Elo system

The most well known statistical method was devised by Arpad Elo in 1960 and elaborated on in his 1978 book The Rating of Chessplayers, Past and Present.^[1] 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.^[2]

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 September 2023,^[update] there are 133 chess players in history who broke 2700, and 14 of them exceeded 2800.

Average rating over time

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.^[3] 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.^[4]

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. 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".^[5][6]

Chessmetrics

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."^[7]

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.^[8]

Nevertheless, Sonas' website does compare players from different eras. Including data until December 2004, the ratings were:

In 2005,^[14] 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:^[15]

Warriors of the Mind

In contrast to Elo and Sonas's systems, Raymond Keene and Nathan Divinsky's book Warriors of the Mind^[16] 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:^[17]

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,^[18] and Warriors of the Mind has been accused of arbitrarily selecting players and bias towards modern players.^[19]

Early efforts

A computer-based process of analyzing chess abilities across history came from Matej Guid and Ivan Bratko at the University of Ljubljana, Slovenia, in 2006.^[20] 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".^[21] 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.^[22]

Markovian model (2017)

In 2017, Jean-Marc Alliot of the Toulouse Computer Science Research Institute (IRIT) presented a new method,^[23] 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.

Larry Kaufman (2023)

GM Larry Kaufman published an article in 2023 estimating the ratings of chess players throughout history by comparing their games with the choices of top engines, using Chess.com accuracy scores. He considered only world championship matches and tournaments (official or unofficial, and including women's championships), Candidates and Interzonal events, and non-title matches between the world champion and top contenders. In order to avoid the problem that draws show much fewer inaccuracies than decisive games, he only considered decisive games. He gave the following estimated ratings for 47 players at their peak years, on a scale corresponding to Elo ratings in 2023. (In his view, ratings inflated from their introduction in the 1970s until about 2006, when deflation began; by 2023, this had more or less cancelled out the earlier inflation, so that the 1970s ratings and the 2023 ratings are comparable, but those in between are not.)^[24]

(Morphy's top four opponents averaged 2021 over the years 1857–1859. The games at the 2020–21 Candidates averaged 2777, and those at the 2019 Women's Candidates averaged 2530. The level of the reference engine is roughly 3400.)^[24]

In some cases, Kaufman offered caveats. La Bourdonnais and Morphy usually played much faster than their opponents, essentially playing rapid rather than classical by today's standards, and so their true strengths were likely about 100 points higher than their games suggest. There were not enough non-handicap games against roughly matched opposition to judge the earlier French players François-André Danican Philidor and Alexandre Deschapelles (moreover, Philidor did not play by the modern rules, as then a player could not have two queens). According to Rod Edwards' Edo ratings, Deschapelles and La Bourdonnais were almost exactly tied in 1821, the one year when both were active.^[24] Regarding Philidor, Harold James Ruthven Murray wrote in his 1913 book A History of Chess: "It was an age of mediocre players, among whom Philidor stood easily first, but even he made mistakes repeatedly which would have been fatal against players of average skill who were not frightened into incapacity by the reputation of the master. At its best Philidor's play falls short of that accuracy of conception and richness of combination which characterized the play of De la Bourdonnais and MacDonnell."^[25] The contemporary Modenese masters (Ercole del Rio, Giambattista Lolli, and Domenico Lorenzo Ponziani) criticised Philidor's analyses of the opening, and modern theory sides with the Modenese masters: Philidor's favoured Bishop's Opening (1.e4 e5 2.Bc4) and Philidor's Defence (1.e4 e5 2.Nf3 d6) are considered inferior nowadays, while the King's Knight Opening (1.e4 e5 2.Nf3, a move Philidor thought was bad) is today considered the best second move for White after 1.e4 e5. The Modenese masters did praise Philidor's endgame analysis, though even that has some problems: Philidor correctly analyses his eponymous position in the rook and bishop versus rook endgame, but he wrongly thought that all positions in this endgame could be reduced to that one, which is false.^[25] IM Jeremy Silman and IM Willy Hendriks both consider the 17th-century player Gioachino Greco superior to Philidor.^[26][27]

Returning to Kaufman's caveats regarding the ratings he gave, Chigorin is likely underrated because of his predilection for gambit play, which increases the number of inaccuracies; similarly, Euwe and Bogoljubow are likely underrated because most of their games considered were against Alekhine, who tended to play extremely sharp openings. Menchik's games that were considered were against stronger opposition, so she is somewhat underrated (her real strength probably passed 2200). There were too few decisive games assessed to judge Fabiano Caruana (because his 2018 title match against Carlsen had all classical games drawn), but Kaufman suggests that "he might well be number two of all time, based on peak FIDE rating and the deflation since Kasparov's peak".^[24]

Kaufman finds that the quality of play rose steadily by about 2.5 Elo points per year from 1900 to 2023 (though the rate may have increased in the most recent years due to the advent of the Internet and strong chess engines); the rate was greater in the 19th century. Correcting for this leads to a list comparing players relatively according to their time, rather than the above list which compares them absolutely. The following list is valid for 2017 (the midpoint of Carlsen's peak):^[24]

Again, Kaufman considers that this somewhat underrates Morphy because of his fast play and the much higher rate of improvement per year before 1900; Kaufman writes "he might have rivaled Fischer for the top spot if we could properly correct for these factors." Finally, Kaufman provided a third list reducing the adjustment for earlier players to 2 Elo points per year rather than 2.5, which Kaufman estimated "should make the list a fairly accurate estimate of how these players would, in fact, rate in 2017 if born around 1987":^[24]

