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. Statistical methods Elo system The best-known statistical method was devised by Arpad Elo in 1960 and 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: 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 later players 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 fourteen of them exceeded 2800. The high peak ratings of Fischer, Karpov, and Kasparov are notable for being achieved last century (1972, 1994, and 1999 respectively). However, Fischer and Karpov are no longer in the top 20. {| class="wikitable sortable" style="font-size:100%;" |+Table of top 20 rated players of all-time, with date their best ratings were first achieved !Rank !Rating !Player !Date !Age |- style="text-align: center;" |011 | 2882 | style="text-align: left;" | Magnus Carlsen |2014-05May 2014 | |- style="text-align: center;" |022 | 2851 | style="text-align: left;" | Garry Kasparov |1999-07July 1999 | |- style="text-align: center;" |033 | 2844 | style="text-align: left;" | Fabiano Caruana |2014-10October 2014 | |- style="text-align: center;" |044 | 2830 | style="text-align: left;" | Levon Aronian |2014-03March 2014 | |- style="text-align: center;" |055 | 2822 | style="text-align: left;" | Wesley So |2017-02February 2017 | |- style="text-align: center;" |066 | 2820 | style="text-align: left;" | Shakhriyar Mamedyarov |2018-09September 2018 | |- style="text-align: center;" |077 | 2819 | style="text-align: left;" | Maxime Vachier-Lagrave |2016-08 August 2016 | |- style="text-align: center;" |088 (tie) | 2817 | style="text-align: left;" | Viswanathan Anand |2011-03March 2011 | |- style="text-align: center;" |088 (tie) | 2817 | style="text-align: left;" | Vladimir Kramnik |