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Comparison of top chess players throughout history

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This article presents a number of methodologies that have been suggested for the task of comparing top chess players throughout history, particularly the question of comparing the greatest players of different eras. Statistical methods offer objectivity but, whilst there is agreement on systems to rate the strengths of current players, there is disagreement and controversy on whether such techniques can be applied to players from different generations who never competed against each other.

Statistical methods

Elo system

Main article: Elo rating system

Perhaps the best-known statistical model is that devised by Arpad Elo. 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:

(Though published in 1978, Elo's list did not include five-year averages for 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.[3]

As of March 2012, there were 85 chess grandmasters in history who broke the 2700 limit and only 6 of them were capable of overcoming the 2800 line. Particularly notable are performances by players like Fischer, Karpov and Kasparov, who achieved their peak ratings in earlier years (1972, 1994, and 1999 respectively).

Table of top 20 rated players ever, with date their best ratings were first achieved
Rank Rating Player Year-month
1 2862.4 Magnus Carlsen 2012-12
2 2851 Garry Kasparov 1999-07
3 2825 Levon Aronian 2012-05
4 2817 Viswanathan Anand 2011-03
5 2813 Veselin Topalov 2006-07
6 2809[4] Vladimir Kramnik 2001-10
7 2793 Teimour Radjabov 2012-11
8 2788 Alexander Morozevich 2008-07
9 2788 Sergey Karjakin 2011-07
10 2787 Vassily Ivanchuk 2007-10
11 2786 Hikaru Nakamura 2012-10
12 2786 Fabiano Caruana 2012-11
13 2785 Bobby Fischer 1972-04
14 2780 Anatoly Karpov 1994-07
15 2773 Alexander Grischuk 2011-01
16 2772 Shakhriyar Mamedyarov 2011-01
17 2768 Ruslan Ponomariov 2011-07
18 2765 Peter Svidler 2011-07
19 2763 Peter Leko 2005-04
20 2762 Gata Kamsky 2012-11

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 in July 2000 rose from 2751 to 2787 in March 2012, a 36-point increase in about 12 years.

The average rating of the TOP 100 players, meanwhile, increased from 2644 to 2700, a 56-point increase.[5]

Many people believe that this rise is mostly due to a system artifact known as ratings inflation, making it impractical to compare players of different eras.[6]

Arpad Elo was of the opinion that it was futile to attempt to use ratings to compare players from different eras; in his view, they could only possibly 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".[7]

Chessmetrics

Main article: Chessmetrics

Many statisticians since Elo have devised similar methods to retrospectively rate players. Jeff Sonas, for example, calls his system 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 apparently suffered.

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".[8] While it may be in the best interest of the fans for chess-players to remain active, it is not clear why a person's rating, which reflects his/her skill at chess, should drop if the player is inactive for a period of time.

Sonas, like Elo, acknowledges that it is useless to try to compare the strength of players from different eras. In his explanation of the Chessmetrics system,[9] he says:

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' Web site does compare players from different eras, and shows that in such cases the Chessmetrics system is rather sensitive to the length of the periods being compared. Including data until December 2004, the rankings were:

Rank 1 year[10] 5 years[11] 10 years[12] 15 years[13] 20 years[14]
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,[15] 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 a list of the highest ratings ever attained according to calculations done at the start of each month, which looks like this:[16]

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

Warriors of the Mind

In contrast to Elo and Sonas's systems, Raymond Keene and Nathan Divinsky's book Warriors of the Mind[17] 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. Considering games played between sixty-four of the strongest players in history, they come up with the following top ten:[18]

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,[19] and Warriors of the Mind has also been accused of arbitrarily selecting players and bias towards modern players.[20]

Moves played compared with computer choices

A computer-based method of analyzing chess abilities across history came from Matej Guid and Ivan Bratko from the Department of Computer and Information Science of University of Ljubljana, Slovenia, in 2006.[21] The basis for their evaluation was the difference between the position values resulting from the moves played by the human chess player and the moves chosen as best by the chess program Crafty. They also compared the average number of errors in the player's game. Opening moves were excluded, in an attempt to negate the progress in chess opening theory.

