2799.4activeplayershadaratingover2800:MagnusCarlsen,VeselinTopalov,ViswanathanAnand,andHikaruNakamura.
November2011markedthefirsttimefiveplayershadaratingof2800orhigher.ThehighesteverFIDEratingwas2882,whichMagnusCarlsenhadontheMay2014list.AlistofthehighestratedplayerseverisatComparisonoftopchessplayersthroughouthistory.
Performancerating
Performanceratingisahypotheticalratingthatwouldresultfromthegamesofasingleeventonly.Somechessorganizationsusethe"algorithmof400"tocalculateperformancerating.Accordingtothisalgorithm,performanceratingforaneventiscalculatedbytaking(1)theratingofeachplayerbeatenandadding400,(2)theratingofeachplayerlosttoandsubtracting400,(3)theratingofeachplayerdrawn,and(4)summingthesefiguresanddividingbythenumberofgamesplayed.Example:2Wins,2Losses
Thiscanbeexpressedbythefollowingformula:
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1.00 +8000.99 +6770.9 +3660.8 +2400.7 +1490.6 +720.5 00.4 720.3 1490.2 2400.1 3660.01 6770.00 800
Example:IfyoubeataplayerwithanEloratingof1000,
IfyoubeattwoplayerswithEloratingsof1000,
Ifyoudraw,
Thisisasimplification,becauseitdoesn'ttakeaccountofKfactors(thisfactorisexplainedfurtherbelow),butitoffersaneasywaytogetanestimateofPR(performancerating).
FIDE,however,calculatesperformanceratingbymeansoftheformula:Opponents'RatingAverage+RatingDifference.RatingDifference isbasedonaplayer'stournamentpercentagescore ,whichisthenusedasthekeyinalookuptablewhere issimplythenumberofpointsscoreddividedbythenumberofgamesplayed.Notethat,incaseofaperfectornoscore is800.ThefulltablecanbefoundintheFIDEhandbook,B.PermanentCommissions1.0.Requirementsforthetitlesdesignatedin0.31,1.48(https://www.fide.com/component/handbook/?id=174&view=article)online.Asimplifiedversionofthistableisontheright.
FIDEtournamentcategories
FIDEclassifiestournamentsintocategoriesaccordingtotheaverageratingoftheplayers.Eachcategoryis25ratingpointswide.Category1isforanaverageratingof2251to2275,category2is2276to2300,etc.Forwomen'stournaments,thecategoriesare200ratingpointslower,soaCategory1isanaverageratingof2051to2075,etc.[6]Thehighestratedtournamenthasbeencategory23,withanaveragefrom2801to2825.Thetopcategoriesareinthetable.
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CategoryAveragerating
Minimum Maximum14 2576 260015 2601 262516 2626 265017 2651 267518 2676 270019 2701 272520 2726 275021 2751 277522 2776 280023 2801 2825
Liveratings
FIDEupdatesitsratingslistatthebeginningofeachmonth.Incontrast,theunofficial"Liveratings"calculatethechangeinplayers'ratingsaftereverygame.TheseLiveratingsarebasedonthepreviouslypublishedFIDEratings,soaplayer'sLiveratingisintendedtocorrespondtowhattheFIDEratingwouldbeifFIDEweretoissueanewlistthatday.
AlthoughLiveratingsareunofficial,interestaroseinLiveratingsinAugust/September2008whenfivedifferentplayerstookthe"Live"No.1ranking.[7]
Theunofficialliveratingsofplayersover2700werepublishedandmaintainedbyHansArildRundeattheLiveRatingwebsite(http://chess.liverating.org)untilAugust2011.Anotherwebsitewww.2700chess.com(http://www.2700chess.com)hasbeenmaintainedsinceMay2011byArtiomTsepotan,whichcoversthetop100playersaswellasthetop50femaleplayers.
Currently,theNo.1spotinboththeofficialFIDEratinglistandtheliveratinglististakenbyMagnusCarlsen.
UnitedStatesChessFederationratings
TheUnitedStatesChessFederation(USCF)usesitsownclassificationofplayers:[8]
2400andabove:SeniorMaster22002399:NationalMaster
22002399plus300gamesabove2200:OriginalLifeMaster[9]20002199:Expert18001999:ClassA16001799:ClassB14001599:ClassC12001399:ClassD
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10001199:ClassE800999:ClassF600799:ClassG400599:ClassH200399:ClassI0199:ClassJ
Ingeneral,abeginnerisaround800,amidlevelplayerisaround1600,andaprofessional,around2400.In2007,themedianratingofallUSCFmemberswas657.[10]
TheKfactorusedbytheUSCF
TheKfactor,intheUSCFratingsystem,canbeestimatedbydividing800bytheeffectivenumberofgamesaplayer'sratingisbasedon(Ne)plusthenumberofgamestheplayercompletedinatournament
(m).[11]
Ratingfloors
TheUSCFmaintainsanabsoluteratingfloorof100forallratings.Thus,nomembercanhavearatingbelow100,nomattertheirperformanceatUSCFsanctionedevents.However,playerscanhavehigherindividualabsoluteratingfloors,calculatedusingthefollowingformula:
where isthenumberofratedgameswon, isthenumberofratedgamesdrawn,and isthenumberofeventsinwhichtheplayercompletedthreeormoreratedgames.
