Who was the greatest chess player of all time?

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.

Ranking a Player's Relative Accuracy of Play
A Complexity Table 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.

Complexity Scores
Representative 10-Year Complexity Scores for the Champions
(Note that Morphy's data is based on only a three-year period.) A ranking, from most complex to least, based on all games, would be Steinitz, Kasparov, Morphy, Fischer, Botvinnik, Euwe, Anand, Tal, Capablanca, Alekhine, Spassky, Smyslov, Petrosian, Kramnik, Lasker, Karpov. As you can read here, Guid and Bratko, who compute complexity differently and only consider actual World Championship matches, give the complexity order as Steinitz, Tal, Fischer, Lasker, Euwe, Alekhine, Kramnik, Kasparov, Botvinnik, Karpov, Smyslov, Petrosian, Spassky, Capablanca.
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
MORPHY 1859 22 1002 78.81 27.22 26.55 30.86
STEINITZ 1873 37 2225 73.53 35.77 40.84 43.42
LASKER 1918 49 1774 75.30 20.16 22.32 23.96
CAPABLANCA 1924 35 2063 82.04 23.90 27.99 28.30
ALEKHINE 1930 37 6558 72.74 23.17 29.29 31.49
EUWE 1934 33 5361 69.77 25.58 31.25 33.59
BOTVINNIK 1945 33 3459 71.80 26.25 34.72 37.59
SMYSLOV 1969 48 9736 69.59 22.33 27.57 29.28
TAL 1979 42 10736 65.95 24.23 30.88 33.91
PETROSIAN 1967 38 8902 67.50 22.29 28.14 29.98
SPASSKY 1971 34 9650 66.50 22.81 29.70 32.37
FISCHER 1972 29 5484 79.78 27.00 31.40 32.59
KARPOV 1983 32 9877 66.76 19.98 25.61 27.25
KASPAROV 2005 42 5591 67.56 27.93 38.95 40.64
KRAMNIK 2004 29 7678 60.37 22.27 29.33 33.15
ANAND 2007 37 7611 61.55 24.99 32.95 37.94
Complete Table of 10-Year Complexity Ratings [ Sorted by Player and Year ]
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
ALEKHINE 1919 26 2915 67.52 28.25 30.84 36.72
ALEKHINE 1920 27 2706 69.39 29.40 31.86 37.50
ALEKHINE 1921 28 2715 73.55 31.07 34.29 38.60
ALEKHINE 1922 29 3217 74.19 28.97 32.88 36.10
ALEKHINE 1923 30 3239 73.91 28.30 32.95 36.78
ALEKHINE 1924 31 2794 74.21 26.85 33.93 36.59
ALEKHINE 1925 32 3339 74.74 25.10 31.30 33.33
ALEKHINE 1926 33 4311 75.11 24.96 30.75 32.74
ALEKHINE 1927 34 5584 71.59 22.99 29.85 31.93
ALEKHINE 1928 35 5584 71.59 22.99 29.85 31.93
ALEKHINE 1929 36 6205 71.07 23.03 29.74 32.27
ALEKHINE 1930 37 6558 72.74 23.17 29.29 31.49
ALEKHINE 1931 38 6741 72.88 23.18 29.38 31.53
ALEKHINE 1932 39 6690 74.09 22.64 28.44 30.45
ALEKHINE 1933 40 6838 74.66 21.99 27.45 29.21
ALEKHINE 1934 41 7382 75.07 22.13 27.45 29.19
ALEKHINE 1935 42 7730 72.83 22.41 28.06 30.37
ALEKHINE 1936 43 8046 72.39 22.24 27.80 30.08
ALEKHINE 1937 44 8009 72.95 22.98 27.62 30.37
