Comparison of top chess players throughout history#Statistical methods

{{main|Elo rating system|List of chess players by peak FIDE rating}}

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.Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. {{ISBN|0-668-04721-6}}. 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.[http://www.chessbase.com/newsdetail.asp?newsid=1160 Arpad Emre Elo – 100th anniversary], Chessbase, 2003

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|post=,|2023|9}} there are 133 chess players in history who broke 2700, and 15 of them exceeded 2800.

:

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.[http://ratings.fide.com/toplist.phtml?list=men World Top chess players and Statistics] at FIDE.com 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.{{cite web|url=http://www.chessbase.com/newsdetail.asp?newsid=5608 |title=ChessBase News | Rating inflation – its causes and possible cures |publisher=Chessbase.com |date=27 July 2009 |access-date=21 October 2013}}

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 {{nowrap|approximate{{tsp}}{{mdash}}{{tsp}}}}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".Chess Life, 1962.{{cite web|title=Arpad Emre Elo – 100th anniversary|date=30 August 2003|url=https://en.chessbase.com/post/arpad-emre-elo-100th-anniversary}}

{{Further|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?|date=June 2022}}

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."[http://www.chessbase.com/newsdetail.asp?newsid=2345 The Greatest Chess Player of All Time – Part I], Jeff Sonas, at Chessbase

Sonas, like Elo, claims that it is impossible to compare the strength of players from different eras, saying:

{{blockquote|text=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.[http://chessmetrics.com/cm/Documents/AboutSystem.htm About the Chessmetrics Rating System] {{webarchive |url=https://web.archive.org/web/20120515101645/http://chessmetrics.com/cm/Documents/AboutSystem.htm |date=15 May 2012 }}, by Jeff Sonas}}

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

In 2005,{{cite web | url=http://www.chessbase.com/newsdetail.asp?newsid=2409 | title=The Greatest Chess Player of All Time – Part IV |author =Sonas, J. | publisher=Chessbase | year=2005}} Part IV gives links to the 3 earlier parts 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:{{cite web | url=http://www.chessbase.com/newsdetail.asp?newsid=2354 | title=The Greatest Chess Player of All Time – Part II |author =Sonas, J. | publisher=Chessbase | year=2005}}

:

In contrast to Elo and Sonas's systems, Raymond Keene and Nathan Divinsky's book Warriors of the MindWarriors of the Mind, Raymond Keene and Nathan Divinsky, (1989) 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:{{cite web|url=http://chess.eusa.ed.ac.uk/Chess/Trivia/AlltimeList.html |title=Divinsky-Keene rankings |url-status=dead |archive-url=https://web.archive.org/web/20091126000035/http://chess.eusa.ed.ac.uk/Chess/Trivia/AlltimeList.html |archive-date=26 November 2009 }}

{{div col|colwidth=25em}}

1. Garry Kasparov, 3096
2. Anatoly Karpov, 2876
3. Bobby Fischer, 2690
4. Mikhail Botvinnik, 2616
5. José Raúl Capablanca, 2552
6. Emanuel Lasker, 2550
7. Viktor Korchnoi, 2535
8. Boris Spassky, 2480
9. Vasily Smyslov, 2413
10. Tigran Petrosian, 2363

{{div col end}}

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,{{cite book|title=The Oxford Companion to Chess|url=https://archive.org/details/oxfordcompaniont0000hoop|url-access=registration|author1=Hooper, David |author2=Whyld, Kenneth |publisher=Oxford University Press|year=1992|isbn=0-19-280049-3}} and Warriors of the Mind has been accused of arbitrarily selecting players and bias towards modern players.{{cite book|title=Chess Explorations|author=Winter, Edward|publisher=Cadogan|year=1996|isbn=1-85744-171-0}}

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 process of analyzing chess abilities across history came from Matej Guid and Ivan Bratko at the University of Ljubljana, Slovenia, in 2006.[http://www.chessbase.com/newsdetail.asp?newsid=3455 Computers choose: who was the strongest player?], Chessbase, 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".[http://www.truechess.com/web/champs.html "Compare the World Champions!"], by Charles Sullivan, TrueChess, 2007

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.{{Cite web|url=https://www.chess.com/article/view/who-was-the-best-world-chess-champion-in-history|title=Who Was The Best World Chess Champion In History?|last=(DanielRensch)|first=Daniel Rensch|website=Chess.com|date=3 January 2017|access-date=3 January 2017}}

In 2017, Jean-Marc Alliot of the Toulouse Computer Science Research Institute ([http://www.irit.fr/ IRIT]) presented a new method,[http://content.iospress.com/articles/icga-journal/icg0012 Who is the master?], ICGA Journal, 39–1, April 2017 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 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. He ignored drawn games, because he believed that previous analyses favoured players who played cautiously, with drawn games generally having fewer inaccuracies than wins.