Higherratingfloorsexistforexperiencedplayerswhohaveachievedsignificantratings.Suchhigherratingfloorsexist,startingatratingsof1200in100pointincrementsupto2100(1200,1300,1400,...,2100).Aplayer'sratingflooriscalculatedbytakingtheirpeakestablishedrating,subtracting200points,andthenroundingdowntothenearestratingfloor.Forexample,aplayerwhohasreachedapeakratingof1464wouldhavearatingfloorof1464200=1264,whichwouldberoundeddownto1200.Underthisscheme,onlyClassCplayersandabovearecapableofhavingahigherratingfloorthantheirabsoluteplayerrating.Allotherplayerswouldhaveafloorofatmost150.
Therearetwowaystoachievehigherratingfloorsotherthanunderthestandardschemepresentedabove.IfaplayerhasachievedtheratingofOriginalLifeMaster,theirratingfloorissetat2200.TheachievementofthistitleisuniqueinthatnootherrecognizedUSCFtitlewillresultinanewfloor.Forplayerswithratingsbelow2000,winningacashprizeof$2,000ormoreraisesthatplayer'sratingfloortotheclosest100pointlevelthatwouldhavedisqualifiedtheplayerforparticipationinthetournament.Forexample,ifaplayerwon$4,000ina1750andundertournament,theplayerwouldnowhavearatingfloorof1800.
Ratingsofcomputers
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Since200506,humancomputerchessmatcheshavedemonstratedthatchesscomputersarecapableofdefeatingeventhestrongesthumanplayers(DeepBlueversusGarryKasparov).However,ratingsofcomputersaredifficulttoquantify.Therehavebeentoofewgamesundertournamentconditionstogivecomputersorsoftwareenginesanaccuraterating.[12]Also,forchessengines,theratingisdependentonthemachineaprogramrunson.
Forsomeratingsestimates,seehere.
Theory
Mathematicaldetails
Performanceisn'tmeasuredabsolutelyitisinferredfromwins,losses,anddrawsagainstotherplayers.Players'ratingdependontheratingsoftheiropponents,andtheresultsscoredagainstthem.Thedifferenceinratingbetweentwoplayersdeterminesanestimatefortheexpectedscorebetweenthem.Boththeaverageandthespreadofratingscanbearbitrarilychosen.Elosuggestedscalingratingssothatadifferenceof200ratingpointsinchesswouldmeanthatthestrongerplayerhasanexpectedscore(whichbasicallyisanexpectedaveragescore)ofapproximately0.75,andtheUSCFinitiallyaimedforanaverageclubplayertohavearatingof1500.
Aplayer'sexpectedscoreishisprobabilityofwinningplushalfhisprobabilityofdrawing.Thusanexpectedscoreof0.75couldrepresenta75%chanceofwinning,25%chanceoflosing,and0%chanceofdrawing.Ontheotherextremeitcouldrepresenta50%chanceofwinning,0%chanceoflosing,and50%chanceofdrawing.Theprobabilityofdrawing,asopposedtohavingadecisiveresult,isnotspecifiedintheElosystem.Insteadadrawisconsideredhalfawinandhalfaloss.
IfPlayerAhasaratingof andPlayerBaratingof ,theexactformula(usingthelogisticcurve)[13]fortheexpectedscoreofPlayerAis
SimilarlytheexpectedscoreforPlayerBis
Thiscouldalsobeexpressedby
and
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where and .Notethatinthelattercase,thesamedenominatorappliestobothexpressions.Thismeansthatbystudyingonlythenumerators,wefindoutthattheexpectedscoreforplayerAis timesgreaterthantheexpectedscoreforplayerB.Itthenfollowsthatforeach400ratingpointsofadvantageovertheopponent,theexpectedscoreismagnifiedtentimesincomparisontotheopponent'sexpectedscore.
Alsonotethat .Inpractice,sincethetruestrengthofeachplayerisunknown,theexpectedscoresarecalculatedusingtheplayer'scurrentratings.
Whenaplayer'sactualtournamentscoresexceedhisexpectedscores,theElosystemtakesthisasevidencethatplayer'sratingistoolow,andneedstobeadjustedupward.Similarlywhenaplayer'sactualtournamentscoresfallshortofhisexpectedscores,thatplayer'sratingisadjusteddownward.Elo'soriginalsuggestion,whichisstillwidelyused,wasasimplelinearadjustmentproportionaltotheamountbywhichaplayeroverperformedorunderperformedhisexpectedscore.Themaximumpossibleadjustmentpergame,calledtheKfactor,wassetatK=16formastersandK=32forweakerplayers.
