Truechess.com Compares the Champions

Who was the greatest chess player of all time?

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The Project's FAQ

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The Project

For 24 hours a day for 15 months (from February 2007 through May 2008), 12 computing threads (on three Intel quad-core Q6600 computers running at 3.0 GHz) analyzed the games of the World Champions. Entire playing careers were analyzed -- for example, 69,084 positions from 2318 games were analyzed for just one player (Smyslov). In all, 617,446 positions from 18,785 games were processed. (For comparison, a previous analysis of the World Champions by Matej Guid and Ivan Bratko -- that you can read about here -- examined about 37,000 positions.)

The commercially-available program Rybka [version 2.3.2a], the strongest chess program available at the time, and a modified version of Bob Hyatt's open-source Crafty program [version 20.14] were used in the project.

Calculating "Raw Error" and "Complexity"

The first 8 moves in each game were ignored, but each subsequent position was searched three separate times. First, a search for a full six minutes (the average search was 17.4 iterations) by Crafty to determine a score for the best move available. A second search, to the same depth as was reached in the first search, assigned a score to the move played in the game. The difference between the move made and the best move in the position is the "raw error" score. Finally, a third search calculates the "complexity" score for the position.

Complexity Graph

Ranking a Player's Relative Accuracy of Play

A Complexity Table (see graph above), constructed from all the positions analyzed, is used to level the playing field between different players. The more complicated the position, the higher the expected raw error will be. For example, a player encountering positions with an average complexity of 30 would be expected to produce moves that average 11 centipawns (0.11 pawn) from the best move. If he actually produces moves that average 8 centipawns, then his score in the "Percent Better Than the Average Grandmaster Move" column would be 27.27 (8 divided by 11 gives 72.73%, which is 27.27% better than the average). This should all become clear if you study the Test Case below.

Verifying the "Blunders"

Using Rybka (running by itself on a quad-core Q6600 computer) with no time limit, I examined each position in which a "raw error" of at least 1.25 pawn occurred. I analyzed until I could determine whether the player's move both (a) exceeded the (arbitrary) blunder-threshold for this project of 0.75 pawn and (b) was a critical error (the move made a "won game" problematical, for example, or turned a likely draw into a possible loss). Some blunder-candidates were examined for as long as 12 hours before a definitive classification was made. The result of this analysis is found in the "Blunders per 1000 Moves" column.

Percent of Points Scored

A third (less-important) column is the "Percent of Points Scored"column. This is determined as you would expect: based on a win equaling one point and a draw equaling a half-point.

Data Used in the Analysis

As already mentioned, the first eight moves were not computer-analyzed. I later decided, because modern players often play far more than the first eight moves from memory, to begin the data analysis with move sixteen. Also, I eventually decided that computer-analysis of the endgame still leaves much to be desired, so moves beyond the 40th are not included. In addition, a position is excluded from the data analysis if the position is rated as (a) worse than -2.00 pawns (because a losing player is apt to try inferior, desperate moves that would skew the analysis) or (b) better than 4.00 pawns, unless a blunder (as defined above) occurs.

For a more complete description of the project, click here.

Complexity Scores

You can see the complexity scores for the champions here.

A Test Case

To see if this approach makes sense, let's analyze the 5 matches that Garry Kasparov and Anatoly Karpov contested from 1984 through 1990. This should be a difficult test case because: (1) Kasparov has the highest "complexity" rating among modern chessplayers and Karpov has the lowest. (2) Therefore, Kasparov's "raw error" scores will be higher.
The question is: Does the "complexity table" correctly adjust the results so that we can conclude that Kasparov and Karpov played to a virtual standoff (over 144 games, Kasparov eked out a 73-71 edge)?

First, let's analyze all the games and see if the analysis indicates an extremely close match:
Kasparov-Karpov Matches, All 144 Games
PLAYER NUMBER OF GAMES NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED BLUNDERS PER 1000 MOVES AVERAGE COMPLEXITY PER POSITION AVERAGE RAW ERROR SCORE AVERAGE GRANDMASTER SCORE (FROM COMPLEXITY TABLE) PERCENT BETTER THAN THE AVERAGE GRANDMASTER MOVE
KASPAROV 144 2450 50.69 7.61 25.88 9.05 10.47 13.56
KARPOV 144 2429 49.31 7.30 16.98 8.33 9.40 11.38

Indeed, there's not a lot of difference between the two players when we look at the numbers that are in boldface. Kasparov's move selection (the Percent Better Than the Average Grandmaster Move column) is better (by 2.18 percentage points). But applying the rule-of-thumb that 1 blunder = 3.5 percentage points, Karpov's lower Blunder Rate reduces Kasparov's margin by 1.09 points, leaving Kasparov with a razor-thin edge of 1.09 points.

