Several methods have been suggested for comparing the greatest chess players in history. There is agreement on a statistical system to rate the strengths of current players, called the Elo system, but disagreement about methods used to compare players from different generations who never competed against each other. This is because the Elo system can only compare players success-rate to their contemporaries.
Statistical methods
Elo system
In 1970, FIDE adopted the Elo rating system for rating current players, so one way to compare players of different eras is to compare their peak Elo ratings. However, due to rating inflation, such a comparison would unduly favor more recent players. For instance, the average of the top 10 active players rose from 2751 in July 2000 to 2794 in July 2014, a 43-point increase in 14 years. The average rating of the top 100 players, meanwhile, increased from 2644 to 2703, a 59-point increase.World Top chess players and Statistics at FIDE.com Elo himself said it was futile to attempt to use ratings to compare players from different eras and that they could only measure the strength of a player as compared to their contemporaries. He also stated that the process of rating players was in any case rather he compared it to "the measurement of the position of a cork bobbing up and down on the surface of agitated water with a yard stick tied to a rope and which is swaying in the wind".Chess Life, 1962.
To account for the impact of rating inflation, the table below ranks players by the largest obtained difference between their rating and that of the World No. 100. This largest difference does not necessarily coincide with a player's highest rating by raw value. The table is incomplete; as of September 2026, only players who have once established a rating of at least 2785 are included, but others who are not included may have a higher Δ. While the table is indicative of players' peak strength, it does not account for a player's longevity.
{| class="wikitable" style="font-size:100%;" |+Table of top rated players by inflation-adjusted peak rating (post-1970) !Rank !Player !Δ !Date !Rating !Age !#100 !Ref |- style="text-align: center;" |1 | style="text-align: left;" | Bobby Fischer |305 |Jul 1972 |2785 | |2480 | |- style="text-align: center;" |2 | style="text-align: left;" | Garry Kasparov |260 |1999-07Jul 1999 | 2851 | |2591 | |- style="text-align: center;" |3 | style="text-align: left;" | Magnus Carlsen |231 |2014-05May 2014 | 2882 | |2651 | |- style="text-align: center;" |4 | style="text-align: left;" | Vladimir Kramnik |213 | |2016-10Jan 2002 | 2809 | |2596 | |- style="text-align: center;" |5 | style="text-align: left;" | Viswanathan Anand |205 |2011-03Jul 1998 | 2795 | |2590 | |- style="text-align: center;" |6 | style="text-align: left;" | Veselin Topalov |194 |2015–07Jul 2006 | 2813 | |2619 | |- style="text-align: center;" |7 | style="text-align: left;" | Fabiano Caruana |193 |2014-10Mar 2020 | 2842 | |2649 | |- style="text-align: center;" |8 | style="text-align: left;" | Hikaru Nakamura |186 |2015-10Oct 2025 | 2816 | |2630 | |- style="text-align: center;" |9 | style="text-align: left;" | Levon Aronian |179 |2014-03Mar 2014 | 2830 | |2651 | |- style="text-align: center;" |10 | style="text-align: left;" | Shakhriyar Mamedyarov |169 |2018-09Sep 2018 | 2820 | |2651 | |- style="text-align: center;" |11 | style="text-align: left;" | Wesley So |167 |2017-02Feb 2017 | 2822 | |2655 | |- style="text-align: center;" | rowspan="2" |12-13 | style="text-align: left;" | Ding Liren |165 |2018-11Oct 2022 | 2811 | |2646 | |- style="text-align: center;" | style="text-align: left;" | Arjun Erigaisi |165 |2024-11Dec 2024 | 2801 | |2636 | |- style="text-align: center;" |14 | Maxime Vachier-Lagrave |164 |2016-08 Aug 2016 |2819 | |2655 | |- style="text-align: center;" |15 | style="text-align: left;" | Alireza Firouzja |159 |2021-11Apr 2022 | 2804 | |2645 | |- style="text-align: center;" | rowspan="3" |16-18 | style="text-align: left;" | Alexander Grischuk |157 |2014-12Dec 2014 | 2810 | |2653 | |- style="text-align: center;" | style="text-align: left;" | Gukesh Dommaraju |157 |2024-10Oct 2024 | 2794 | |2637 | |- style="text-align: center;" | style="text-align: left;" | Alexander Morozevich |157 |2008-07Jul 2008 | 2788 | |2631 | |- style="text-align: center;" |19 | style="text-align: left;" | Ian Nepomniachtchi |150 |2023-03Apr 2023 |2795 | |2645 | |- style="text-align: center;" | rowspan="2"|20-21 | style="text-align: left;" | Teimour Radjabov |144 |2012-11Feb 2013 |2793 | |2649 | |- style="text-align: center;" | style="text-align: left;" | Anish Giri |144 |2015-10Oct 2015 | 2798 | |2654 | |- style="text-align: center;"
Chessmetrics
Many statisticians besides Elo have devised similar methods to retrospectively rate players. Jeff Sonas' rating system is called "Chessmetrics". This system takes account of many games played after the publication of Elo's book, and claims to take account of the rating inflation that the Elo system has allegedly suffered from.
