Methods for comparing top chess players throughout history

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.

Statistical methods

Elo system

Main article: Elo rating system

Perhaps the best-known statistical model is that devised by Arpad Elo. In his 1978 book The Rating of Chessplayers, Past and Present, 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:

• 2725 – José Raúl Capablanca
• 2720 – Mikhail Botvinnik, Emanuel Lasker
• 2700 – Mikhail Tal
• 2690 – Alexander Alekhine, Paul Morphy, Vasily Smyslov.

(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.)

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.

As of March 2012, there were 85 chess grandmasters in history who broke the 2700 limit and only 6 of them were 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 earlier years (1972, 1994, 1999).

Table of top 20 rated players ever, with date their best ratings were first achieved

Rank	Rating	Player	Year-month	Country
1	2851	Garry Kasparov	1999-07	Russia
2	2835	Magnus Carlsen	2012-01	Norway
3	2820	Levon Aronian	2012-03	Armenia
4	2817	Viswanathan Anand	2011-03	India
5	2813	Veselin Topalov	2006-07	Bulgaria
6	2809	Vladimir Kramnik	2001-10	Russia
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	2784	Teimour Radjabov	2012-03	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	2767	Fabiano Caruana	2012-03	Italy
18	2765	Peter Svidler	2011-07	Russia
19	2763	Peter Leko	2005-04	Hungary
20	2761	Boris Gelfand	2010-01	Israel
21	2761	Pavel Eljanov	2010-09	Ukraine
22	2761	Vugar Gashimov	2012-01	Azerbaijan

Average rating over time

The average Elo rating of top players has risen over time. For instance, the average of the TOP 10 active players in July 2000 rose from 2751 to 2787 in March 2012, a 36-point increased average during nearly 12 years.

Average rating of the TOP 100 players increased meanwhile from 2644 to 2700, with a 56-points up in a result.

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".

By country

Even though, the country which each of super-grandmasters represent 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 ever 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").

'Historical table of best country by amount of strongest players' (as of March 2012)

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	25	2740	Garry Kasparov	2851
2	Ukraine	5	2750	Vassily Ivanchuk	2787
3	China	5	2728	Wang Yue	2756
4	United States	4	2754	Bobby Fischer	2785
5	Hungary	4	2733	Peter Leko	2763
6	Azerbaijan	3	2772	Teimour Radjabov	2784
7	Armenia	3	2761	Levon Aronian	2820
8	France	3	2727	Etienne Bacrot	2731
9	Israel	3	2722	Boris Gelfand	2761
10	Netherlands	3	2714	Anish Giri	2722
11	India	2	2764	Viswanathan Anand	2817
12	Bulgaria	2	2763	Veselin Topalov	2813
13	England	2	2734	Michael Adams	2755
14	Cuba	2	2728	Leinier Domínquez Pérez	2730
15	Germany	2	2718	Emanuel Lasker	2720
16	Czech Republic	2	2718	David Navara	2731
17	Poland	2	2714	Radoslaw Wojtaszek	2726
18	Georgia	2	2709	Baadur Jobava	2715
19	Norway	1	2835	Magnus Carlsen	2835
20	Latvia	1	2755	Alexei Shirov	2755
21	Italy	1	2767	Fabiano Caruana	2767
22	Spain	1	2724	Francisco Vallejo Pons	2724
23	Vietnam	1	2717	Quang Liem Le	2717
24	Slovenia	1	2710	Alexander Beliavsky	2710
25	Romania	1	2707	Liviu-Dieter Nisipeanu	2707
26	Uzbekistan	1	2706	Rustam Kasimdzhanov	2706
27	Switzerland	1	2705	Vadim Milov	2705
28	Moldova	1	2700	Viktor Bologan	2700
29	Denmark	1	2700	Peter Heine Nielsen	2700

Chessmetrics

Main article: Chessmetrics

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". 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, he says:

Of course, a rating always indicates the level of dominance of a particular player against contemporary peers; it says nothing about whether the player is stronger/weaker in their actual technical chess skill than a player far removed from them in time. So while we cannot say that Bobby Fischer in the early 1970s or Jose Capablanca in the early 1920s were the "strongest" players of all time, we can say with a certain amount of confidence that they were the two most dominant players of all time. That is the extent of what these ratings can tell us.

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	5 years	10 years	15 years	20 years
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, 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.

Warriors of the Mind

In contrast to Elo and Sonas's systems, Raymond Keene and Nathan Divinsky's book Warriors of the Mind 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:

1. Garry Kasparov, 3096
2. Anatoly Karpov, 2876
3. Bobby Fischer, 2690
4. Mikhail Botvinnik, 2616
5. José Raúl Capablanca, 2552
6. Emanuel Lasker, 2550
7. Viktor Korchnoi, 2535
8. Boris Spassky, 2480
9. Vasily Smyslov, 2413
10. 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 also been criticised for its arbitrary selection process and bias towards modern players.

Actual moves played compared with computer choices

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. 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:

1. José Raúl Capablanca
2. Vladimir Kramnik
3. Anatoly Karpov
4. Garry Kasparov
5. Boris Spassky
6. Tigran Petrosian
7. Emanuel Lasker
8. Bobby Fischer
9. Alexander Alekhine
10. Vasily Smyslov
11. Mikhail Tal
12. Mikhail Botvinnik
13. Max Euwe
14. Wilhelm Steinitz

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. 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.

Analysis by Rybka 3 and comparisons with modern ratings http://web.zone.ee/chessanalysis/summary450.pdf

Subjective lists

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.

Bobby Fischer (1964)

In 1964 Bobby Fischer listed his top 10 in Chessworld magazine: Morphy, Staunton, Steinitz, Tarrasch, Chigorin, Alekhine, Capablanca, Spassky, Tal, Reshevsky.

Irving Chernev (1976)

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.

Viswanathan Anand (2008)

When interviewed shortly after Fischer's death, then current world champion Viswanathan Anand ranked Kasparov first and Fischer second.

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.

Leonard Barden (2008)

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.

Vladimir Kramnik (2011)

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.

World Champions by world title reigns

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

See also

• List of FIDE chess world number ones