SupposingPlayerAwasexpectedtoscore pointsbutactuallyscored points.Theformulaforupdatinghisratingis
Thisupdatecanbeperformedaftereachgameoreachtournament,orafteranysuitableratingperiod.Anexamplemayhelpclarify.SupposePlayerAhasaratingof1613,andplaysinafiveroundtournament.Heorshelosestoaplayerrated1609,drawswithaplayerrated1477,defeatsaplayerrated1388,defeatsaplayerrated1586,andlosestoaplayerrated1720.Theplayer'sactualscoreis(0+0.5+1+1+0)=2.5.Theexpectedscore,calculatedaccordingtotheformulaabove,was(0.506+0.686+0.785+0.539+0.351)=2.867.Thereforetheplayer'snewratingis(1613+32(2.52.867))=1601,assumingthataKfactorof32isused.
Notethatwhiletwowins,twolosses,andonedrawmayseemlikeaparscore,itisworsethanexpectedforPlayerAbecausehisorheropponentswerelowerratedonaverage.ThereforePlayerAisslightlypenalized.IfPlayerAhadscoredtwowins,oneloss,andtwodraws,foratotalscoreofthreepoints,thatwouldhavebeenslightlybetterthanexpected,andtheplayer'snewratingwouldhavebeen(1613+32(32.867))=1617.
ThisupdatingprocedureisatthecoreoftheratingsusedbyFIDE,USCF,Yahoo!Games,theInternetChessClub(ICC)andtheFreeInternetChessServer(FICS).However,eachorganizationhastakenadifferentroutetodealwiththeuncertaintyinherentintheratings,particularlytheratingsofnewcomers,andtodealwiththeproblemofratingsinflation/deflation.Newplayersareassignedprovisionalratings,whichareadjustedmoredrasticallythanestablishedratings.
Theprinciplesusedintheseratingsystemscanbeusedforratingothercompetitionsforinstance,internationalfootballmatches.
Eloratingshavealsobeenappliedtogameswithoutthepossibilityofdraws,andtogamesinwhichtheresultcanalsohaveaquantity(small/bigmargin)inadditiontothequality(win/loss).SeeGoratingwithEloformore.
Seealso:Hubbertcurve
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Mathematicalissues
TherearethreemainmathematicalconcernsrelatingtotheoriginalworkofElo,namelythecorrectcurve,thecorrectKfactor,andtheprovisionalperiodcrudecalculations.A2012studyledbyateamofSwedishpsychologistsatLundUniversityhasspawnedargumentsfortheinclusionofafourthconcern,albeittheoreticalintangibles.[14]
Mostaccuratedistributionmodel
ThefirstmathematicalconcernaddressedbytheUSCFwastheuseofthenormaldistribution.Theyfoundthatthisdidnotaccuratelyrepresenttheactualresultsachieved,particularlybythelowerratedplayers.Insteadtheyswitchedtoalogisticdistributionmodel,whichtheUSCFfoundprovidedabetterfitfortheactualresultsachieved.FIDEstillusesthenormaldistributionasthebasisforratingcalculationsassuggestedbyElohimself.[15]
MostaccurateKfactor
Thesecondmajorconcernisthecorrect"Kfactor"used.ThechessstatisticianJeffSonasbelievesthattheoriginalK=10value(forplayersratedabove2400)isinaccurateinElo'swork.IftheKfactorcoefficientissettoolarge,therewillbetoomuchsensitivitytojustafew,recentevents,intermsofalargenumberofpointsexchangedineachgame.ToolowaKvalue,andthesensitivitywillbeminimal,andthesystemwillnotrespondquicklyenoughtochangesinaplayer'sactuallevelofperformance.
Elo'soriginalKfactorestimationwasmadewithoutthebenefitofhugedatabasesandstatisticalevidence.SonasindicatesthataKfactorof24(forplayersratedabove2400)maybemoreaccuratebothasapredictivetooloffutureperformance,andalsomoresensitivetoperformance.[16]
CertainInternetchesssitesseemtoavoidathreelevelKfactorstaggeringbasedonratingrange.ForexampletheICCseemstoadoptaglobalK=32exceptwhenplayingagainstprovisionallyratedplayers.TheUSCF(whichmakesuseofalogisticdistributionasopposedtoanormaldistribution)hasstaggeredtheKfactoraccordingtothreemainratingrangesof:
Playersbelow2100:Kfactorof32usedPlayersbetween2100and2400:Kfactorof24usedPlayersabove2400:Kfactorof16used.
