elo rating system

24/09/2015 EloratingsystemWikipedia,thefreeencyclopedia

https://en.wikipedia.org/wiki/Elo_rating_system 1/19

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



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.



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



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:



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.



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



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



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



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



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]



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.



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]



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.



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



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/).



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.

4. "AbouttheUSCF"(http://www.uschess.org/about/about.php).UnitedStatesChessFederation.Retrieved20081110.

5. "DeloitteChessRatingCompetition"(http://blog.kaggle.com/2011/04/24/thedeloittefidechesscompetitionplaybyplay/).

6. FIDEHandbook,SectionB.0.0(http://www.fide.com/component/handbook/?id=57&view=article),FIDEwebsite7. AnandlostNo.1toMorozevich(Chessbase,August242008(http://www.chessbase.com/newsdetail.asp?

newsid=4860)),thenregainedit,thenCarlsentookNo.1(Chessbase,September52008(http://www.chessbase.com/newsdetail.asp?newsid=4892)),thenIvanchuk(Chessbase,September112008(http://www.chessbase.com/newsdetail.asp?newsid=4901)),andfinallyTopalov(Chessbase,September132008(http://www.chessbase.com/newsdetail.asp?newsid=4908))

8. USChessFederation(http://archive.uschess.org/ratings/ratedist.php)9. USCFGlossaryQuote:"aplayerwhocompetesinover

300gameswitharatingover2200"(http://main.uschess.org/content/view/7327#Master)fromTheUnitedStatesChessFederation

10. USCFRatingsDistribution2008(http://www.eddins.net/steve/chess/2008/06/06/131)



11. "ApproximatingFormulasfortheUSCFRatingSystem"(http://math.bu.edu/people/mg/ratings/approx/approx.html),UnitedStatesChessFederation,MarkGlickman,DepartmentofMathematicsandStatisticsatBostonUniversity,22February2001

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.

18. "FIDEOnline.FIDERatingRegulationsvalidfrom1July2013till1July2014"(http://www.fide.com/fide/handbook.html?id=161&view=article).Fide.com.20130701.Retrieved20140701.

19. "FIDEOnline.ChangestoRatingRegulationsnewsrelease"(http://www.fide.com/component/content/article/1fidenews/5421changestoratingregulations.html).Fide.com.20110721.Retrieved20120219.

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

22. "ChessNewsTheNunnPlanfortheWorldChessChampionship"(http://www.chessbase.com/newsdetail.asp?newsid=2440).ChessBase.com.Retrieved20120219.

23. "IntroducingPlaneswalkerPoints"(http://www.wizards.com/Magic/Magazine/Article.aspx?x=mtg/daily/feature/159b).September6,2011.RetrievedSeptember9,2011.

24. "GettingtothePoints"(http://www.wizards.com/Magic/Magazine/Article.aspx?x=mtg/daily/twtw/159).September9,2011.RetrievedSeptember9,2011.

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?

id=73&view=article).FIDE.Retrieved20090823.31. [2](http://www.sjakk.no/nsf/elosystem_index.html)Archived

(https://web.archive.org/web/20131205025157/http://www.sjakk.no/nsf/elosystem_index.html)December5,2013attheWaybackMachine

32. NateSilver,"WeAreElo?"June28,2006.[3](http://baseballprospectus.com/article.php?articleid=5247)33. "PostseasonOdds,ELOversion"(http://www.baseballprospectus.com/statistics/ps_oddselo.php).

Baseballprospectus.com.Retrieved20120219.34. GlennO'Brien'sratingspage(http://www.glennobrien.net/ratings.html)35. "HowWeCalculateNBAEloRatings,"FiveThirtyEight,May21,2015.[4]

(http://fivethirtyeight.com/features/howwecalculatenbaeloratings/).AlsoseeReubenFischerBaumandNateSilver,"TheCompleteHistoryoftheNBA,"FiveThirtyEight,May21,2015.[5](http://fivethirtyeight.com/interactives/thecompletehistoryofeverynbateambyelo/#bulls)



36. NateSilver,"IntroducingNFLEloRatings,"September4,2014(http://fivethirtyeight.com/datalab/introducingnfleloratings),andNeilPaine,"NFLEloRatingsAreBack,"FiveThirtyEight,September10,2015(http://fivethirtyeight.com/datalab/nfleloratingsareback/).

37. "EloHockey.com"(http://elohockey.com/).Retrieved20140617.38. "GoldenTeeFanPlayerRatingPage"(http://www.goldenteefan.com/statistics/playerratinghandicap/).Retrieved

20131231.39. "Guildladder"(http://wiki.guildwars.com/wiki/Guild_ladder).Wiki.guildwars.com.Retrieved20120219.40. "WorldofWarcraftEurope>TheArena"(http://www.woweurope.com/en/info/basics/arena/index.html).Wow

europe.com.20111214.Retrieved20120219.41. "Matchmaking|LoLLeagueofLegends"(http://na.leagueoflegends.com/learn/gameplay/matchmaking).

Na.leagueoflegends.com.20100706.Retrieved20120219.42. "ROBLOXContests"(http://blog.roblox.com/?p=2032).February9,2010.Retrieved9February2010.43. "QuidditchManagerHelpandRules"(http://beta.quidditchmanager.com/help.php).QuidditchManager.com.

20120825.Retrieved20131020.44. "AirMechdeveloperexplainswhytheyuseElo"(https://www.carbongames.com/forums/viewtopic.php?

p=83043#p83043).RetrievedJanuary15,2015.45. "Play!PokmonGlossary:Elo"(http://www.pokemon.com/us/playpokemon/about/tournamentsglossary/#elo).

RetrievedJanuary15,2015.46. "AlgorithmCompetitionRatingSystem"

(http://apps.topcoder.com/wiki/display/tc/Algorithm+Competition+Rating+System).December23,2009.RetrievedSeptember16,2011.

47. "FAQ:Whataretheratingandthedivisions?"(http://www.codeforces.com/help).RetrievedSeptember16,2011.48. "RatingDistribution"(http://www.codeforces.com/blog/entry/870).RetrievedSeptember16,2011.49. "Regardingrating:Part2"(http://www.codeforces.com/blog/entry/893).RetrievedSeptember16,2011.50. BabyNameGame(http://www.monkie.biz).51. "UsingComparativeHumanDescriptionsforSoftBiometrics"

(http://eprints.soton.ac.uk/272922/1/IJCB%20(3).pdf),D.A.ReidandM.S.Nixon,InternationalJointConferenceonBiometrics(IJCB),2011

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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