Now let's look at only the decisive games in the match:

Kasparov-Karpov Matches, Decisive Games Only
PLAYER NUMBER OF GAMES NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED BLUNDERS PER 1000 MOVES AVERAGE COMPLEXITY PER POSITION AVERAGE RAW ERROR SCORE AVERAGE GRANDMASTER SCORE (FROM COMPLEXITY TABLE) PERCENT BETTER THAN THE AVERAGE GRANDMASTER MOVE
KASPAROV 40 830 50.69 11.45 31.26 10.50 11.18 6.08
KARPOV 40 809 49.31 9.56 20.96 10.29 9.82 -4.79

Once again, I would judge that the statistics indicate a very close competition with a very slight edge for Kasparov. Kasparov's move selection is about 11% better than Karpov's, enough to offset Karpov's superior blunder rate. The rule-of-thumb that 1 blunder = 3.5 percentage points yields a result (10.87 - (1.89 * 3.5)) of 4.25 points, enough to rate Kasparov slightly better than Karpov in the five matches.

Examine the "raw" data

You will be able to sort it various ways, but WARNING! there is a lot of data to examine.
The unsummarized data is available here.
You can see essentially the same data (with "raw error" scores rather than complexity-adjusted scores) by going here.

Summarized Statistical Rankings

If you prefer to look at the rankings with draws included, then click here.

Ranking of Champions Based on Best Year   [ Excluding Draws ]

A one-year period of games represents too small a sample upon which to make a judgment -- interesting, but not very meaningful.
RANKING PLAYER YEAR AGE TOTAL MOVES ANALYZED (MOVES 16 - 40) NUMBER OF DECISIVE GAMES (MINIMUM = 10) PERCENT OF POINTS SCORED BLUNDERS PER 1000 MOVES PERCENT BETTER THAN THE AVERAGE GRAND- MASTER MOVE
1 FISCHER 1968 25 504 19 86.54 0.00 40.45
2 ANAND 2006 36 780 18 62.82 0.00 31.36
TIED-3 SMYSLOV 1976 55 837 20 57.94 0.00 21.62
TIED-3 KRAMNIK 1992 17 1197 38 72.08 0.00 21.20
TIED-5 SPASSKY 1980 43 678 16 60.00 0.00 17.86
TIED-5 BOTVINNIK 1945 33 428 16 90.00 0.00 17.27
TIED-5 EUWE 1925 24 492 23 85.00 0.00 16.98
TIED-5 CAPABLANCA 1915 26 302 12 92.86 0.00 16.41
TIED-5 PETROSIAN 1973 44 796 20 63.33 2.36 26.39
10 KASPAROV 2001 38 790 18 71.43 0.00 14.95
11 KARPOV 1974 23 1128 23 64.91 2.15 16.59
12 TAL 1960 23 875 26 70.83 3.95 21.68
13 ALEKHINE 1930 37 458 22 95.83 2.34 13.36
14 LASKER 1909 40 682 27 76.56 1.76 5.37
15 MORPHY 1858 21 617 28 71.21 5.93 1.52
16 STEINITZ 1894 58 570 24 53.45 17.13 -16.04

Ranking of Champions Based on Best 2-Year Period   [ Excluding Draws ]

A two-year period of data is still a very small sample for the purpose of selecting the world's greatest chess player. However, perhaps you have noticed that Anand reached his peak strength just as he became World Champion in 2007.
RANKING PLAYER 2-YEAR PERIOD ENDING AGE TOTAL MOVES ANALYZED (MOVES 16 - 40) NUMBER OF DECISIVE GAMES (MINIMUM = 20) PERCENT OF POINTS SCORED BLUNDERS PER 1000 MOVES PERCENT BETTER THAN THE AVERAGE GRAND- MASTER MOVE
1 FISCHER 1969 26 524 20 87.04 0.00 37.27
2 ANAND 2007 37 1615 34 61.49 0.00 23.35
3 KRAMNIK 2000 25 1553 24 59.71 1.90 27.43
4 BOTVINNIK 1932 20 564 23 83.93 0.00 17.78
5 KASPAROV 2001 38 1708 34 66.48 1.42 20.02
TIED-6 SMYSLOV 1976 55 1367 33 59.69 1.62 19.60
TIED-6 CAPABLANCA 1916 27 669 25 87.10 3.58 26.11
8 PETROSIAN 1973 44 1734 47 65.85 2.09 16.66
TIED-9 SPASSKY 1986 49 1904 51 60.61 5.80 22.07
TIED-9 KARPOV 1984 33 1745 40 63.12 2.28 10.75
TIED-9 TAL 1987 50 953 31 63.22 6.94 25.08
TIED-9 ALEKHINE 1921 28 657 25 76.25 6.99 24.39
13 LASKER 1910 41 1140 37 73.59 3.92 10.55
14 EUWE 1934 33 710 26 75.00 8.10 20.87
15 MORPHY 1859 22 711 35 75.61 5.09 -2.98
16 STEINITZ 1873 37 669 30 80.77 16.07 13.94