One caveat is that a Chessmetrics rating takes into account the frequency of play. According to Sonas, "As soon as you go a month without playing, your Chessmetrics rating will start to drop."The Greatest Chess Player of All Time – Part I, Jeff Sonas, at Chessbase
Sonas, like Elo, claims that it is impossible to compare the strength of players from different eras, saying:
Nevertheless, Sonas' website does compare players from different eras. Including data until December 2004, the ratings were:
Rank 1-year peak 5-year peak 10-year peak 15-year peak 20-year peak 1 Bobby Fischer, 2881 Garry Kasparov, 2875 Garry Kasparov, 2863 Garry Kasparov, 2862 Garry Kasparov, 2856 2 Garry Kasparov, 2879 Emanuel Lasker, 2854 Emanuel Lasker, 2847 Anatoly Karpov, 2820 Anatoly Karpov, 2818 3 Mikhail Botvinnik, 2871 José Capablanca, 2843 Anatoly Karpov, 2821 Emanuel Lasker, 2816 Emanuel Lasker, 2809 4 José Capablanca, 2866 Mikhail Botvinnik, 2843 José Capablanca, 2813 José Capablanca, 2798 Alexander Alekhine, 2781 5 Emanuel Lasker, 2863 Bobby Fischer, 2841 Bobby Fischer, 2810 Alexander Alekhine, 2794 Viktor Korchnoi, 2766 6 Alexander Alekhine, 2851 Anatoly Karpov, 2829 Mikhail Botvinnik, 2810 Mikhail Botvinnik, 2789 Vasily Smyslov, 2759 In 2005, Part IV gives links to the 3 earlier parts Sonas used Chessmetrics to evaluate historical annual performance ratings and came to the conclusion that Kasparov was dominant for the most years, followed by Karpov and Lasker. He also published the following list of the highest ratings ever attained according to calculations done at the start of each month:
{| class="wikitable sortable" style="font-size:100%;" !Rank !Rating !Player |- | align=center | 1 | align=center | 2895 | Bobby Fischer |- | align=center | 2 | align=center | 2886 | Garry Kasparov |- | align=center | 3 | align=center | 2885 | Mikhail Botvinnik |- | align=center | 4 | align=center | 2878 | Emanuel Lasker |- | align=center | 5 | align=center | 2877 | José Capablanca |- | align=center | 6 | align=center | 2860 | Alexander Alekhine |- | align=center | 7 | align=center | 2848 | Anatoly Karpov |- | align=center | 8 | align=center | 2833 | Viswanathan Anand |- | align=center | 9 | align=center | 2826 | Vladimir Kramnik |- | align=center | 10 | align=center | 2826 | Wilhelm Steinitz
Warriors of the Mind In contrast to Elo and Sonas's systems, Raymond Keene and Nathan Divinsky's book Warriors of the MindWarriors of the Mind, Raymond Keene and Nathan Divinsky, (1989) attempts to establish a rating system claiming to compare directly the strength of players active in different eras, and so determine the strongest player of all time (through December 2004). Considering games played between sixty-four of the strongest players in history, they came up with the following top ten:
Garry Kasparov, 3096 Anatoly Karpov, 2876 Bobby Fischer, 2690 Mikhail Botvinnik, 2616 José Raúl Capablanca, 2552 Emanuel Lasker, 2550 Viktor Korchnoi, 2535 Boris Spassky, 2480 Vasily Smyslov, 2413 Tigran Petrosian, 2363
These "Divinsky numbers" are not on the same scale as Elo ratings (the last person on the list, Johannes Zukertort, has a Divinsky number of 873, which would be a beginner-level Elo rating). Keene and Divinsky's system has met with limited acceptance, and Warriors of the Mind has been accused of arbitrarily selecting players and bias towards modern players.