FIDEusesthefollowingranges:[17]
K=40,foraplayernewtotheratinglistuntilthecompletionofeventswithatotalof30gamesandforallplayersuntiltheir18thbirthday,aslongastheirratingremainsunder2300.K=20,forplayerswitharatingalwaysunder2400.K=10,forplayerswithanypublishedratingofatleast2400andatleast30gamesplayedinpreviousevents.Thereafteritremainspermanentlyat10.
FIDEusedthefollowingrangesbeforeJuly2014:[18]
K=30(was25),foraplayernewtotheratinglistuntilthecompletionofeventswithatotalof30games.[19]
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K=15,forplayerswitharatingalwaysunder2400.K=10,forplayerswithanypublishedratingofatleast2400andatleast30gamesplayedinpreviousevents.Thereafteritremainspermanentlyat10.
ThegradationoftheKfactorreducesratingschangesatthetopendoftheratingspectrum,reducingthepossibilityforrapidratingsinflationordeflationforthosewithalowKfactor.Thismightintheoryapplyequallytoanonlinechesssiteorovertheboardplayers,sinceitismoredifficultforplayerstogetmuchhigherratingswhentheirKfactorisreduced.Whenplayingonline,itmaysimplybetheselectionofhighlyratedopponentsthatenables2800+playerstofurtherincreasetheirrating,[20]sinceagrandmasterontheICCplayingsitecanplayastringofdifferentopponentswhoareallratedover2100.Inovertheboardevents,itwouldonlybeinveryhighlevelallplayalleventsthataplayerwouldbeabletoengagethatnumberof2700+opponents,whileinanormalopenSwisspairedchesstournament,frequentlytherewouldbemanyopponentsratedlessthan2500,reducingtheratingsgainspossiblefromasinglecontest.
Practicalissues
Gameactivityversusprotectingone'srating
Insomecasestheratingsystemcandiscouragegameactivityforplayerswhowishtoprotecttheirrating.[21]Inordertodiscourageplayersfromsittingonahighrating,arecentproposalbyBritishGrandmasterJohnNunnforchoosingqualifierstothechessworldchampionshipincludedanactivitybonus,tobecombinedwiththerating.[22]
Beyondthechessworld,concernsoverplayersavoidingcompetitiveplaytoprotecttheirratingscausedWizardsoftheCoasttoabandontheElosystemforMagic:theGatheringtournamentsinfavourofasystemoftheirowndevisingcalled"PlaneswalkerPoints".[23][24]
Selectivepairing
Amoresubtleissueisrelatedtopairing.Whenplayerscanchoosetheirownopponents,theycanchooseopponentswithminimalriskoflosing,andmaximumrewardforwinning.SuchaluxuryofbeingabletohandpickyouropponentsisnotpresentinOvertheBoardElotypecalculations,andthereforethismayaccountstronglyfortheratingsontheICCusingElowhicharewellover2800.
Particularexamplesof2800+ratedplayerschoosingopponentswithminimalriskandmaximumpossibilityofratinggaininclude:choosingcomputersthattheyknowtheycanbeatwithacertainstrategychoosingopponentsthattheythinkareoverratedoravoidingplayingstrongplayerswhoareratedseveralhundredpointsbelowthem,butmayholdchesstitlessuchasIMorGM.Inthecategoryofchoosingoverratedopponents,newentrantstotheratingsystemwhohaveplayedfewerthan50gamesareintheoryaconvenienttargetastheymaybeoverratedintheirprovisionalrating.TheICCcompensatesforthisissuebyassigningalowerKfactortotheestablishedplayeriftheydowinagainstanewratingentrant.TheKfactorisactuallyafunctionofthenumberofratedgamesplayedbythenewentrant.
Therefore,Eloratingsonlinestillprovideausefulmechanismforprovidingaratingbasedontheopponent'srating.Itsoverallcredibility,however,needstobeseeninthecontextofatleasttheabovetwomajorissuesdescribedengineabuse,andselectivepairingofopponents.
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TheICChasalsorecentlyintroduced"autopairing"ratingswhicharebasedonrandompairings,butwitheachwininarowensuringastatisticallymuchharderopponentwhohasalsowonxgamesinarow.Withpotentiallyhundredsofplayersinvolved,thiscreatessomeofthechallengesofamajorlargeSwisseventwhichisbeingfiercelycontested,withroundwinnersmeetingroundwinners.Thisapproachtopairingcertainlymaximizestheratingriskofthehigherratedparticipants,whomayfaceverystiffoppositionfromplayersbelow3000,forexample.Thisisaseparateratinginitself,andisunder"1minute"and"5minute"ratingcategories.Maximumratingsachievedover2500areexceptionallyrare.