ALEKHINE 1938 45 8851 72.93 23.38 28.05 30.97
ALEKHINE 1939 46 8716 74.00 23.51 28.30 30.83
ALEKHINE 1940 47 8258 72.78 23.40 28.40 31.18
ALEKHINE 1941 48 8073 72.32 23.25 27.90 30.76
ALEKHINE 1942 49 7981 71.59 23.32 27.89 31.07
ALEKHINE 1943 50 7847 71.72 23.64 28.28 31.28
ALEKHINE 1944 51 7076 72.22 23.86 28.46 31.49
ALEKHINE 1945 52 6492 74.38 24.07 27.99 30.65
ALEKHINE 1946 53 5211 74.62 24.39 28.13 31.02
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
ANAND 1993 23 11219 63.86 23.76 28.04 31.68
ANAND 1994 24 11604 63.73 23.97 28.35 32.27
ANAND 1995 25 11869 63.20 23.64 28.11 31.85
ANAND 1996 26 11299 62.86 23.55 28.44 32.09
ANAND 1997 27 10886 62.48 23.77 29.09 33.22
ANAND 1998 28 10655 62.23 23.63 29.36 33.69
ANAND 1999 29 10440 61.89 23.47 29.57 34.38
ANAND 2000 30 9849 61.37 23.76 30.60 35.55
ANAND 2001 31 9244 61.74 24.19 32.24 37.17
ANAND 2002 32 8287 61.65 24.61 32.07 37.11
ANAND 2003 33 7786 61.17 24.88 32.08 37.34
ANAND 2004 34 7709 61.92 25.29 33.22 37.89
ANAND 2005 35 8057 62.19 25.49 33.09 37.86
ANAND 2006 36 7950 62.26 25.74 33.60 38.90
ANAND 2007 37 7611 61.55 24.99 32.95 37.94
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
BOTVINNIK 1939 27 3735 70.41 23.65 29.87 33.19
BOTVINNIK 1940 28 3618 69.21 23.36 30.82 34.32
BOTVINNIK 1941 29 3620 68.14 22.86 30.68 34.49
BOTVINNIK 1942 30 3405 66.76 23.04 31.23 35.62
BOTVINNIK 1943 31 3412 67.71 23.71 31.47 34.78
BOTVINNIK 1944 32 3468 69.32 23.95 31.40 34.17
BOTVINNIK 1945 33 3459 71.80 26.25 34.72 37.59
BOTVINNIK 1946 34 3330 72.56 26.65 33.27 36.30
BOTVINNIK 1947 35 3318 74.40 26.35 33.40 35.59
BOTVINNIK 1948 36 3167 74.84 26.27 33.04 35.32
BOTVINNIK 1949 37 2782 75.00 26.37 31.78 34.13
BOTVINNIK 1950 38 2569 75.39 27.12 31.89 34.35
BOTVINNIK 1951 39 3105 70.47 24.96 29.61 32.78
BOTVINNIK 1952 40 3941 69.63 24.78 29.34 32.38
BOTVINNIK 1953 41 3643 69.21 24.23 29.00 32.22
BOTVINNIK 1954 42 3981 66.58 23.69 28.77 32.66
BOTVINNIK 1955 43 3966 63.07 21.20 24.57 27.87
BOTVINNIK 1956 44 3933 63.24 21.36 25.37 28.83
BOTVINNIK 1957 45 4058 60.43 21.36 25.07 29.65
BOTVINNIK 1958 46 4469 60.17 21.39 25.06 29.33
BOTVINNIK 1959 47 4566 60.13 21.21 25.05 29.30
BOTVINNIK 1960 48 5225 59.34 21.04 25.05 29.74
BOTVINNIK 1961 49 5143 61.62 22.89 27.38 31.82
BOTVINNIK 1962 50 4732 62.20 22.92 27.57 32.12
BOTVINNIK 1963 51 5400 61.80 22.52 27.47 32.47
BOTVINNIK 1964 52 5090 63.16 22.73 27.97 32.51
BOTVINNIK 1965 53 5086 64.21 23.53 28.88 33.50
BOTVINNIK 1966 54 5238 64.05 23.28 28.46 32.97
BOTVINNIK 1967 55 5416 66.67 23.11 28.32 31.95
BOTVINNIK 1968 56 4799 67.27 23.26 28.80 32.55
BOTVINNIK 1969 57 5266 67.03 22.80 27.71 31.06
