Chessmetrics ratings vs. FIDE ratings

Although they certainly provide an interesting historical perspective, the Chessmetrics ratings are not going to be very useful for modern players unless they are more "accurate" than the official FIDE ratings. How can we measure this? Well, there is a well-known exponential formula for estimating the average score for a player if you know the FIDE ratings of the player and the opponent. In case it's not quite well-known enough, I'll tell you that the exact formula is 1.0 / (1.0 + 10^((OppRating - OwnRating)/400)). By applying this formula to each game that someone plays in a year, you can add up the average predicted scores and compare them to the actual score by the player during that year. If the numbers match exactly, then I say that the accuracy of the prediction is 100%. If they don't match exactly, then I calculate the accuracy as 1.0 - (ABS(PredictedScore - ActualScore) / NumGames). Having done this once for the FIDE ratings, it is then possible to do the same thing for the Chessmetrics ratings, using a somewhat different formula for calculating the predicted score in a game.

The time period doesn't have to be yearly; it could be on a per-game basis, or monthly, but yearly seemed as good as any, and better than most. So, I went through the last 25 years of comparisons between FIDE accuracy and Chessmetrics accuracy, and the Chessmetrics ratings seem to win every single year. The difference is sometimes pretty small, but 25 out of 25 should leave no doubt that the Chessmetrics ratings are more accurate at predicting future results than the FIDE ratings. The above graph illustrates this, and the following data shows just how many games were involved as evidence that the Chessmetrics ratings are more accurate.

I should point out that I would love to do a comparison which also included the Professional ratings, but unfortunately the ratings themselves are not widely available, especially for more than just the top-50. I have been able to track down the complete lists for the past few months, but that's about all. Nevertheless, at some point I plan to take all available Professional ratings and do a three-way comparison.


Chessmetrics accuracy FIDE Accuracy # Games # Players

In a similar fashion, it is possible to go through player-by-player and report on their career Chessmetrics and FIDE accuracies, based on the same yearly calculations of accuracy, but broken down by player rather than summed up into a single value for each year. Once again, the advantage seems quite clear: out of the 120 players who played the most rated games during those 25 years (counting only games where each player had a certain minimum rating), over 80% of those players performed more in line with the Chessmetrics predictions than the FIDE predictions. Here is the list of players, along with the comparison of rating systems for each player.