Ratingsinflationanddeflation
Anincreaseordecreaseintheaverageratingoverallplayersintheratingsystemisoftenreferredtoasratinginflationorratingdeflationrespectively.Forexample,ifthereisinflation,amodernratingof2500meanslessthanahistoricalratingof2500,whilethereverseistrueifthereisdeflation.Usingratingstocompareplayersbetweendifferenterasismademoredifficultwheninflationanddeflationispresent.(SeealsoComparisonoftopchessplayersthroughouthistory.)
Itiscommonlybelievedthat,atleastatthetoplevel,modernratingsareinflated.ForinstanceNigelShortsaidinSeptember2009,"TherecentChessBasearticleonratinginflationbyJeffSonaswouldsuggestthatmyratinginthelate1980swouldbeapproximatelyequivalentto2750intoday'smuchdebauchedcurrency".[25](Short'shighestratinginthe1980swas2665inJuly1988,whichwasequaltothirdintheworld.Whenhemadethiscomment,2665wouldhaverankedhim65th,while2750wouldhaverankedhimequal10th.IntheSeptember2012FIDEratinglist,2665wouldhaverankedhimequal86th,while2750wouldhaverankedhim13th.)
Ithasbeensuggestedthatanoverallincreaseinratingsreflectsgreaterskill.Theadventofstrongchesscomputersallowsasomewhatobjectiveevaluationoftheabsoluteplayingskillofpastchessmasters,basedontheirrecordedgames,butthisisalsoameasureofhowcomputerliketheplayers'movesare,notmerelyameasureofhowstronglytheyhaveplayed.[26]
Thenumberofpeoplewithratingsover2700hasincreased.Around1979therewasonlyoneactiveplayer(AnatolyKarpov)witharatingthishigh.In1992ViswanathanAnandwasonlythe8thplayerinchesshistorytoreachthe2700markatthatpointoftime.[27]Thisincreasedto15playersby1994.33playershada2700+ratingin2009and44asofSeptember2012.Thecurrentbenchmarkforeliteplayersliesbeyond2800.
Onepossiblecauseforthisinflationwastheratingfloor,whichforalongtimewasat2200,andifaplayerdroppedbelowthistheywerestrickenfromtheratinglist.Asaconsequence,playersataskillleveljustbelowthefloorwouldonlybeontheratinglistiftheywereoverrated,andthiswouldcausethemtofeedpointsintotheratingpool.[26]InJuly2000theaverageratingofthetop100was2644.ByJuly2012ithadincreasedto2703.[27]
InapureElosystem,eachgameendsinanequaltransactionofratingpoints.IfthewinnergainsNratingpoints,theloserwilldropbyNratingpoints.Thispreventspointsfromenteringorleavingthesystemwhengamesareplayedandrated.However,playerstendtoenterthesystemasnoviceswithalowratingandretirefromthesystemasexperiencedplayerswithahighrating.Therefore,inthelongrunasystemwithstrictlyequaltransactionstendstoresultinratingdeflation.[28]
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In1995,theUSCFacknowledgedthatseveralyoungscholasticplayerswereimprovingfasterthanwhattheratingsystemwasabletotrack.Asaresult,establishedplayerswithstableratingsstartedtoloseratingpointstotheyoungandunderratedplayers.Severaloftheolderestablishedplayerswerefrustratedoverwhattheyconsideredanunfairratingdecline,andsomeevenquitchessoverit.[29]
Combattingdeflation
Becauseofthesignificantdifferenceintimingofwheninflationanddeflationoccur,andinordertocombatdeflation,mostimplementationsofEloratingshaveamechanismforinjectingpointsintothesysteminordertomaintainrelativeratingsovertime.FIDEhastwoinflationarymechanisms.First,performancesbelowa"ratingsfloor"arenottracked,soaplayerwithtrueskillbelowthefloorcanonlybeunratedoroverrated,nevercorrectlyrated.Second,establishedandhigherratedplayershavealowerKfactor.NewplayershaveaK=30,whichdropstoK=15after30playedgames,andtoK=10whentheplayerreaches2400.[30]
ThecurrentsystemintheUnitedStatesincludesabonuspointschemewhichfeedsratingpointsintothesysteminordertotrackimprovingplayers,anddifferentKvaluesfordifferentplayers.[29]Somemethods,usedinNorwayforexample,differentiatebetweenjuniorsandseniors,andusealargerKfactorfortheyoungplayers,evenboostingtheratingprogressby100%forwhentheyscorewellabovetheirpredictedperformance.[31]
RatingfloorsintheUSAworkbyguaranteeingthataplayerwillneverdropbelowacertainlimit.Thisalsocombatsdeflation,butthechairmanoftheUSCFRatingsCommitteehasbeencriticalofthismethodbecauseitdoesnotfeedtheextrapointstotheimprovingplayers.Apossiblemotivefortheseratingfloorsistocombatsandbagging,i.e.deliberateloweringofratingstobeeligibleforlowerratingclasssectionsandprizes.[29]
Useoutsideofchess
AmericancollegefootballusedtheElomethodasaportionofitsBowlChampionshipSeriesratingsystemsfrom1998to2013,afterwhichtheBCSwasreplacedbytheCollegeFootballPlayoff.JeffSagarinofUSATodaypublishesteamrankingsformostAmericansports,includingElosystemratingsforcollegefootball.TheoperatorsoftheBCSusedhisEloratingsaspartofaformulatodeterminetheannualparticipantsintheBCSNationalChampionshipGame.TheuseofratingsystemswaseffectivelyscrappedwiththecreationoftheCollegeFootballPlayoffin2014participantsintheCFPanditsassociatedbowlgameswillbechosenbyaselectioncommittee.
