Who is the best chess player of all time? Who is the most interesting? Would Paul Morphy (born 1837) beat Magnus Carlsen (born 1990) if they could play each other? When it comes to chess, everyone has an opinion, and several methodologies has also been developed in an effort to compare the greatest chess players in history. Statistical methods is one way to go, but they don’t really work for comparing players from different generations that never had a chance to play each other.
For contemporary players, Fédération Internationale des Échecs (FIDE) base their ranking list on the elo rating system. This is a statistical model devised by Arpad Elo in 1960 and further elaborated by him in the 1970’s. FIDE adopted it in 1970 and uses it to calculate the relative skill levels of players. The difference in rating between two rated opponents is used as a predictor of the outcome of the match. So, two chess players with identical rating is expected to score the same number of wins. A player rated 100 points above his opponent is expected to score 64 percent. A player rated 200 points above his opponent is expected to score 76 percent.
As of August 2015, there are 99 chess players that has ever reached an elo rating of 2700. Of these 99 players, only nine have reached an elo rating of 2800. The list below display the top twenty elo-rated chess players of all time. As you can see, most of them achieved their top rating in 2005 or later. There are three exceptions: Bobby Fischer (April 1972), Anatoly Karpv (July 1994) and Garry Kasparov (July 1999).
| Rank | Rating | Player | When was the player’s best rating first achieved? |
| 1 | 2882 | Magnus Carlsen | May 2014 |
| 2 | 2851 | Garry Kasparov | July 1999 |
| 3 | 2844 | Fabiano Caruana | October 2014 |
| 4 | 2830 | Levon Aronian | March 2014 |
| 5 | 2817 | Viswanathan Anand | March 2011 |
| 6 | 2816 | Veselin Topalov | July 2015 |
| 7 | 2814 | Hikaru Nakamura | July 2015 |
| 8 | 2811 | Vladimir Kramnik | May 2013 |
| 9 | 2810 | Alexander Grischuk | December 2014 |
| 10 | 2797 | Anish Giri | February 2015 |
| 11 | 2793 | Teimour Radjabov | November 2012 |
| 12 (tie) | 2788 | Alexander Morozevich | July 2008 |
| 12 (tie) | 2788 | Sergey Karjakin | July 2011 |
| 12 (tie) | 2788 | Wesley So | February 2015 |
| 15 | 2787 | Vassily Ivanchuk | October 2007 |
| 16 | 2785 | Bobby Fischer | April 1972 |
| 17 | 2782 | Ding Liren | September 2015 |
| 18 | 2780 | Anatoly Karpov | July 1994 |
| 19 | 2777 | Boris Gelfand | November 2013 |
| 20 (tie) | 2775 | Shakhriyar Mamedyarov | August 2013 |
| 20 (tie) | 2775 | Maxime Vachier-Lagrave | February 2015 |
The table below show the World Chess Champions in order of championship wins. In this table, a successful defense of ones title count as a win, even if the match itself was drawn.
Between 1993 and 2006, two rivaling international chess organizations (FIDE and PCA) and both arranged World Chess Championships and crowned World Chess Champions.
| Champion | Total | Undisputed | FIDE | Classical | Years as Undisputed Champion | Years as FIDE/Classical Champion | Total reign |
| Emanuel Lasker | 6 | 6 | 27 | 27 | |||
| Garry Kasparov | 6 | 4 | 2 | 8 | 7 | 15 | |
| Anatoly Karpov | 6 | 3 | 3 | 10 | 6 | 16 | |
| Mikhail Botvinnik | 5 | 5 | 13 | 13 | |||
| Viswanathan Anand | 5 | 4 | 1 | 6 | 2 | 8 | |
| Alexander Alekhine | 4 | 4 | 17 | 17 | |||
| Wilhelm Steinitz | 4 | 4 | 8 | 8 | |||
| Vladimir Kramnik | 3 | 1 | 2 | 1 | 6 | 7 | |
| Tigran Petrosian | 2 | 2 | 6 | 6 | |||
| Magnus Carlsen | 2 | 2 | 2 | 2 | |||
| José Raúl Capablanca | 1 | 1 | 6 | 6 | |||
| Boris Spassky | 1 | 1 | 3 | 3 | |||
| Bobby Fischer | 1 | 1 | 3 | 3 | |||
| Max Euwe | 1 | 1 | 2 | 2 | |||
| Vasily Smyslov | 1 | 1 | 1 | 1 | |||
| Mikhail Tal | 1 | 1 | 1 | 1 | |||
| Ruslan Ponomariov | 1 | 1 | 2 | 2 | |||
| Alexander Khalifman | 1 | 1 | 1 | 1 | |||
| Rustam Kasimdzhanov | 1 | 1 | 1 | 1 | |||
| Veselin Topalov | 1 | 1 | 1 | 1 |
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