This article examines a number of methodologies that have been suggested for the task of comparing top chess players throughout history, particularly the question of comparing the greatest players of different eras. Statistical methods offer objectivity but, whilst there is agreement on systems to rate the strengths of current players, there is disagreement and controversy on whether such techniques can be applied to players from different generations who never competed against each other.
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Perhaps the best-known statistical model is that devised by Arpad Elo. In his 1978 book The Rating of Chessplayers, Past and Present,[1] he gave ratings to players corresponding to their performance over the best five-year span of their career. According to this system the highest ratings achieved were:
(Though published in 1978, Elo's list did not include five-year averages for Bobby Fischer and Anatoly Karpov. It did list January 1978 ratings of 2780 for Fischer and 2725 for Karpov.[2])
In 1970, FIDE adopted Elo's system for rating current players, so one way to compare players of different eras is to compare their Elo ratings. The best-ever Elo ratings are tabulated below.[3]
As of January 2012, there were 84 chess grandmasters in history who broke the 2700 limit and only 6 of them were even capable of overcoming the 2800 line. Most astonishing were performances by players like R.J. Fischer, A. Karpov and G. Kasparov, who achieved their peak ratings in early era (1972, 1994, 1999).
Rank | Rating | Player | Year-month | Country |
---|---|---|---|---|
1 | 2851 | Garry Kasparov | 1999-07 | Russia |
2 | 2835 | Magnus Carlsen | 2012-01 | Norway |
3 | 2817 | Viswanathan Anand | 2011-03 | India |
4 | 2813 | Veselin Topalov | 2006-07 | Bulgaria |
5 | 2811 | Vladimir Kramnik | 2002-01 | Russia |
6 | 2808 | Levon Aronian | 2011-03 | Armenia |
7 | 2788 | Alexander Morozevich | 2008-07 | Russia |
8 | 2788 | Sergey Karjakin | 2011-07 | Russia |
9 | 2787 | Vassily Ivanchuk | 2007-10 | Ukraine |
10 | 2785 | Bobby Fischer | 1972-04 | United States |
11 | 2781 | Teimour Radjabov | 2011-11 | Azerbaijan |
12 | 2780 | Anatoly Karpov | 1994-07 | Russia |
13 | 2774 | Hikaru Nakamura | 2011-03 | United States |
14 | 2773 | Alexander Grischuk | 2011-01 | Russia |
15 | 2772 | Shakhriyar Mamedyarov | 2011-01 | Azerbaijan |
16 | 2768 | Ruslan Ponomariov | 2011-07 | Ukraine |
17 | 2765 | Peter Svidler | 2011-07 | Russia |
18 | 2763 | Peter Leko | 2005-04 | Hungary |
19 | 2761 | Boris Gelfand | 2010-01 | Israel |
20 | 2761 | Pavel Eljanov | 2010-09 | Ukraine |
The average Elo rating of top players has risen over time. For instance, the average of the top 100 active players rose from 2644 in July 2000 to 2697 in March 2011, a 53-point increase. Few months later, in January 2012, an increase of average rating is highly visible. TOP 100 active players have had an average ELO rating 2701,59 points.[4] Many people believe that this rise is mostly due to a system artifact known as ratings inflation, making it impractical to compare players of different eras.
Arpad Elo was of the opinion that it was futile to attempt to use ratings to compare players from different eras; in his view, they could only possibly measure the strength of a player as compared to his or her contemporaries. He also stated that the process of rating players was in any case rather approximate; 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".[5]
Even though, the country which each super-grandmaster represents in international venues (like chess olympiads, world team, european team competitions and other strongest international chess tournaments) is not most important argument for considering 'talent of a country for chess' as a whole criterion, (some players did not never represent their native country because of emigration, or for several other reasons), this table could be seen one standpoint of world chess federation divisions and for best records of FIDE membering countries.
This table includes all historical players peak rating by published FIDE ELO rating lists from 1970 to 2012.
Some (pre-1970) ratings published by Arpad Elo, which overlap 2700 ELO rating, are also included. ("2725 – José Raúl Capablanca - CUB"),("2720 – Mikhail Botvinnik - RUS"),("2720 – Emanuel Lasker - GER"),("2700 – Mikhail Tal - RUS").