Ranking of Champions Based on Best 3-Year Period   [ Excluding Draws ]

An argument can be made that three years of data is enough to identify that player, who at his peak, was the best. (Notice that I've made two entries for Capablanca -- the one marked as *TIED-2* from 1917 is superior to the entry for 1916, but the 1917 entry is based on only 25 decisive games. Because Lasker and Capablanca played in an era with far fewer tournament opportunities, I thought it fair to include extra entries for them.)
RANKING PLAYER 3-YEAR PERIOD ENDING AGE TOTAL MOVES ANALYZED (MOVES 16 - 40) NUMBER OF DECISIVE GAMES (MINIMUM = 30) PERCENT OF POINTS SCORED BLUNDERS PER 1000 MOVES PERCENT BETTER THAN THE AVERAGE GRAND- MASTER MOVE
1 FISCHER 1970 27 2046 70 82.00 1.47 25.45
TIED-2 BOTVINNIK 1932 20 894 36 84.09 0.00 14.39
TIED-2 KASPAROV 2001 38 2370 55 69.29 1.70 18.35
*TIED-2* CAPABLANCA 1917 28 669 25 87.10 3.58 26.11
TIED-4 CAPABLANCA 1916 27 1160 42 82.14 4.52 20.70
TIED-4 KRAMNIK 2000 25 2405 45 58.65 2.19 18.45
TIED-4 ANAND 2007 37 2585 53 60.36 2.61 15.91
TIED-4 KARPOV 1976 25 2967 70 67.26 5.29 18.93
TIED-4 LASKER 1911 42 1140 37 73.59 3.92 10.55
9 EUWE 1934 33 1298 42 70.00 6.59 21.05
10 SPASSKY 1964 27 3114 92 70.34 6.16 17.66
TIED-11 ALEKHINE 1931 38 1905 72 79.41 4.24 9.42
TIED-11 PETROSIAN 1962 33 2977 104 74.47 5.70 14.25
TIED-11 SMYSLOV 1955 34 2503 71 65.67 8.00 16.93
14 TAL 1974 37 3891 134 70.24 9.12 18.74
15 MORPHY 1859 22 1002 50 78.81 8.49 0.34
16 STEINITZ 1873 37 669 30 80.77 16.07 13.94

Ranking of Champions Based on Best 5-Year Period   [ Excluding Draws ]

I think we can safely conclude that the greatest short-term chess peak was Fischer's run-up to, and victory at, the 1972 match against Spassky. (Notice I have made extra entries for Capablanca (marked as *TIED-2*) and Lasker (*TIED-6*)).
RANKING PLAYER 5-YEAR PERIOD ENDING AGE TOTAL MOVES ANALYZED (MOVES 16 - 40) NUMBER OF DECISIVE GAMES (MINIMUM = 50) PERCENT OF POINTS SCORED BLUNDERS PER 1000 MOVES PERCENT BETTER THAN THE AVERAGE GRAND- MASTER MOVE
1 FISCHER 1972 29 2968 97 80.14 2.54 26.24
2 KASPAROV 2002 39 3067 68 68.68 2.08 17.60
*TIED-2* CAPABLANCA 1919 30 1149 44 88.89 3.20 19.57
3 CAPABLANCA 1918 29 1439 51 83.09 3.67 18.40
4 BOTVINNIK 1934 22 1482 57 74.38 2.79 12.25
5 KRAMNIK 2001 26 4084 85 60.74 6.30 25.16
6 KARPOV 1978 27 5057 126 67.63 4.76 13.45
*TIED-6* LASKER 1913 44 1140 37 73.59 3.92 10.55
TIED-7 ALEKHINE 1931 38 3191 96 71.51 4.79 9.22
TIED-7 ANAND 2007 37 4010 93 62.34 5.88 13.89
TIED-9 PETROSIAN 1962 33 4845 149 70.90 5.52 11.82
TIED-9 SPASSKY 1966 29 5505 146 66.30 6.25 14.70
11 SMYSLOV 1957 36 3897 106 65.09 6.58 11.20
TIED-12 LASKER 1911 42 1817 56 72.62 6.02 7.19
TIED-12 EUWE 1934 33 2083 66 66.67 9.07 18.56
TIED-12 TAL 1978 41 4914 147 64.26 8.54 15.23
15 STEINITZ 1886 50 2091 82 68.52 21.06 -8.15