NationalScrabbleorganizationscomputenormallydistributedEloratingsexceptintheUnitedKingdom,whereadifferentsystemisused.TheNorthAmericanScrabblePlayersAssociationhasthelargestratedpopulationofactivemembers,numberingabout2,000asofearly2011.LexulousalsousestheElosystem.
ThepopularFirstInternetBackgammonServercalculatesratingsbasedonamodifiedElosystem.Newplayersareassignedaratingof1500,withthebesthumansandbotsratingover2000.Thesameformulahasbeenadoptedbyseveralotherbackgammonsites,suchasPlay65,DailyGammon,GoldTokenandVogClub.VogClubsetsanewplayer'sratingat1600.
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TheEuropeanGoFederationadoptedanElobasedratingsysteminitiallypioneeredbytheCzechGoFederation.TheGroshin'sScoreanElobasedgame.
Inothersports,individualsmaintainrankingsbasedontheEloalgorithm.Theseareusuallyunofficial,notendorsedbythesport'sgoverningbody.TheWorldFootballEloRatingsranknationalteamsinmen'sfootball.In2006,EloratingswereadaptedforMajorLeagueBaseballteamsbyNateSilverofBaseballProspectus.[32]Basedonthisadaptation,BaseballProspectusalsomakesElobasedMonteCarlosimulationsoftheoddsofwhetherteamswillmaketheplayoffs.[33]GlennO'Brienpublishesrankingsusingseveralratingsystems,includingvariantsoftheEloratingsystem.[34]OneofthefewElobasedrankingsendorsedbyasport'sgoverningbodyistheFIFAWomen'sWorldRankings,basedonasimplifiedversionoftheEloalgorithm,whichFIFAusesasitsofficialrankingsystemfornationalteamsinwomen'sfootball.
In2015,NateSilverandReubenFischerBaumproducedEloratingsforeveryNationalBasketballAssociationteamandseasonthroughthe2014season.[35]
Sportsreference.comusestheEloratingsystemtoratethebestprofessionalplayersinbasketball,football,baseball(battersandpitchersratedseparately),andhockey(goaliesandskatersratedseparately).In2014FiveThirtyEightcreatedElobasedratingsandwinprojectionsfortheAmericanprofessionalNationalFootballLeague.[36]
TheEnglishKorfballAssociationratedteamsbasedonEloratings,todeterminehandicapsfortheircupcompetitionforthe2011/12season.
Elohockey.comusestheEloratingsystemtoranknationalicehockeyteams.[37]
Rugbyleagueratings.comusestheEloratingsystemtorankinternationalandclubrugbyleagueteams.
VariousonlinegamesuseEloratingsforplayerversusplayerrankings.Since2005,GoldenTeeLivehasratedplayersbasedontheElosystem.Newplayersstartat2100,withtopplayersratingover3000.[38]InGuildWars,EloratingsareusedtorecordguildratinggainedandlostthroughGuildversusGuildbattles,whicharetwoteamfights.TheinitialKvaluewas30,butwaschangedto5inJanuary2007,thenchangedto15inJuly2009.[39]WorldofWarcraftformerlyusedtheEloRatingsystemwhenteamingupandcomparingArenaplayers,butnowusesasystemsimilartoMicrosoft'sTrueSkill.[40]TheMOBAgameLeagueofLegendsusedanEloratingsystempriortothesecondseasonofcompetitiveplay.[41]ThegamePuzzlePiratesusestheEloratingsystemtodeterminethestandingsinthevariouspuzzles.RobloxintroducedtheEloratingin2010.[42]ThebrowsergameQuidditchManagerusestheEloratingtomeasureateam'sperformance.[43]AnotherrecentgametostartusingtheEloratingsystemisAirMech,usingElo[44]ratingsfor1v1,2v2,and3v3random/teamMatchmaking.QuakeLiveusesanEloratingsystemthroughQLranks.com(http://www.qlranks.com/),whichscansplayers'profilesaftereachgameandupdatesthewebsiteaccordingly.