Rank per amount of 2700+ players | Country with such players | Amount of super-grandmasters in peak | Average rating from country's players peak rating | Best player of the country | Highest achieved rating by the country |
---|---|---|---|---|---|
1 | Russia | 24 | 2 742 | Garry Kasparov | 2 851 |
2 | Ukraine | 5 | 2 750 | Vassily Ivanchuk | 2 787 |
3 | China | 5 | 2 728 | Yue Wang | 2 756 |
4 | United States | 4 | 2 754 | Bobby Fischer | 2 785 |
5 | Hungary | 4 | 2 733 | Peter Leko | 2 763 |
6 | Azerbaijan | 3 | 2 771 | Teimour Radjabov | 2 781 |
7 | France | 3 | 2 727 | Etienne Bacrot | 2 731 |
8 | Israel | 3 | 2 722 | Boris Gelfand | 2 761 |
9 | Netherlands | 3 | 2 714 | Anish Giri | 2 722 |
10 | India | 2 | 2 764 | Viswanathan Anand | 2 817 |
11 | Bulgaria | 2 | 2 763 | Veselin Topalov | 2 813 |
? | Armenia | 3 | Мовсесян | Levon Aronian | 2 808 |
13 | Spain | 2 | 2 740 | Alexei Shirov | 2 755 |
14 | England | 2 | 2 734 | Michael Adams | 2 755 |
15 | Cuba | 2 | 2 728 | Leinier Dominguez Perez | 2 730 |
16 | Germany | 2 | 2 718 | Emanuel Lasker | 2 720 |
17 | Czech Republic | 2 | 2 718 | David Navara | 2 731 |
18 | Poland | 2 | 2 714 | Radoslaw Wojtaszek | 2 726 |
19 | Georgia | 2 | 2 709 | Baadur Jobava | 2 715 |
20 | Norway | 1 | 2 835 | Magnus Carlsen | 2 835 |
22 | Italy | 1 | 2 736 | Fabiano Caruana | 2 736 |
23 | Vietnam | 1 | 2 717 | Quang Liem Le | 2 717 |
24 | Slovenia | 1 | 2 710 | Alexander Beliavsky | 2 710 |
25 | Romania | 1 | 2 707 | Liviu-Dieter Nisipeanu | 2 707 |
26 | Uzbekistan | 1 | 2 706 | Rustam Kasimdzhanov | 2 706 |
27 | Switzerland | 1 | 2 705 | Vadim Milov | 2 705 |
28 | Moldova | 1 | 2 700 | Viktor Bologan | 2 700 |
29 | Denmark | 1 | 2 700 | Peter Heine Nielsen | 2 700 |
Many statisticians since Elo have devised similar methods to retrospectively rate players. Jeff Sonas, for example, calls his system 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 apparently suffered.
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".[6] While it may be in the best interest of the fans for chess-players to remain active, it is not clear why a person's rating, which reflects his/her skill at chess, should drop if the player is inactive for a period of time.
Sonas, like Elo, acknowledges that it is useless to try to compare the strength of players from different eras. In his explanation of the Chessmetrics system,[7] he says:
Nevertheless Sonas' Web site does compare players from different eras, and shows that in such cases the Chessmetrics system is rather sensitive to the length of the periods being compared. Including data until December 2004, the rankings were:
Position | 1 year[8] | 5 years[9] | 10 years[10] | 15 years[11] | 20 years[12] |
---|---|---|---|---|---|
1 | Bobby Fischer | Garry Kasparov | Garry Kasparov | Garry Kasparov | Garry Kasparov |
2 | Garry Kasparov | Emanuel Lasker | Emanuel Lasker | Anatoly Karpov | Anatoly Karpov |
3 | Mikhail Botvinnik | José Capablanca | Anatoly Karpov | Emanuel Lasker | Emanuel Lasker |
4 | José Capablanca | Mikhail Botvinnik | José Capablanca | José Capablanca | Alexander Alekhine |
5 | Emanuel Lasker | Bobby Fischer | Bobby Fischer | Alexander Alekhine | Viktor Korchnoi |
6 | Alexander Alekhine | Anatoly Karpov | Mikhail Botvinnik | Mikhail Botvinnik | Vasily Smyslov |
In a 2005 ChessBase article,[13] Sonas uses Chessmetrics to evaluate historical annual performance ratings and comes to the conclusion that Kasparov was dominant for the most years, followed closely by Karpov and Lasker.