He estimated ratings for players at their peak years, on a scale corresponding to Elo ratings in 2023. He estimated ratings for 47 players, with the following top ten:{{cite web |url=https://www.chess.com/article/view/chess-accuracy-ratings-goat |title=Accuracy, Ratings, and GOATs |last=Kaufman |first=Larry |date=4 September 2023 |website=Chess.com |publisher= |access-date=7 September 2023 |quote=Correction: There was one error, I missed Capa's match with Kostic in 1919 due to Kostic's first name being given inconsistently. Fixing this raises Capa to 2633 in the absolute list, to 2868 (third place) in the list where number 1 in 1900 = Carlsen, and to 2821 (shared sixth place) in the list of where they would be if age 30 now. Probably there are other similar data errors I haven't caught., especially among the players of long ago.}}

{{div col|colwidth=25em}}

1. Magnus Carlsen, 2858 (peak years 2013–2021)
2. Garry Kasparov, 2821 (peak years 1993–2001)
3. Bobby Fischer, 2802 (peak years 1970–1972)
4. Ian Nepomniachtchi, 2786 (peak years 2020–2022)
5. Vladimir Kramnik, 2785 (peak years 2000–2007)
6. Viswanathan Anand, 2780 (peak years 2007–2014)
7. Veselin Topalov, 2773 (peak years 2005–2009)
8. Anatoly Karpov, 2746 (peak years 1974–1984)
9. Mikhail Tal, 2711 (peak years 1958–1960)
10. Vasily Smyslov, 2687 (peak years 1953–1957)

{{div col end}}

(Kaufman noted however that Fabiano Caruana could not be considered by his methodology because his World Championship match had all classical games drawn. He speculated that Caruana "might well be number two of all time".)

Kaufman concluded that the quality of play rose steadily by about 2.5 Elo points per year from 1900 to 2023, though he conceded that the rate was greater in the 19th century and thus that Paul Morphy "might have rivaled Fischer for the top spot if we could properly correct for these factors". He corrected ratings for 2.5 points per year before for 2017 (the midpoint of Carlsen's peak), to estimate players' strength relatively according to their time:

{{div col|colwidth=25em}}

1. Bobby Fischer, 2917
2. Garry Kasparov, 2871
3. José Raúl Capablanca, 2868
4. Alexander Alekhine, 2864
5. Emanuel Lasker, 2862
6. Magnus Carlsen, 2858
7. Mikhail Tal, 2856
8. Harry Nelson Pillsbury, 2853
9. Vasily Smyslov, 2842
10. Reuben Fine, 2842

{{div col end}}

He made a third list correcting by 2 points per year before 2017, instead of 2.5 points per year. That list again had Fischer first (2894) and Kasparov second (2861); and had Carlsen third on 2858.

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.Bobby Fischer, "The Ten Greatest Masters in History", Chessworld, Vol. 1, No. 1 (Jan.-Feb. 1964), pp. 56–61.{{cite web|url=http://chess.eusa.ed.ac.uk/Chess/Trivia/Fishers10.html|title=Fischer's Top 10|url-status=dead|archive-url=https://web.archive.org/web/20090206215606/http://chess.eusa.ed.ac.uk/Chess/Trivia/Fishers10.html|archive-date=6 February 2009}} He considered Morphy to be "perhaps the most accurate", writing: "In a set match he would beat anyone alive today."the Even More Complete Chess Addict, by Mike Fox and Richard James, 1993, pp. 129–30

In 1970, Fischer named Morphy, Steinitz, Capablanca, Botvinnik, Petrosian, Tal, Spassky, Reshevsky, Svetozar Gligorić, and Bent Larsen the greatest chess players in history.CHESS magazine, November 1970, p. 70

In 1974, popular chess author Irving Chernev published an article titled Who were the greatest? in the English magazine CHESS.CHESS magazine, April 1974, pp. 201–202 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.Twelve Great Chess Players and Their Best Games, Irving Chernev, 1995 (reprint of 1976 edition).

In a 1992 interview GM Miguel Quinteros gave the opinion:{{cite book

|last1=Seirawan

|first1=Yasser

|author-link1=Yasser Seirawan

|last2=Stefanovic

|first2=George

|title=No Regrets • Fischer–Spassky 1992

|publisher=International Chess Enterprises

|year=1992

|chapter=Belgrade; Interview with GM Miguel Quinteros

|page=255

|isbn=1-879479-09-5}} "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."

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.{{cite web|url=http://in.rediff.com/millenni/anand.htm|title=The Grandmaster on his ten greatest chess players|url-status=dead|archive-url=https://web.archive.org/web/20031120152003/http://in.rediff.com/millenni/anand.htm|archive-date=20 November 2003}}

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."He (Fischer) and Kasparov were the greatest in history, but I judge Kasparov as a little ahead. Fischer was a phenomenon from 1970 to 1972 while Kasparov was on top for many years." – [http://www.chessbase.com/newsprint.asp?newsid=4450 Morelia-Linares Super-GM starts today] {{webarchive|url=https://web.archive.org/web/20090206172430/http://www.chessbase.com/newsprint.asp?newsid=4450 |date=6 February 2009 }}, Chessbase, 15 February 2008

In 2012, Anand stated that he considered Fischer the best player and also the greatest, because of the hurdles he faced.[http://www.thehindu.com/sport/other-sports/article3486974.ece Anand takes a dig at Kasparov], Viswanathan Anand, The Hindu

