Comparison of top chess players throughout history
This article presents a number of methodologies that have been suggested for the task of comparing the greatest chess players in history. Statistical methods offer objectivity but, while there is agreement on systems to rate the strengths of current players, there is disagreement on whether such techniques can be applied to players from different generations who never competed against each other.
CAPS stands for Computer Aggregated Precision Score. CAPS is a new system created by chess.com that compares players from different eras by finding the percentage of moves that matches that of a computer. A score is then assigned based on percentage of matches and move value (for example, if the move was not the best, but still good, points are awarded). CAPS ignores both style and psychology.
An article can be found here:
https://www.chess.com/article/view/better-than-ratings-chess-com-s-new-caps-system
According to the system, Carlsen was the best player ever, with a CAPS score of 98.36 and a top engine match of 85.26%. He was followed closely by Kramnik, and then Kasparov.
A comparison of the top players can be found here:
Perhaps the best-known statistical model is that devised by Arpad Elo in 1960 and further elaborated on 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:
(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 December 2015, there were 101 chess players in history who broke 2700 and nine of them exceeded 2800. Particularly notable are the peak ratings of Fischer, Karpov and Kasparov, who achieved their peak ratings in earlier years (1972, 1994, and 1999 respectively).
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