Ranking of Champions Based on Best 10-Year Period   [ Excluding Draws ]

You might consider a ten-year period useful for selecting the greatest chessplayer of all time. If so, then Fischer's play from 1963 through 1972 has never been equalled. (Again, notice the extra entries for Capablanca and Lasker, both marked by asterisks in the "Ranking" column.)
RANKING PLAYER 10-YEAR PERIOD ENDING AGE TOTAL MOVES ANALYZED (MOVES 16 - 40) NUMBER OF DECISIVE GAMES (MINIMUM = 100) PERCENT OF POINTS SCORED BLUNDERS PER 1000 MOVES PERCENT BETTER THAN THE AVERAGE GRAND- MASTER MOVE
1 FISCHER 1972 29 5484 195 79.78 4.14 23.02
*2* CAPABLANCA 1924 35 2063 70 82.04 2.62 13.03
TIED-2 KASPAROV 2005 42 5591 129 67.56 4.51 13.23
TIED-2 KRAMNIK 2004 29 7678 170 60.37 5.50 18.76
TIED-4 CAPABLANCA 1930 41 4167 120 69.92 6.27 15.46
TIED-4 BOTVINNIK 1945 33 3459 101 71.80 3.80 5.66
TIED-4 SMYSLOV 1969 48 9736 283 69.59 5.30 11.65
TIED-4 KARPOV 1983 32 9877 254 66.76 5.07 10.11
*8* LASKER 1918 49 1774 56 75.30 5.21 9.12
8 SPASSKY 1971 34 9650 263 66.50 7.36 11.71
9 PETROSIAN 1967 38 8902 251 67.50 7.40 10.00
10 ALEKHINE 1930 37 6558 219 72.74 7.54 8.57
TIED-11 ANAND 2007 37 7611 178 61.55 8.38 10.29
TIED-11 LASKER 1899 30 3412 126 75.00 6.85 2.62
13 TAL 1979 42 10736 340 65.95 10.10 12.63
14 EUWE 1934 33 5361 183 69.77 10.76 8.56
15 STEINITZ 1873 37 2225 110 73.53 22.52 -6.49

Ranking of Champions Based on Best 15-Year Period   [ Excluding Draws ]

Surprise! Fischer does not top this table (because his best 15-year period includes the teenage years before 1960 when he was not yet a super-Grandmaster). Kasparov's best 15-year period fares a little poorly because of his relatively high "blunder" rate. Capablanca's appearance on top is well-earned, of course, but Smyslov's 2nd-place ranking is unexpected. The players who share third with Fischer and Kasparov -- Botvinnik, Karpov, and Kramnik -- were also great champions. (Notice the extra *1* entry for Capablanca and the *8* entry for Lasker, both based on less than the "minimum" of 150 decisive games.)
RANKING PLAYER 15-YEAR PERIOD ENDING AGE TOTAL MOVES ANALYZED (MOVES 16 - 40) NUMBER OF DECISIVE GAMES (MINIMUM = 150) PERCENT OF POINTS SCORED BLUNDERS PER 1000 MOVES PERCENT BETTER THAN THE AVERAGE GRAND- MASTER MOVE
*1* CAPABLANCA 1924 35 3081 107 80.65 4.39 13.99
1 CAPABLANCA 1929 40 5136 158 73.49 5.32 15.83
2 SMYSLOV 1976 55 13638 395 66.33 4.03 9.72
TIED-3 KARPOV 1990 39 16048 392 64.43 5.07 9.28
TIED-3 FISCHER 1972 29 10964 371 71.95 6.71 14.63
TIED-3 BOTVINNIK 1945 33 5048 158 71.54 4.45 5.83
TIED-3 KASPAROV 2005 42 9691 242 67.77 7.66 16.67
TIED-3 KRAMNIK 2006 31 13057 321 61.55 7.33 14.85
*8* LASKER 1923 54 2254 68 70.91 6.34 8.42
8 PETROSIAN 1973 44 13308 367 65.25 7.31 10.41
9 SPASSKY 1975 38 13548 372 65.03 8.37 11.80
TIED-10 ANAND 2007 37 12297 305 61.87 8.90 9.99
TIED-10 ALEKHINE 1934 41 9960 336 74.39 6.23 4.15
TIED-10 TAL 1988 51 13287 385 61.76 10.15 13.68
13 LASKER 1904 35 4095 153 75.88 8.27 3.63
14 EUWE 1952 51 7533 264 67.14 11.11 10.11
15 STEINITZ 1894 58 3734 154 63.50 21.93 -10.84

Who Was "The Greatest"?

Here is the short case for -- and against -- each champion:

The Greatest Was ...

I think you can reach your own conclusion!   And of course, it depends -- what are the necessary qualifications for the world's greatest chess player?

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