 Player Name 

Ratio Which
 Karpov, Anatoly E203096.9%96.5%1.005Chessmetrics
 Timman, Jan H188395.9%95.3%1.006Chessmetrics
 Korchnoi, Viktor L183796.4%96.3%1.001Chessmetrics
 Beliavsky, Alexander G142795.4%94.6%1.008Chessmetrics
 Andersson, Ulf142496.5%96.3%1.002Chessmetrics
 Ljubojevic, Ljubomir136396.2%95.5%1.007Chessmetrics
 Kasparov, Garry K120794.9%95.9%0.99FIDE
 Portisch, Lajos120396.4%96.5%0.999FIDE
 Romanishin, Oleg M119697.3%96.5%1.008Chessmetrics
 Miles, Anthony J117594.9%94.8%1.001Chessmetrics
 Short, Nigel D116796.8%96.6%1.002Chessmetrics
 Vaganian, Rafael A114896%95.2%1.009Chessmetrics
 Ivanchuk, Vassily112895.8%95.9%0.999FIDE
 Hübner, Robert111896.9%96.9%1Chessmetrics
 Shirov, Alexei108796.7%95.8%1.009Chessmetrics
 Anand, Viswanathan107195.9%96.2%0.997FIDE
 Gulko, Boris F106696.2%95.7%1.006Chessmetrics
 Adams, Michael106496.5%96.9%0.997FIDE
 Nikolic, Predrag106296.6%96.2%1.003Chessmetrics
 Jussupow, Artur M105996.7%96.2%1.006Chessmetrics
 Hort, Vlastimil104597%96%1.011Chessmetrics
 Piket, Jeroen103196.7%94.1%1.027Chessmetrics
 Khalifman, Alexander100597.4%96.8%1.006Chessmetrics
 Tal, Mikhail99695.8%94.7%1.012Chessmetrics
 Gelfand, Boris97096.9%96.3%1.005Chessmetrics
 Tukmakov, Vladimir B96495.6%95%1.006Chessmetrics
 Psakhis, Lev B94996.9%95.6%1.013Chessmetrics
 Balashov, Yury S94796.4%95.7%1.007Chessmetrics
 Seirawan, Yasser91097.4%96.7%1.008Chessmetrics
 Ribli, Zoltán90997.5%96.1%1.015Chessmetrics
 Kramnik, Vladimir90695.6%95.3%1.003Chessmetrics
 Ehlvest, Jaan90296.6%95.3%1.013Chessmetrics
 Speelman, Jonathan S90196.5%96.1%1.004Chessmetrics
 Sokolov, Ivan87096.4%96.1%1.004Chessmetrics
 Sax, Gyula85195.3%95.6%0.997FIDE
 Polugaevsky, Lev A84496.5%95.6%1.009Chessmetrics
 Bareev, Evgeny83096.7%95.4%1.013Chessmetrics
 Spassky, Boris V82596.9%95.5%1.016Chessmetrics
 Dreev, Alexey81096.1%94.4%1.018Chessmetrics
 Gurevich, Mikhail N80595.5%95.2%1.003Chessmetrics
 Lputian, Smbat G79195.9%95.9%1FIDE
 Lautier, Joel79095.7%95.1%1.007Chessmetrics
 Sveshnikov, Evgeny E77894.5%92.8%1.018Chessmetrics
 Tseshkovsky, Vitaly V77894.9%94.5%1.004Chessmetrics
 van der Wiel, John T H77195.8%95.6%1.002Chessmetrics
 Chernin, Alexander M76396%95.7%1.003Chessmetrics
 Malaniuk, Vladimir P76196.6%94.4%1.023Chessmetrics
 Larsen, Bent75995.1%94.7%1.004Chessmetrics
 van Wely, Loek75996.8%96.4%1.004Chessmetrics
 Nunn, John D M75895.8%95.6%1.002Chessmetrics
 Ftácnik, Lubomír74896.4%95.5%1.009Chessmetrics
 Polgar, Judit73796.2%95.2%1.01Chessmetrics
 Dolmatov, Sergey V73096.8%96.5%1.003Chessmetrics
 Smyslov, Vassily V72394.5%93.7%1.009Chessmetrics
 Browne, Walter S68194.9%93.9%1.01Chessmetrics
 Georgiev, Kiril65394.4%94.6%0.998FIDE
 Yudasin, Leonid G65395.1%93.6%1.016Chessmetrics
 Geller, Efim P65293.3%93%1.003Chessmetrics
 Smejkal, Jan65296.2%94.9%1.014Chessmetrics
 Topalov, Veselin65294.9%96.4%0.984FIDE
 Epishin, Vladimir64695.1%93.7%1.015Chessmetrics
 Lobron, Eric64695.5%95.4%1.001Chessmetrics
 Razuvaev, Yury S63794.7%94.5%1.002Chessmetrics
 Smirin, Ilia63696.2%94.6%1.017Chessmetrics
 Christiansen, Larry M61894.5%93.8%1.008Chessmetrics
 Kuzmin, Gennady P60495.5%94.2%1.014Chessmetrics
 Sosonko, Gennadi58796.7%96%1.007Chessmetrics
 Adorján, András58095.7%95.9%0.998FIDE
 Salov, Valery B58095.3%95.3%0.999FIDE
 Kupreichik, Viktor D57293.8%93.1%1.008Chessmetrics
 Azmaiparashvili, Zurab A56996%94.5%1.016Chessmetrics
 Sokolov, Andrey Y56995%93.3%1.019Chessmetrics
 Hjartarson, Jóhann55494.2%93.8%1.004Chessmetrics
 Torre, Eugenio55493.6%93.8%0.997FIDE
 deFirmian, Nicholas E54696.4%95.6%1.008Chessmetrics
 Rozentalis, Eduardas54495.1%94.2%1.009Chessmetrics
 Akopian, Vladimir54196.2%96.7%0.995FIDE
 Oll, Lembit54196.3%95.2%1.011Chessmetrics
 Kurajica, Bojan53294.7%93.8%1.01Chessmetrics
 Illescas Cordoba, Miguel52195.8%94.8%1.011Chessmetrics
 Chandler, Murray G51893.8%93.4%1.004Chessmetrics
 Gligoric, Svetozar51596.1%95.8%1.004Chessmetrics
 Hansen, Curt51093.9%93.8%1Chessmetrics
 Hodgson, Julian M50995.6%94.5%1.012Chessmetrics
 Petrosian, Tigran V50298.1%97.5%1.006Chessmetrics
 Kamsky, Gata49795.8%95.4%1.004Chessmetrics
 Yermolinsky, Alex V49294.5%94.3%1.002Chessmetrics
 Benjamin, Joel L49096.7%95.6%1.011Chessmetrics
 Uhlmann, Wolfgang49093.8%94.2%0.996FIDE
 Gavrikov, Victor N48993.2%94.1%0.99FIDE
 Svidler, Peter48994.7%94.8%0.999FIDE
 Tiviakov, Sergei48994.9%94.8%1.001Chessmetrics
 Leko, Peter48596.2%95.9%1.004Chessmetrics
 Vyzmanavin, Alexey48595.7%95.2%1.006Chessmetrics
 Gheorghiu, Florin48493.8%93.6%1.002Chessmetrics
 Lerner, Konstantin Z48495.9%94.5%1.015Chessmetrics
 Rashkovsky, Nukhim N48494.6%93.6%1.011Chessmetrics
 Mikhalchishin, Adrian B48095.2%94.2%1.01Chessmetrics
 Novikov, Igor A47895.2%94.8%1.004Chessmetrics
 Krasenkow, Michal47694%94%1.001Chessmetrics
 Dorfman, Iosif D47494.8%93.7%1.012Chessmetrics
 Eingorn, Viacheslav S46696.9%95.9%1.01Chessmetrics
 Nogueiras, Jesus46596.6%97.2%0.994FIDE
 Dvoiris, Semen I45193.3%93.1%1.003Chessmetrics
 Kavalek, Lubomir44596.4%95.9%1.006Chessmetrics
 Kindermann, Stefan43994.9%95%0.999FIDE
 Kharitonov, Andrey Y43395.3%93.2%1.023Chessmetrics
 Lutz, Christopher43196.3%95.6%1.007Chessmetrics
 Bologan, Viktor43093.2%92.8%1.004Chessmetrics
 Bagirov, Vladimir K42895.6%93.6%1.021Chessmetrics
 Faragó, Iván42695.2%95.3%0.999FIDE
 Glek, Igor V41793.5%92.9%1.007Chessmetrics
 Pétursson, Margeir41695.7%95.2%1.005Chessmetrics
 Yakovich, Yuri41596.2%95.7%1.006Chessmetrics
 Kožul, Zdenko40995.7%95.9%0.997FIDE
 Velimirovic, Dragoljub40992.5%92.8%0.997FIDE
 Rogers, Ian39895.1%94.3%1.008Chessmetrics
 Dzindzichashvili, Roman Y39792.8%93.5%0.992FIDE
 Hulak, Krunoslav38794.7%93.6%1.012Chessmetrics
 Smagin, Sergey38493%91.2%1.02Chessmetrics

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