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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

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,.

Table of top 20 rated players ever, with date their best ratings were achieved for the first time
Rank	Rating	Player	Year-month
1	2851	Garry Kasparov	1999-07
2	2813	Veselin Topalov	2006-07
3	2809	Vladimir Kramnik	2001-10
4	2803	Viswanathan Anand	2006-04
5	2788	Alexander Morozevich	2008-07
6	2787	Vassily Ivanchuk	2007-10
7	2786	Magnus Carlsen	2008-10
8	2785	Bobby Fischer	1972-04
9	2780	Anatoly Karpov	1994-07
10	2765	Peter Svidler	2006-01
11	2763	Péter Lékó	2005-04
	2763	Levon Aronian	2006-07
13	2760	Shakhriyar Mamedyarov	2008-01
14	2755	Michael Adams	2000-07
	2755	Alexei Shirov	2008-01
16	2751	Teimour Radjabov	2008-04
17	2745	Gata Kamsky	1996-07
18	2743	Ruslan Ponomariov	2002-04
19	2739	Evgeny Bareev	2003-10
20	2737	Boris Gelfand	2008-01
	2737	Dmitry Jakovenko	2008-10

The average Elo rating of top players has risen over time. For instance, the average of the top 100 has risen from 2645 in July 2001 to 2665 in July 2006. 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.

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".

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, for example in spring 2008 its 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	Vassily 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 number of years, followed closely by Lasker and Karpov.

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:

These "Divinsky numbers" are not on the same scale as Elo ratings (the last person on the list, Johann Zukertort, has a Divinsky number of 873). 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

One of the latest methods of analyzing chess abilities across history has come from Matej Guid and Ivan Bratko from the Department of Computer and Information Science of Ljubljana University. 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. 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. As of 2006 Crafty's ELO rating was 2657, below many historical top human players and several other computer programs.

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

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

Irving Chernev

In 1976 chess author Irving Chernev published the book Golden Dozen, in which he ranked his all-time top twelve: 1. Capablanca, 2. Alekhine, 3. Lasker, 4. Fischer, 5. Botvinnik, 6. Petrosian, 7. Tal, 8. Smyslov, 9. Spassky, 10. Bronstein, 11. Rubinstein 12. Nimzowitsch

Leonard Barden

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.

Viswanathan Anand

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

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 champion
Emanuel Lasker	7	7			27
Garry Kasparov	6	4		2	15
Anatoly Karpov	6	3	3		16
Mikhail Botvinnik	5	5			13
Alexander Alekhine	4	4			17
Wilhelm Steinitz	4	4			8
Vladimir Kramnik	3	1		2	6
Tigran Petrosian	2	2			6
Viswanathan Anand	2	1	1		2
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