The method received a number of criticisms, including: the study used a modified version of Crafty rather than the standard version; even the standard version of Crafty was not strong enough to evaluate the world champions' play; one of the modifications restricted the search depth to 12 half-moves, which is often insufficient.[22] As of 2006 Crafty's Elo rating was 2657, below many historical top human players and several other computer programs.

A similar project was conducted in 2007 using Rybka 2.3.2a and a modified version of Crafty 20.14.[23] It arrived at the following results:[24][25]

Position best year best 2-year period best 3-year period best 5-year period best 10-year period best 15-year period
1 Fischer Fischer Fischer Fischer; Kasparov Fischer; Capablanca Capablanca
2 Kramnik Kramnik; Capablanca; Kasparov Capablanca; Kasparov Karpov; Kramnik
3 Kasparov Capablanca Kramnik
4 Botvinnik Smyslov Kramnik; Botvinnik Kasparov Smyslov; Kasparov
5 Capablanca Karpov; Smyslov Botvinnik Karpov; Smyslov
6 Karpov Kramnik Smyslov Fischer
7 Smyslov; Tal Botvinnik; Alekhine Karpov Karpov; Lasker Botvinnik; Spassky Botvinnik; Spassky; Petrosian
8 Spassky; Lasker
9 Petrosian Anand Alekhine; Anand Anand
10 Euwe Tal; Spassky Anand Lasker; Petrosian Anand
11 Spassky Petrosian Petrosian; Spassky Tal
12 Alekhine; Anand Lasker; Euwe Tal; Alekhine Tal; Alekhine Alekhine; Lasker
13 Euwe; Tal
14 Lasker Petrosian Euwe Euwe Euwe
15 Morphy Morphy Morphy Steinitz Steinitz Steinitz
16 Steinitz Steinitz Steinitz

An analysis done with Rybka 3 and comparisons with modern ratings can be found at http://web.zone.ee/chessanalysis/summary450.pdf.

Subjective lists

Several prominent players and writers have attempted to rank the greatest players. Generally these lists attempt to combine the two methods above—performance, and analysis of games.

Bobby Fischer (1964)

In 1964 Bobby Fischer listed his top 10 in Chessworld magazine: Morphy, Staunton, Steinitz, Tarrasch, Chigorin, Alekhine, Capablanca, Spassky, Tal, Reshevsky.[26][27] He considered Morphy the best, saying "In a set match he would beat anyone alive today."[28]

Irving Chernev (1976)

In 1976 chess author Irving Chernev published the 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.[29]

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.[30]

When interviewed 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 many years.[31]

In 2012, Anand stated that he considered Fischer as the greatest on account of the hurdles he faced.[32]

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 :

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.[33]

Vladimir Kramnik (2005, 2011)

In a 2005 interview, Vladimir Kramnik (World Champion 2000 to 2007) stated, "The other world champions had something 'missing'. I can't say the same about Kasparov: he can do everything."[34]

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".[35]

Leonard Barden (2008)

In his 2008 obituary of Bobby Fischer, Leonard Barden wrote that most experts ranked Kasparov as the greatest ever, with either Fischer or Karpov second.[36]

Levon Aronian (2012)

In a 2012 interview, Levon Aronian stated that he considers Alexander Alekhine the greatest player of all time.[37]

Magnus Carlsen (2012)

In 2012, Magnus Carlsen said that Kasparov is the greatest player of all time, saying that while Fischer may have been better at his best, Kasparov remained at the top for much longer.[38]

World Champions by world title reigns

The number of world championship wins, or world championship reigns, can be considered as a guide to player greatness. 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.