Morphy is similarly again underrated in Kaufman's view, and Kaufman estimates that he should be somewhere between fourth to nineteenth place on the above list if the factors affecting him could be corrected for. Fischer focused solely on chess and might be overrated compared to the others, whereas Reshevsky and Lasker were not full-time professionals and could be underrated.^[24]

Kaufman has contended for some time that the standard of play in the past was much worse than it is today, both based on annotating past games and from his own tournament experience going back to the 1960s. He writes regarding games of the 1930s: "It seemed to me that the superstar players played at a much lower level than today's stars, perhaps at the level of an ordinary grandmaster today, while most of the players of that time who are not famous today were likely not even of what we would now call master strength [2200]. This is partly due to unfamiliarity with what are now considered standard plans and ideas, but also to missing more tactics." Regarding the game Aron Nimzowitsch–Savielly Tartakower, Karlsbad 1929, he writes "If someone told me this was a recent game, I would guess the players to be rated around 2000. But they were among the top five at the time!" He mentions Kasparov as saying in the 1980s that even Ljubomir Ljubojević (who had finished last "in a certain tournament") "was stronger than Capablanca had been half a century earlier", and writes: "Although not a diplomatic thing to say, it was probably true".^[28]

Other players have agreed with Kaufman's contention of significant improvement over the years. GM John Nunn analysed the games of the Carlsbad 1911 chess tournament with the help of Fritz, and concluded that the average rating of the players at the tournament was 2129.^[29] In 1912, Tarrasch wrote that "the level of the masters back then [at Paris 1878] roughly equals that of the stronger participants in the main tournament of today"; IM Willy Hendriks suggests, based on what this difference between the best and simply a main tournament would mean in the modern era, that this was an improvement of 150–200 points between 1878 and 1912. Steinitz (in 1883) and Joseph Henry Blackburne (in 1889) also commented that the level of play was much better than it had been 25 years earlier. Hendriks suggests, based on all these remarks, that "a strong club player of today would not fare badly amidst the strongest players of halfway through the 19th century". As for earlier players, Hendriks guesses that "Greco, Philidor, and the Modenese masters...could compete with the strongest players of the first half of the 19th century", and estimates the ratings of La Bourdonnais, McDonnell, Staunton, and Pierre Saint-Amant on a modern scale to have been "slightly above 2000".^[30]

Bobby Fischer (1964 and 1970)

In 1964, Bobby Fischer listed his top 10 in Chessworld magazine: Morphy, Staunton, Steinitz, Tarrasch, Chigorin, Alekhine, Capablanca, Spassky, Tal, and Reshevsky.^[31][32] He considered Morphy to be "perhaps the most accurate", writing: "In a set match he would beat anyone alive today."^[33]

In 1970, Fischer named Morphy, Steinitz, Capablanca, Botvinnik, Petrosian, Tal, Spassky, Reshevsky, Svetozar Gligorić and Bent Larsen the greatest chess players in history.^[34]

Irving Chernev (1974)

In 1974, popular chess author Irving Chernev published an article titled Who were the greatest? in the English magazine CHESS.^[35] 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.^[36]

Miguel Quinteros (1992)

In a 1992 interview GM Miguel Quinteros gave the opinion:^[37] "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."

Viswanathan Anand (2000, 2008 and 2012)

In 2000, when Karpov, Korchnoi and Kasparov were still active, Anand listed his top 10 as: Fischer, Morphy, Lasker, Capablanca, Steinitz, Tal, Korchnoi, Keres, Karpov and Kasparov.^[38]

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.^[39]

In 2012, Anand stated that he considered Fischer the best player and also the greatest, because of the hurdles he faced.^[40]

Chess Informant readers (2001)

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.^[41]

David Edmonds and John Eidinow (2004)

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.^[42]

Vladimir Kramnik (2005 and 2011)

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."^[43]

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".^[44]

Leonard Barden (2008)

In his 2008 obituary of Bobby Fischer, Leonard Barden wrote that most experts ranked Kasparov as the best ever player, with probably Fischer second and Karpov third.^[45]

Levon Aronian (2012, 2015, and 2022)

In a 2012 interview, Levon Aronian stated that he considers Alexander Alekhine the best player of all time.^[46]

In a 2015 interview after the 8th round of the Sinquefield Cup, Levon Aronian stated that he considers Garry Kasparov the strongest player of all time.^[47]

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' (Greatest Of All Time), 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."^[48]

Magnus Carlsen (2012, 2015, 2020 and 2021)

In 2012, Magnus Carlsen said that Kasparov is the greatest player of all time, adding that while Fischer may have been better at his best, Kasparov remained at the top for much longer.^[49]

In December 2015 he said he would like to play Fischer and Kasparov at their peak performance.^[50]

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."^[51] He made a similar claim in 2021, saying "Garry Kasparov, in my opinion, the greatest player there's ever been..."^[52]

Hikaru Nakamura (2021 and 2023)

In 2021, Hikaru Nakamura published a Youtube video entitled "Hikaru's Hot Takes on the Ten Best Chess Players of All Time"^[53] in which he reviewed a chess.com article on "The 10 Best Chess Players Of All Time."^[54] 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.

During Game 6 of World Chess Championships 2023, as he was commenting on the game, Hikaru mentioned Magnus Carlsen, Garry Kasparov, Vishy Anand, Bobby Fischer, Anatoly Karpov, José Raúl Capablanca and Vladimir Kramnik as the top chess players of all time in order.^{[citation needed]}

Anatoly Karpov (2021)

Karpov named Capablanca, Alekhine, Fischer, himself, and Kasparov as his top five in 2021.^[55]