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Several methods have been suggested for comparing the greatest chess players in history. There is agreement on a statistical system to rate the strengths of current players, called the Elo system, but disagreement about methods used to compare players from different generations who never competed against each other.

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The most well known statistical method was devised by Arpad Elo in and elaborated on in his book The Rating of Chessplayers, Past and Present. According to this system the highest ratings achieved were:. Though published in , Elo's list did not include five-year averages for later players Bobby Fischer and Anatoly Karpov. It did list January ratings of for Fischer and for Karpov.

In , 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 September , [update] there are chess players in history who broke , and 15 of them exceeded The average Elo rating of top players has risen over time.

For instance, the average of the top 10 active players rose from in July to in July , a point increase in 14 years.

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The average rating of the top players, meanwhile, increased from to , a point increase. Elo said it was futile to attempt to use ratings to compare players from different eras and that they could only measure the strength of a player as compared to their contemporaries. Many statisticians besides Elo have devised similar methods to retrospectively rate players.

Jeff Sonas' rating system is called "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 allegedly suffered. One caveat is that a Chessmetrics rating takes into account the frequency of play.