BOTVINNIK 1970 58 4918 67.77 22.67 27.76 30.77
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
CAPABLANCA 1918 29 2368 78.81 23.73 28.39 29.14
CAPABLANCA 1919 30 2167 83.49 24.17 27.66 28.22
CAPABLANCA 1920 31 2167 83.49 24.17 27.66 28.22
CAPABLANCA 1921 32 2197 82.71 23.10 26.93 27.44
CAPABLANCA 1922 33 2387 83.05 24.22 27.93 28.44
CAPABLANCA 1923 34 2172 82.41 23.95 28.01 28.35
CAPABLANCA 1924 35 2063 82.04 23.90 27.99 28.30
CAPABLANCA 1925 36 2082 77.98 25.71 31.75 31.76
CAPABLANCA 1926 37 1856 77.00 25.23 31.66 31.51
CAPABLANCA 1927 38 2839 69.16 22.94 31.54 33.54
CAPABLANCA 1928 39 3106 68.10 23.10 32.45 34.74
CAPABLANCA 1929 40 3987 69.82 22.55 30.76 32.59
CAPABLANCA 1930 41 4167 69.92 22.53 30.46 32.54
CAPABLANCA 1931 42 4289 70.78 23.19 31.21 33.25
CAPABLANCA 1932 43 4010 69.74 22.63 30.95 33.19
CAPABLANCA 1933 44 4010 69.74 22.63 30.95 33.19
CAPABLANCA 1934 45 3710 69.34 22.40 30.61 32.91
CAPABLANCA 1935 46 3933 69.11 20.97 28.30 31.15
CAPABLANCA 1936 47 4526 69.57 20.96 27.74 30.24
CAPABLANCA 1937 48 3787 72.25 21.25 27.23 28.88
CAPABLANCA 1938 49 3623 70.67 20.83 26.45 28.50
CAPABLANCA 1939 50 2974 67.86 20.50 26.60 28.99
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
EUWE 1929 28 8645 68.15 26.71 31.53 36.38
EUWE 1930 29 7787 68.15 26.45 30.87 35.19
EUWE 1931 30 7008 68.90 26.22 30.71 34.46
EUWE 1932 31 6760 70.45 26.25 31.42 34.61
EUWE 1933 32 5450 69.42 25.89 31.20 33.94
EUWE 1934 33 5361 69.77 25.58 31.25 33.59
EUWE 1935 34 5510 66.50 24.95 30.12 32.99
EUWE 1936 35 5365 66.17 24.76 30.16 33.12
EUWE 1937 36 5732 62.66 23.19 27.50 31.07
EUWE 1938 37 5424 62.33 22.03 26.18 29.84
EUWE 1939 38 5736 63.45 22.04 26.16 29.68
EUWE 1940 39 6038 63.28 22.23 26.51 30.37
EUWE 1941 40 5942 64.74 22.56 26.96 30.75
EUWE 1942 41 5513 65.30 23.14 27.44 31.11
EUWE 1943 42 5480 65.00 23.06 27.33 31.00
EUWE 1944 43 4803 63.83 23.25 27.33 31.32
EUWE 1945 44 4355 65.21 23.01 27.66 31.61
EUWE 1946 45 4890 68.49 24.21 28.52 32.24
EUWE 1947 46 4573 70.68 25.37 29.94 33.30
EUWE 1948 47 4637 67.18 26.80 31.49 35.28
EUWE 1949 48 4489 66.08 26.17 30.73 34.87
EUWE 1950 49 4978 66.78 25.48 30.56 34.39
EUWE 1951 50 4747 66.42 24.95 29.80 33.85
EUWE 1952 51 4865 66.37 24.50 29.16 33.15
EUWE 1953 52 5547 64.04 23.87 28.45 33.41
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
FISCHER 1965 22 8353 68.05 24.38 27.93 30.75
FISCHER 1966 23 8566 69.53 24.41 28.05 30.73
FISCHER 1967 24 7996 69.19 24.54 28.61 31.60
FISCHER 1968 25 7800 70.74 25.32 29.74 32.64
FISCHER 1969 26 6269 72.94 25.74 30.49 33.10
FISCHER 1970 27 6622 75.00 25.68 30.47 32.66
FISCHER 1971 28 6464 77.09 25.70 30.11 31.96
FISCHER 1972 29 5484 79.78 27.00 31.40 32.59