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 5 2 7
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
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

See also

References

  1. ^ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
  2. ^ Arpad Emre Elo – 100th anniversary, Chessbase, 2003
  3. ^ 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. Since July 2009 they are released on two-monthly basis.
  4. ^ The graph on the FIDE site and Chessgames.com gives Kramnik's peak rating as 2811, [1], [2], It was discussed many times that Kramnik possibly played some additional games which FIDE did not calculated [3], but this appears to be incorrect: it is contradicted by the official FIDE's published ratings for January [4] and April [5] 2002, Kramnik's Top lists records [6]; and also by the reports in TWIC for January [7] and April [8] 2002.
  5. ^ World Top chess players and Statistics at FIDE.com
  6. ^ http://www.chessbase.com/newsdetail.asp?newsid=5608
  7. ^ Chess Life, 1962.
  8. ^ The Greatest Chess Player of All Time – Part I, Jeff Sonas, at Chessbase
  9. ^ About the Chessmetrics Rating System, by Jeff Sonas
  10. ^ "Peak Average Ratings: 1 year peak range".
  11. ^ "Peak Average Ratings: 5 year peak range".
  12. ^ "Peak Average Ratings: 10 year peak range".
  13. ^ "Peak Average Ratings: 15 year peak range".
  14. ^ "Peak Average Ratings: 20 year peak range".
  15. ^ Sonas, J. (2005). "The Greatest Chess Player of All Time – Part IV". Chessbase. Part IV gives links to the 3 earlier parts
  16. ^ Sonas, J. (2005). "The Greatest Chess Player of All Time – Part II". Chessbase.
  17. ^ Warriors of the Mind, Raymond Keene and Nathan Divinsky, (1989)
  18. ^ http://chess.eusa.ed.ac.uk/Chess/Trivia/AlltimeList.html Divinsky-Keene rankings
  19. ^ Hooper, David;Whyld, Kenneth (1992). The Oxford Companion to Chess. Oxford University Press. ISBN 0-19-280049-3.{{cite book}}: CS1 maint: multiple names: authors list (link)
  20. ^ Winter, Edward (1996). Chess Explorations. Cadogan. ISBN 1-85744-171-0.
  21. ^ Computers choose: who was the strongest player?, Chessbase, 2006
  22. ^ Review of "Computer Analysis of World Chess Champions", by Søren Riis, Chessbase, 2006
  23. ^ "Compare the World Champions!", by Charles Sullivan, TrueChess, 2007
  24. ^ http://www.truechess.com/web/champs.html
  25. ^ http://www.truechess.com/web/champsdraws.html
  26. ^ Bobby Fischer, "The Ten Greatest Masters in History", Chessworld, Vol. 1, No. 1 (Jan.-Feb. 1964), pp. 56-61.
  27. ^ "Fischer's Top 10".
  28. ^ the Even More Complete Chess Addict, by Mike Fox and Richard James, 1993, pp. 129-30
  29. ^ Twelve Great Chess Players and Their Best Games, Irving Chernev, 1995 (reprint of 1976 edition).
  30. ^ The Grandmaster on his ten greatest chess players, Viswanathan Anand, rediff.com
  31. ^ "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." - Morelia-Linares Super-GM starts today, Chessbase, February 15, 2008
  32. ^ Anand takes a dig at Kasparov, Viswanathan Anand, The Hindu
  33. ^ Edmonds, David; Eidinow, John (2004). Bobby Fischer Goes to War. HarperCollins Publishers Inc. p. 310. ISBN 0-06-051024-2.
  34. ^ http://www.kramnik.com/eng/interviews/getinterview.aspx?id=61
  35. ^ "Vladimir Kramnik on Chess, Anand, Topalov, and his future". 2011-08-31.
  36. ^ "Most experts place him (Fischer) the second or third best ever, behind Kasparov but probably ahead of Karpov." - Obituary of Bobby Fischer, Leonard Barden, The Guardian, 19 January 2008
  37. ^ http://whychess.com/en/node/2836
  38. ^ http://www.vg.no/sport/artikkel.php?artid=10060899
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