Comparison of top chess players throughout history Information
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.
The best-known statistical 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. 
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.
Table of top 20 rated players of all-time, with date their best ratings were first achieved Rank Rating Player Date Age 1 2882 Magnus Carlsen May 2014 23 years, 5 months 2 2851 Garry Kasparov July 1999 36 years, 2 months 3 2844 Fabiano Caruana October 2014 22 years, 2 months 4 2830 Levon Aronian March 2014 31 years, 4 months 5 2822 Wesley So February 2017 23 years, 3 months 6 2820 Shakhriyar Mamedyarov September 2018 33 years, 4 months 7 2819 Maxime Vachier-Lagrave August 2016 25 years, 9 months 8 (tie) 2817 Viswanathan Anand March 2011 41 years, 2 months 8 (tie) 2817 Vladimir Kramnik October 2016 41 years, 3 months 10 (tie) 2816 Veselin Topalov July 2015 40 years, 3 months 10 (tie) 2816 Hikaru Nakamura October 2015 27 years, 9 months 10 (tie) 2816 Ding Liren November 2018 26 years 13 2810 Alexander Grischuk December 2014 31 years, 1 month 14 2804 Alireza Firouzja December 2021 18 years, 5 months 15 2798 Anish Giri October 2015 21 years, 3 months 16 2793 Teimour Radjabov November 2012 25 years, 7 months 17 2792 Ian Nepomniachtchi May 2021 30 years, 9 months 18 (tie) 2788 Alexander Morozevich July 2008 30 years, 11 months 18 (tie) 2788 Sergey Karjakin July 2011 21 years, 5 months 20 2787 Vassily Ivanchuk October 2007 38 years, 6 months
The average Elo rating of top players has risen over time. For instance, the average of the top 10 active players rose from 2751 in July 2000 to 2794 in July 2014, a 43-point increase in 14 years. The average rating of the top 100 players, meanwhile, increased from 2644 to 2703, a 59-point increase.  Many people believe that this rise is mostly due to an anomaly known as ratings inflation, making it impractical to compare players of different eras. 
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 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".  
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.[ according to whom?]
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." 
Sonas, like Elo, claims that it is impossible to compare the strength of players from different eras, saying:
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 José 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' website does compare players from different eras. Including data until December 2004, the ratings were:
|Rank||1-year peak ||5-year peak ||10-year peak ||15-year peak ||20-year peak |
|1||Bobby Fischer, 2881||Garry Kasparov, 2875||Garry Kasparov, 2863||Garry Kasparov, 2862||Garry Kasparov, 2856|
|2||Garry Kasparov, 2879||Emanuel Lasker, 2854||Emanuel Lasker, 2847||Anatoly Karpov, 2820||Anatoly Karpov, 2818|
|3||Mikhail Botvinnik, 2871||José Capablanca, 2843||Anatoly Karpov, 2821||Emanuel Lasker, 2816||Emanuel Lasker, 2809|
|4||José Capablanca, 2866||Mikhail Botvinnik, 2843||José Capablanca, 2813||José Capablanca, 2798||Alexander Alekhine, 2781|
|5||Emanuel Lasker, 2863||Bobby Fischer, 2841||Bobby Fischer, 2810||Alexander Alekhine, 2794||Viktor Korchnoi, 2766|
|6||Alexander Alekhine, 2851||Anatoly Karpov, 2829||Mikhail Botvinnik, 2810||Mikhail Botvinnik, 2789||Vasily Smyslov, 2759|
In 2005,  Sonas used Chessmetrics to evaluate historical annual performance ratings and came to the conclusion that Kasparov was dominant for the most years, followed by Karpov and Lasker. He also published the following list of the highest ratings ever attained according to calculations done at the start of each month: 
Rank Rating Player 1 2895 Bobby Fischer 2 2886 Garry Kasparov 3 2885 Mikhail Botvinnik 4 2878 Emanuel Lasker 5 2877 José Capablanca 6 2860 Alexander Alekhine 7 2848 Anatoly Karpov 8 2833 Viswanathan Anand 9 2826 Vladimir Kramnik 10 2826 Wilhelm Steinitz
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 (through December 2004). Considering games played between sixty-four of the strongest players in history, they came up with the following top ten: 
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 been accused of arbitrarily selecting players and bias towards modern players. 
The idea of this approach is to compare the moves played by humans to top engine moves, with the rationale that players more likely to choose these moves are also stronger.
A computer-based method of analyzing chess abilities across history came from Matej Guid and Ivan Bratko at the University of Ljubljana, Slovenia, in 2006.  A similar project was conducted for World Champions in 2007–08 using Rybka 2.3.2a (then-strongest chess program) and a modified version of Guid and Bratko's program "Crafty".  CAPS (Computer Aggregated Precision Score) is a system created by Chess.com that compares players from different eras by finding the percentage of moves that matches that of a chess engine. 
In 2017 Jean-Marc Alliot of the Toulouse Computer Science Research Institute ( IRIT) presented a new method,  based on a Markovian interpretation of a chess game. Starting with those of Wilhelm Steinitz, all 26,000 games played since then by chess world champions have been processed by a supercomputer using the Stockfish chess engine (rated above 3310 Elo).