DespitequestionsoftheappropriatenessofusingtheElosystemtorategamesinwhichluckisafactor,tradingcardgamemanufacturersoftenuseEloratingsfortheirorganizedplayefforts.TheDCI(formerlyDuelists'ConvocationInternational)usedEloratingsfortournamentsofMagic:TheGatheringandotherWizardsoftheCoastgames.However,theDCIabandonedthissystemin2012infavourofanewcumulativesystemof"PlaneswalkerPoints",chieflybecauseoftheabovenotedconcernthatElo
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encourageshighlyratedplayerstoavoidplayingto"protecttheirrating".[23][24]PokmonUSAusestheElosystemtorankitsTCGorganizedplaycompetitors.[45]Prizesforthetopplayersinvariousregionsincludedholidaysandworldchampionshipsinvitesuntilthe20112012season,whereawardswerebasedonasystemofChampionshipPoints,theirrationalebeingthesameastheDCI'sforMagic:TheGathering.Similarly,Decipher,Inc.usedtheElosystemforitsrankedgamessuchasStarTrekCustomizableCardGameandStarWarsCustomizableCardGame.
Moreover,onlinejudgesitesarealsousingEloratingsystemoritsderivatives.Forexample,TopCoderisusingamodifiedversionbasedonnormaldistribution,[46]whileCodeforcesisusinganotherversionbasedonlogisticdistribution.[47][48][49]
Useoutsideofgaming
TheEloratingsystemhasbeenusedinacrowdsourcingapplicationfordeterminingbestqualityphotographs.AcompanycalledBrilliantArchascreatedthe"Keep/Toss"game.TwophotographsarepresentedandworkersinAmazon'sMechanicalTurksimplyselectwhichphotographtheybelieveisthebetterphotograph.ThreevotesarecastforeachphotographandanEloscoreisdeterminedforallphotographs.Thephotographswithascoreaboveacertainthresholdarethenselectedforfurtherprocessing.Theresultshavebeenwellreceived.
ParentscanusetheEloratingsystemtoselectagivennamefortheirbaby.IntheBabyNameGame,playersselecttheirpreferrednamefromtwooptions.Resultsarethencollatedtodeterminethename'sEloscoreandultimatewinningname.Thisprocesshasbeenfoundtoreducethecomplexityofselectingababyname.[50]
Additionally,theEloratingsystemhasbeenusedinsoftbiometrics.[51]Softbiometricsconcernstheidentificationofindividualsusinghumandescriptions.ComparativedescriptionswereutilizedalongsidetheEloratingsystemtoproviderobustanddiscriminative'relativemeasurements',permittingaccurateidentification.
TheEloratingsystemhasalsobeenusedinbiologyforassessingmaledominancehierarchies.[52]
Referencesinthemedia
TheEloratingsystemwasfeaturedprominentlyinTheSocialNetworkduringthealgorithmscenewhereMarkZuckerbergreleasedFacemash.InthesceneEduardoSaverinwritesmathematicalformulasfortheEloratingsystemonZuckerberg'sdormitoryroomwindow.Behindthescenes,themovieclaims,theElosystemisemployedtorankgirlsbytheirattractiveness.Theequationsdrivingthealgorithmareshownbriefly,writtenonthewindow.[53]
References1. Wood,Ben."EnemydownusesEloinitsCounterstrike:SourceMultilplayerLadders"
(http://www.enemydown.eu/news/502).TWNAGroup.2. NateSilverandReubenFischerBaum,"HowWeCalculateNBAEloRatings,"FiveThirtyEight.com,May21,
2015(http://fivethirtyeight.com/features/howwecalculatenbaeloratings/).
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GraphsofprobabilitiesandEloratingchanges(forK=16and32)ofexpectedoutcome(solidcurve)andunexpectedoutcome(dottedcurve)vsinitialratingdifferenceForexample,playerAstartswitha1400ratingandBwith1800inatournamentusingK=32(browncurves).Thebluedashdotlinedenotestheinitialratingdifferenceof400(18001400).TheprobabilityofBwinning,theexpectedoutcome,is0.91(intersectionofblacksolidcurveandblueline)ifthishappens,A'sratingdecreasesby3(intersectionofbrownsolidcurveandblueline)to1397andB'sincreasesbythesameamountto1803.Conversely,theprobabilityofAwinning,theunexpectedoutcome,is0.09(intersectionofblackdottedcurveandblueline)ifthishappens,A'sratingincreasesby29(intersectionofbrowndottedcurveandblueline)to1429andB'sdecreasesbythesameamountto1771.
3. Redman,Tim."RememberingRichard,PartII"(http://www.uschess.org/ratings/RedmanremembersRichard.pdf)(PDF).UnitedStatesChessFederation.