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.{{cite book| last=Gligorić| first=Svetozar| author-link=Svetozar Gligorić

|title=Shall We Play Fischerandom Chess?| publisher=B.T. Batsford Ltd| year=2002| page=8| isbn=0-7134-8764-X}}

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.{{cite book

| last1=Edmonds

| first1=David

| author-link1=David Edmonds (philosopher)

| last2=Eidinow

| first2=John

| title=Bobby Fischer Goes to War

| page=[https://archive.org/details/isbn_9780060510244/page/310 310]

| publisher=HarperCollins Publishers Inc

| year=2004

| isbn=0-06-051024-2

| url-access=registration

| url=https://archive.org/details/isbn_9780060510244/page/310

}}

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."{{cite web |url=http://www.kramnik.com/eng/interviews/getinterview.aspx?id=61 |title=The most important interviews by GM Vladimir Kramnik, World Chess Champion 2000–2007 |publisher=Kramnik.com |access-date=21 October 2013 |archive-url=https://web.archive.org/web/20080512052013/http://www.kramnik.com/eng/interviews/getinterview.aspx?id=61 |archive-date=12 May 2008 |url-status=dead }}

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".{{cite web |url=http://whychess.org/node/1605 |title=Vladimir Kramnik on Chess, Anand, Topalov, and his future |date=31 August 2011 |access-date=28 May 2012 |archive-url=https://web.archive.org/web/20120623012745/http://www.whychess.org/node/1605 |archive-date=23 June 2012 |url-status=dead }}

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."Most experts place him (Fischer) the second or third best ever, behind Kasparov but probably ahead of Karpov." – [https://www.theguardian.com/obituaries/story/0,,2243266,00.html Obituary of Bobby Fischer], Leonard Barden, The Guardian, 19 January 2008

In a 2012 interview, Levon Aronian stated that he considers Alexander Alekhine the best player of all time.{{cite web |url=http://whychess.com/en/node/2836 |title=Aronian names Alekhine best player of all time |publisher=WhyChess |date=22 August 2012 |access-date=21 October 2013 |archive-url=https://web.archive.org/web/20121119113805/http://whychess.com/en/node/2836 |archive-date=19 November 2012 |url-status=dead }}

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.https://www.youtube.com/watch?v=WGdywyQlo2E "Well, in my opinion Garry is the strongest player of all time"

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."https://www.youtube.com/watch?v=bqK_eEA-9GQ The Soviet School of Trash Talking

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.{{cite web|url=http://www.vg.no/sport/artikkel.php?artid=10060899 |title=Magnus Carlsen: – Jeg tar verdensrekorden – VG Nett om Sjakk |publisher=Vg.no |date=1 January 1970 |access-date=21 October 2013}}

In December 2015 he said he would like to play Fischer and Kasparov at their peak performance.[https://edition.cnn.com/2015/12/16/sport/magnus-carlsen-chess-world-number-one/ Chess prodigy Magnus Carlsen: 'Bobby Fischer is my dream opponent'.], 2015-12-16, CNN

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."[https://www.theguardian.com/sport/2020/jan/09/magnus-carlsen-i-will-always-be-proud-no1-fantasy-football-chess Magnus Carlsen: ‘You need to be very fortunate to be No 1 in fantasy football’], The Guardian, 10 January 2020 He made a similar claim in 2021, saying "Garry Kasparov, in my opinion, the greatest player there's ever been..."[https://www.youtube.com/watch?v=lxz4NWDZgug Magnus Carlsen ranks Garry Kasparov], chess24 YouTube channel, 6 May 2021

In 2021, Hikaru Nakamura published a Youtube video entitled "Hikaru's Hot Takes on the Ten Best Chess Players of All Time"{{cite web | url=https://www.youtube.com/watch?v=bffwNThqDQc | title=Hikaru's Hot Takes on the Ten Best Chess Players of All Time - YouTube | website=YouTube | date=24 August 2021 }} in which he reviewed a chess.com article on "The 10 Best Chess Players Of All Time."{{cite web | url=https://www.chess.com/article/view/best-chess-players-of-all-time | title=The 10 Best Chess Players of All Time | date=30 March 2023 }} 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.{{cn|date=October 2023}}

Karpov named Capablanca, Alekhine, Fischer, himself, and Kasparov as his top five in 2021.{{Cite web |title=Karpov at 70: "My great blunder was I agreed to hold the match with Kasparov in the Soviet Union" |url=https://chess24.com/en/read/news/karpov-at-70-my-great-blunder-was-i-agreed-to-hold-the-match-with-kasparov-in-the-soviet-union |access-date=July 4, 2022 |website=chess24.com |language=en}}

{{Unreferenced section|date=June 2013}}

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.

{{portal|border=no|Biography|Chess|World}}

• List of FIDE chess world number ones

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{{reflist|30em}}

• {{commons category-inline|Chess players}}

{{Chess}}

{{DEFAULTSORT:Comparison of top chess players throughout history}}

*Comparison of top chess players

Category:History of chess

Category:Chess rating systems

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