Moves played compared with computer choices The idea of this approach is to compare the moves played by humans to top engine moves, with the rationale that players more likely to choose these moves are also stronger.
Early efforts A computer-based process of analyzing chess abilities across history came from Matej Guid and Ivan Bratko at the University of Ljubljana, Slovenia, in 2006.Computers choose: who was the strongest player?, Chessbase, 2006 A similar project was conducted for World Champions in 2007–08 using Rybka 2.3.2a (then-strongest chess program) and a modified version of Guid and Bratko's program "Crafty"."Compare the World Champions!", by Charles Sullivan, TrueChess, 2007
Computer Aggregated Precision Score (2017) CAPS (Computer Aggregated Precision Score) is a system created by Chess.com that compares players from different eras by finding the percentage of moves that matches that of a chess engine. In this system, Magnus Carlsen scored the highest among world champions, with a CAPS of 98.36, a projected Elo of 2961, a top engine match of 85.26%, from 461 games and 18,850 moves. Other notable champions include Vladimir Kramnik (98.15 CAPS, 2868 projected Elo, 84.51% top engine match, 1,139 games/40,233 moves), Garry Kasparov (98.01 CAPS, 2816 projected Elo, 84.37% top engine match, 956 games/30,752 moves), Bobby Fischer (97.89 CAPS, 2775 projected Elo, 83.50% top engine match, 379 games/13,842 moves).
Markovian model (2017) In 2017, Jean-Marc Alliot of the Toulouse Computer Science Research Institute (IRIT) presented a new method, based on a Markovian interpretation of a chess game. Starting with those of Wilhelm Steinitz, all 26,000 games played since then by chess world champions have been processed by a supercomputer using the Stockfish chess engine (rated above 3310 Elo).
These predictions have proven not only to be extremely close to the actual results when players have played concrete games against one another, but to also fare better than those based on Elo scores. The results demonstrate that the level of chess players has been steadily increasing. Magnus Carlsen (in 2013) tops the list, while Vladimir Kramnik (in 1999) is second, Bobby Fischer (in 1971) is third, and Garry Kasparov (in 2001) is fourth.
Larry Kaufman (2023) Larry Kaufman published an article in 2023 estimating the ratings of chess players throughout history by comparing their games with the choices of top engines, using Chess.com accuracy scores. He considered only world championship matches and tournaments (official or unofficial, and including women's championships), Candidates and Interzonal events, and non-title matches between the world champion and top contenders. He ignored drawn games, because he believed that previous analyses favoured players who played cautiously, with drawn games generally having fewer inaccuracies than wins.
He estimated ratings for players at their peak years by converting their adjusted “Quality” scores (based on Chess.com engine accuracy in decisive games) to a scale corresponding to Elo ratings in 2023. He estimated ratings for 47 players, with the following top ten:
Magnus Carlsen, 2858 (peak years 2013–2021) Garry Kasparov, 2821 (peak years 1993–2001) Bobby Fischer, 2802 (peak years 1970–1972) Ian Nepomniachtchi, 2786 (peak years 2020–2022) Vladimir Kramnik, 2785 (peak years 2000–2007) Viswanathan Anand, 2780 (peak years 2007–2014) Veselin Topalov, 2773 (peak years 2005–2009) Anatoly Karpov, 2746 (peak years 1974–1984)