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.

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 Bobb 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 first achieved**
Rank	Rating	Player	Year-month	Country
1	2851	Garry Kasparov	1999-07	Russia
2	2826	Magnus Carlsen	2010-07	Norway
3	2817	Viswanathan Anand	2011-03	India
4	2813	Veselin Topalov	2006-07	Bulgaria
5	2809	Vladimir Kramnik	2001-10	Russia
6	2808	Levon Aronian	2011-03	Armenia
7	2788	Alexander Morozevich	2008-07	Russia
8	2787	Vassily Ivanchuk	2007-10	Ukraine
9	2785	Bobby Fischer	1972-01	United States
10	2780	Anatoly Karpov	1994-07	Russia
11	2776	Sergey Karjakin	2011-01	Russia
12	2774	Hikaru Nakamura	2011-03	United States
13	2773	Alexander Grischuk	2011-01	Russia
14	2772	Shakhriyar Mamedyarov	2011-01	Azerbaijan
15	2765	Peter Svidler	2006-01	Russia
16	2763	Peter Leko	2005-04	Hungary
17	2761	Teimour Radjabov	2009-01	Azerbaijan
17	2761	Boris Gelfand	2010-01	Israel
17	2761	Pavel Eljanov	2010-09	Ukraine
20	2760	Dmitry Jakovenko	2009-01	Russia

The average Elo rating of top players has risen over time. For instance, the average of the top 100 active player rose from 2644 in July 2000 to 2697 in March 2011, a 53-point increase. 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".

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 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:

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 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:

José Raúl Capablanca
Vladimir Kramnik
Anatoly Karpov
Garry Kasparov
Boris Spassky
Tigran Petrosian
Emanuel Lasker
Bobby Fischer
Alexander Alekhine
Vasily Smyslov
Mikhail Tal
Mikhail Botvinnik
Max Euwe
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

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