In contrast to Elo and Sonas's systems, Raymond Keene and Nathan Divinsky's book Warriors of the Mind[14] 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. Considering games played between sixty-four of the strongest players in history, they come up with the following top ten:[15]
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,[16] and Warriors of the Mind has also been criticised for its arbitrary selection process and bias towards modern players.[17]
A computer-based method of analyzing chess abilities across history came from Matej Guid and Ivan Bratko from the Department of Computer and Information Science of University of Ljubljana, Slovenia, in 2006.[18] The basis for their evaluation was the difference between the position values resulting from the moves played by the human chess player and the moves chosen as best by a chess program, Crafty. They also compared the average number of errors in the player's game. Opening moves were excluded, in an attempt to negate the progress in chess opening theory. According to their analysis, the leader was José Raúl Capablanca, followed closely by Vladimir Kramnik.
The "Classical" World Chess Championship matches were analyzed, and the results for the fourteen Classical World Champions were presented.
Players with fewest average errors:
The method received a number of criticisms, including: the study used a modified version of Crafty rather than the standard version; even the standard version of Crafty was not strong enough to evaluate the world champions' play; one of the modifications restricted the search depth to 12 half-moves, which is often insufficient.[19] As of 2006 Crafty's Elo rating was 2657, below many historical top human players and several other computer programs.
A similar project was also conducted in 2007 using Rybka 2.3.2a and a modified version of Crafty 20.14.[20]
Analysis by Rybka 3 and comparisons with modern ratings http://web.zone.ee/chessanalysis/summary450.pdf
A number of prominent players and writers have attempted to rank the greatest players. Generally these lists attempt to combine the two methods above—performance, and analysis of games.
In 1964 Bobby Fischer listed his top 10 in Chessworld magazine: Morphy, Staunton, Steinitz, Tarrasch, Chigorin, Alekhine, Capablanca, Spassky, Tal, Reshevsky.[21][22]
In 1976 chess author Irving Chernev published the book The Golden Dozen, in which he ranked his all-time top twelve: 1. Capablanca, 2. Alekhine, 3. Em. Lasker, 4. Fischer, 5. Botvinnik, 6. Petrosian, 7. Tal, 8. Smyslov, 9. Spassky, 10. Bronstein, 11. Rubinstein, and 12. Nimzowitsch.[23]
When interviewed shortly after Fischer's death, then current world champion Viswanathan Anand ranked Kasparov first and Fischer second.[24]
Earlier in 2000, when Karpov, Korchnoi and Kasparov were still active, Anand listed his top 10 as: Fischer, Morphy, Em. Lasker, Capablanca, Steinitz, Tal, Korchnoi, Keres, Karpov and Kasparov.[25]
In his 2008 obituary of Bobby Fischer, Leonard Barden wrote that most experts ranked Kasparov as the greatest ever, with either Fischer or Karpov second.[26]
In an interview with Vladislav Tkachiev for the website WhyChess, former World Champion Vladimir Kramnik stated that he considered Viswanathan Anand as a colossal talent and one of the greatest in the whole history of chess.[27]
The number of world championship wins, or world championship reigns, can be considered as a guide to player greatness. The table below organises the world champions in order of championship wins. (For the purpose of this table, a successful defence counts as a win, even if the match was drawn.) The table is made more complicated by the split between the "Classical" and FIDE world titles between 1993 and 2006.
Champion | Total | Undisputed | FIDE | Classical | Years as Undisputed Champion | Years as FIDE/Classical Champion |
---|---|---|---|---|---|---|
Emanuel Lasker | 6 | 6 | 27 | |||
Garry Kasparov | 6 | 4 | 2 | 8 | 7 | |
Anatoly Karpov | 6 | 3 | 3 | 10 | 6 | |
Mikhail Botvinnik | 5 | 5 | 13 | |||
Alexander Alekhine | 4 | 4 | 17 | |||
Wilhelm Steinitz | 4 | 4 | 8 | |||
Viswanathan Anand | 4 | 3 | 1 | 4 | 2 | |
Vladimir Kramnik | 3 | 1 | 2 | 1 | 6 | |
Tigran Petrosian | 2 | 2 | 6 | |||
José Raúl Capablanca | 1 | 1 | 6 | |||
Boris Spassky | 1 | 1 | 3 | |||
Bobby Fischer | 1 | 1 | 3 | |||
Max Euwe | 1 | 1 | 2 | |||
Vasily Smyslov | 1 | 1 | 1 | |||
Mikhail Tal | 1 | 1 | 1 | |||
Ruslan Ponomariov | 1 | 1 | 2 | |||
Alexander Khalifman | 1 | 1 | 1 | |||
Rustam Kasimdzhanov | 1 | 1 | 1 | |||
Veselin Topalov | 1 | 1 | 1 |