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12. Forinstance,seethecommentsatChessBase.comChessNewsAdamsvsHydra:Man0.5Machine5.5(http://www.chessbase.com/newsdetail.asp?newsid=2476)
13. Elo,ArpadE(2008)."8.4LogisticProbabilityasaRatingBasis".TheRatingofChessplayers,Past&Present.BronxNY10453:ISHIPressInternational.ISBN9780923891275.
14. LundUniversitySocialCognition:TheoreticalintangiblesoftheELOsystemstudy,2012http://www.psy.lu.se/o.o.i.s/15545
15. DanielRoss(20071216)."ArpadEloandtheEloRatingSystem"(http://www.chessbase.com/newsdetail.asp?newsid=4326).Chessbasearticle.Retrieved20120219.
16. AkeySonasarticleisJeffSonas:TheSonasRatingFormulaBetterthanElo?(http://www.chessbase.com/newsdetail.asp?newsid=562)
17. "FIDEOnline.FIDERatingRegulationseffectivefrom1July2014"(http://www.fide.com/fide/handbook.html?id=172&view=article).Fide.com.20140701.Retrieved20140701.
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20. "ICCHelp:kfactor"(http://www.chessclub.com/help/kfactor).Chessclub.com.20021018.Retrieved20120219.
21. AParent'sGuidetoChess(http://www.chesscafe.com/text/skittles176.pdf)Skittles,DonHeisman,Chesscafe.com,August4,2002
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25. NigelShortonbeingnumberoneinBritainagain(http://www.chessbase.com/newsdetail.asp?newsid=5736),Chessbase,4September2009
26. Sonas,Jeff(July27,2009)."RatingInflationItsCausesandPossibleCures"(http://www.chessbase.com/newsdetail.asp?newsid=5608).ChessBase.Retrieved20090823.
27. "ViswanathanAnand"(http://www.chessgames.com/perl/chessplayer?pid=12088).Chessgames.com.28. Bergersen,PerA."ELOSYSTEMET"(http://www.sjakk.no/nsf/elosystem_main.html)(inNorwegian).
NorwegianChessFederation.Retrieved21October2013.29. AconversationwithMarkGlickman[1](http://www.glicko.net/ratings/clarticle.pdf),PublishedinChessLife
October2006issue30. "FIDEHandbook8.0.TheworkingoftheFIDERatingSystem"(http://www.fide.com/fide/handbook?
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32. NateSilver,"WeAreElo?"June28,2006.[3](http://baseballprospectus.com/article.php?articleid=5247)33. "PostseasonOdds,ELOversion"(http://www.baseballprospectus.com/statistics/ps_oddselo.php).
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(http://fivethirtyeight.com/features/howwecalculatenbaeloratings/).AlsoseeReubenFischerBaumandNateSilver,"TheCompleteHistoryoftheNBA,"FiveThirtyEight,May21,2015.[5](http://fivethirtyeight.com/interactives/thecompletehistoryofeverynbateambyelo/#bulls)
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36. NateSilver,"IntroducingNFLEloRatings,"September4,2014(http://fivethirtyeight.com/datalab/introducingnfleloratings),andNeilPaine,"NFLEloRatingsAreBack,"FiveThirtyEight,September10,2015(http://fivethirtyeight.com/datalab/nfleloratingsareback/).
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p=83043#p83043).RetrievedJanuary15,2015.45. "Play!PokmonGlossary:Elo"(http://www.pokemon.com/us/playpokemon/about/tournamentsglossary/#elo).
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52. Prschmannetal.(2010)."Malereproductivesuccessanditsbehaviouralcorrelatesinapolygynousmammal,theGalpagossealion(Zalophuswollebaeki)"(http://onlinelibrary.wiley.com/doi/10.1111/j.1365294X.2010.04665.x/abstract).MolecularEcology19.doi:10.1111/j.1365294X.2010.04665.x(https://dx.doi.org/10.1111%2Fj.1365294X.2010.04665.x).
53. Screenplayfor"TheSocialNetwork,"SonyPictures(http://flash.sonypictures.com/video/movies/thesocialnetwork/awards/thesocialnetwork_screenplay.pdf),p.16
Furtherreading
Elo,Arpad(1978).TheRatingofChessplayers,PastandPresent.Arco.ISBN0668047216.Harkness,Kenneth(1967).OfficialChessHandbook.McKay.
Externallinks
GoBase.org:IntroductiontotheEloRatingSystem(http://gobase.org/rating/elo.html)MarkGlickman'sresearchpage,withanumberoflinkstotechnicalpapersonchessratingsystems(http://www.glicko.net/research.html)MultiplayerEloCalculator(http://elo.divergentinformatics.com)ELORatingimplementationintheDprogramminglanguage(https://github.com/Extrawurst/eloratingd)
Retrievedfrom"https://en.wikipedia.org/w/index.php?title=Elo_rating_system&oldid=681655821"
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Categories: Chessratingsystems Sportsrecordsandstatistics
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