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
KARPOV 1976 25 8917 70.08 20.63 26.04 27.34
KARPOV 1977 26 9848 70.85 20.36 25.51 26.69
KARPOV 1978 27 10193 68.81 19.75 24.57 26.12
KARPOV 1979 28 10082 68.55 19.92 24.90 26.23
KARPOV 1980 29 10405 68.56 19.81 24.88 26.31
KARPOV 1981 30 10085 68.05 20.18 25.26 26.83
KARPOV 1982 31 10361 67.38 20.17 25.63 27.10
KARPOV 1983 32 9877 66.76 19.98 25.61 27.25
KARPOV 1984 33 9569 66.26 19.96 25.49 27.12
KARPOV 1985 34 9662 65.21 19.50 24.38 26.13
KARPOV 1986 35 9947 63.68 18.68 23.47 25.65
KARPOV 1987 36 9947 62.01 18.28 22.99 25.59
KARPOV 1988 37 11009 63.46 18.72 23.83 26.10
KARPOV 1989 38 11333 63.26 18.56 23.46 25.77
KARPOV 1990 39 11060 62.60 18.53 23.67 26.20
KARPOV 1991 40 11605 61.85 18.25 23.43 26.20
KARPOV 1992 41 11899 62.05 18.31 23.30 26.14
KARPOV 1993 42 12682 62.43 18.47 23.22 26.01
KARPOV 1994 43 13219 63.43 18.65 23.28 26.02
KARPOV 1995 44 13395 64.58 18.99 24.02 26.55
KARPOV 1996 45 13395 64.44 19.25 24.34 26.93
KARPOV 1997 46 12690 64.33 19.53 24.70 27.33
KARPOV 1998 47 11208 62.84 19.11 24.33 27.15
KARPOV 1999 48 10780 61.99 18.79 24.41 27.46
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
KASPAROV 1984 21 7224 67.68 29.95 35.91 39.29
KASPAROV 1985 22 7995 67.35 28.87 35.26 38.71
KASPAROV 1986 23 8311 67.54 28.16 34.83 38.40
KASPAROV 1987 24 8293 66.28 27.34 33.92 37.48
KASPAROV 1988 25 8588 67.34 26.89 33.85 36.83
KASPAROV 1989 26 8912 68.17 26.95 34.19 36.62
KASPAROV 1990 27 8996 66.60 26.79 33.06 35.82
KASPAROV 1991 28 8695 66.36 26.00 32.06 34.81
KASPAROV 1992 29 8905 66.26 26.26 32.65 35.52
KASPAROV 1993 30 8893 66.22 26.32 33.12 36.08
KASPAROV 1994 31 9137 68.07 27.68 35.15 37.67
KASPAROV 1995 32 8894 68.34 28.28 36.16 38.70
KASPAROV 1996 33 8637 68.53 29.05 37.34 39.70
KASPAROV 1997 34 8618 69.49 29.69 38.38 40.68
KASPAROV 1998 35 7568 68.39 29.68 39.37 42.05
KASPAROV 1999 36 7205 68.18 30.40 40.35 43.22
KASPAROV 2000 37 7245 68.04 29.43 40.22 42.77
KASPAROV 2001 38 7176 68.55 29.84 41.20 43.35
KASPAROV 2002 39 6829 68.03 29.10 40.74 42.87
KASPAROV 2003 40 6490 67.59 29.01 40.19 42.29
KASPAROV 2004 41 6184 66.81 27.68 39.23 41.50
KASPAROV 2005 42 5591 67.56 27.93 38.95 40.64
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
KRAMNIK 2000 25 11239 64.76 24.84 30.90 34.54
KRAMNIK 2001 26 10305 63.25 24.35 30.76 34.52
KRAMNIK 2002 27 9151 62.05 24.02 30.57 34.72
KRAMNIK 2003 28 8117 60.89 23.35 30.47 34.47
KRAMNIK 2004 29 7678 60.37 22.27 29.33 33.15
KRAMNIK 2005 30 7505 58.26 21.15 27.37 31.50
KRAMNIK 2006 31 6836 58.55 20.59 27.76 31.41
KRAMNIK 2007 32 6490 58.11 20.72 28.30 32.68