These predictions have proven not only to be extremely close to the actual results when players have played concrete games against one another, but to also fare better than those based on Elo scores. The results demonstrate that the level of chess players has been steadily increasing. Magnus Carlsen (in 2013) tops the list, while Vladimir Kramnik (in 1999) is second, Bobby Fischer (in 1971) is third, and Garry Kasparov (in 2001) is fourth.
Many prominent players and chess writers have offered their own rankings of players.
In 1964, Bobby Fischer listed his top 10 in Chessworld magazine: Morphy, Staunton, Steinitz, Tarrasch, Chigorin, Alekhine, Capablanca, Spassky, Tal, and Reshevsky.   He considered Morphy to be "perhaps the most accurate", writing: "In a set match he would beat anyone alive today." 
In 1974, popular chess author Irving Chernev published an article titled Who were the greatest? in the English magazine CHESS.  He followed this up with his 1976 book The Golden Dozen, in which he ranked his all-time top twelve: 1. Capablanca, 2. Alekhine, 3. Lasker, 4. Fischer, 5. Botvinnik, 6. Petrosian, 7. Tal, 8. Smyslov, 9. Spassky, 10. Bronstein, 11. Rubinstein, and 12. Nimzowitsch. 
In a 1992 interview GM Miguel Quinteros gave the opinion:  "I think Fischer was and still is the greatest chess player of all time. [...] During his absence other good chess players have appeared. But no one equals Fischer's talent and perfection."
When interviewed in 2008 shortly after Fischer's death, he ranked Fischer and Kasparov as the greatest, with Kasparov a little ahead by virtue of being on top for so many years. 
In 2012, Anand stated that he considered Fischer the best player and also the greatest, because of the hurdles he faced. 
Svetozar Gligorić reported in his book Shall We Play Fischerandom Chess? (Batsford, 2002):
At the beginning of 2001 a large poll for the "Ten Greatest Chess Players of the 20th Century, selected by Chess Informant readers" resulted in Fischer having the highest percentage of votes and finishing as No. 1, ahead of Kasparov, Alekhine, Capablanca, Botvinnik, Karpov, Tal, Lasker, Anand and Korchnoi. 
BBC award-winning journalists, from their book Bobby Fischer Goes to War: How the Soviets Lost the Most Extraordinary Chess Match of All Time (HarperCollins, 2004):
Fischer, some will maintain, was the outstanding player in chess history, though there are powerful advocates too for Lasker, Capablanca, Alekhine, and Kasparov. Many chess players will dismiss such comparisons as meaningless, akin to the futile attempt to grade the supreme musicians of all time. But the manner in which Fischer stormed his way to Reykjavik, his breathtaking dominance at the Palma de Majorca Interzonal, the trouncings of Taimanov, Larsen, and Petrosian—all this was unprecedented. There never has been an era in modern chess during which one player has so overshadowed all others. 
In a 2005 interview, Vladimir Kramnik (World Champion from 2000 to 2007) did not name a greatest player, but stated: "The other world champions had something 'missing'. I can't say the same about Kasparov: he can do everything." 
In an interview in 2011, Vladimir Kramnik said about Anand: "I always considered him to be a colossal talent, one of the greatest in the whole history of chess", "I think that in terms of play Anand is in no way weaker than Kasparov", and "In the last 5–6 years he's made a qualitative leap that's made it possible to consider him one of the great chess players". 
In a 2022 interview after the 5th round of the first leg in FIDE Grand Prix 2022, when asked if he thought that in the future Garry Kasparov or Magnus Carlsen would be considered the 'GOAT', Levon Aronian stated that "I kind of feel that Magnus will be the greatest for a long long time, because for me he is probably already the greatest but it is still continuing. It will take a long time to beat his achievements." 
In December 2015 he said he would like to play Fischer and Kasparov at their peak performance. 
In January 2020, Carlsen said, "Kasparov had 20 years uninterrupted as the world No 1. And I would say for very few of those years was there any doubt that he was the best player. He must be considered as the best in history."  He made a similar claim in 2021, saying "Garry Kasparov, in my opinion, the greatest player there's ever been..." 
In 2021, Hikaru Nakamura published a youtube video entitled "Hikaru's Hot Takes on the Ten Best Chess Players of All Time"  in which he reviewed a chess.com article on "The 10 Best Chess Players Of All Time."  In this video he suggested that it was unfair to exclude Paul Morphy and Viswanathan Anand from the 10 greatest players of all time. Hikaru stated that Bobby Fischer should "obviously be number 3" and that Garry Kasparov and Magnus Carlsen should be at number 1 and number 2 respectively with the caveat that Kasparov is only number 1 due to his time as number 1 in the world being greater than Carlsen's. At the end of the video, Hikaru said he "can live with" the top 5 as: Kasparov, Carlsen, Fischer, Capablanca and Karpov but he would put from 6 through 10: Anand, Kramnik, Botvinnik, Lasker, Morphy.
The table below organises the world champions in order of championship wins. (For the purpose of this table, a successful defence counts as a win, even if the match was drawn.) The table is made more complicated by the split between the "Classical" and FIDE world titles between 1993 and 2006.
|José Raúl Capablanca||1||1||6||6|
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- This table is based on one created by Przemek Jahr of Poland, which was reported in Chessbase 2-7-2005. FIDE ratings were officially compiled and released quarterly, in January, April, July, and October until July 2009. Starting in July 2009 they were released on a two-monthly basis, and since July 2012 FIDE publishes its ratings monthly.
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