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
LASKER 1898 29 3011 73.79 23.96 27.50 30.40
LASKER 1899 30 3412 75.00 23.60 27.40 29.90
LASKER 1900 31 3403 76.21 23.65 27.22 29.49
LASKER 1901 32 3453 76.19 23.74 27.25 29.49
LASKER 1902 33 2905 75.35 23.84 27.49 29.88
LASKER 1903 34 2815 74.46 23.64 27.30 29.73
LASKER 1904 35 2678 75.93 25.19 29.21 31.13
LASKER 1905 36 1949 77.84 25.16 28.72 30.06
LASKER 1906 37 1271 81.75 26.70 30.06 30.98
LASKER 1907 38 1554 80.26 26.61 31.23 32.11
LASKER 1908 39 1898 77.72 24.85 29.71 31.55
LASKER 1909 40 2042 76.02 23.95 26.56 28.98
LASKER 1910 41 2150 72.77 22.13 25.37 27.88
LASKER 1911 42 2100 72.73 21.94 25.27 27.83
LASKER 1912 43 2100 72.73 21.94 25.27 27.83
LASKER 1913 44 2100 72.73 21.94 25.27 27.83
LASKER 1914 45 2205 73.04 21.24 24.53 27.14
LASKER 1915 46 2205 73.04 21.24 24.53 27.14
LASKER 1916 47 2301 74.07 20.94 24.06 26.45
LASKER 1917 48 1968 73.66 20.03 22.44 24.86
LASKER 1918 49 1774 75.30 20.16 22.32 23.96
LASKER 1919 50 1092 74.51 18.82 22.93 24.25
LASKER 1920 51 634 78.33 20.65 24.51 25.26
LASKER 1921 52 899 64.77 18.31 23.02 25.26
LASKER 1922 53 899 64.77 18.31 23.02 25.26
LASKER 1923 54 1114 68.42 21.10 27.71 30.41
LASKER 1924 55 1166 70.34 20.06 25.96 27.98
LASKER 1925 56 1543 70.25 21.03 27.60 29.51
LASKER 1926 57 1447 68.49 21.50 28.54 30.80
LASKER 1927 58 1447 68.49 21.50 28.54 30.80
LASKER 1928 59 1297 67.91 22.28 29.45 32.20
LASKER 1929 60 1297 67.91 22.28 29.45 32.20
LASKER 1930 61 1297 67.91 22.28 29.45 32.20
LASKER 1931 62 1032 76.42 24.81 31.10 32.20
LASKER 1932 63 1032 76.42 24.81 31.10 32.20
LASKER 1933 64 817 75.00 22.65 28.20 29.36
LASKER 1934 65 663 68.57 23.64 26.99 29.80
LASKER 1935 66 649 66.18 18.72 20.47 22.45
LASKER 1936 67 1188 59.09 18.57 21.15 25.42
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
PETROSIAN 1958 29 7984 63.74 22.65 27.90 30.92
PETROSIAN 1959 30 8386 64.24 22.57 27.92 30.65
PETROSIAN 1960 31 8733 66.85 23.13 28.80 30.99
PETROSIAN 1961 32 8862 67.25 23.28 28.99 31.01
PETROSIAN 1962 33 9217 67.86 22.96 29.04 30.76
PETROSIAN 1963 34 9287 67.61 22.53 28.91 30.63
PETROSIAN 1964 35 8960 68.12 22.51 28.47 29.99
PETROSIAN 1965 36 8761 67.81 22.45 28.30 30.15
PETROSIAN 1966 37 9047 67.39 22.37 28.19 30.10
PETROSIAN 1967 38 8902 67.50 22.29 28.14 29.98
PETROSIAN 1968 39 8866 68.00 22.18 27.84 29.63
PETROSIAN 1969 40 8784 67.40 21.67 27.51 29.36
PETROSIAN 1970 41 8759 64.77 21.11 27.07 29.32
PETROSIAN 1971 42 8435 62.78 20.58 26.91 29.55
PETROSIAN 1972 43 8485 62.59 20.61 26.75 29.55
PETROSIAN 1973 44 8498 63.13 20.84 27.08 29.60
PETROSIAN 1974 45 8449 62.50 20.91 27.04 29.99
PETROSIAN 1975 46 8814 62.25 21.34 27.61 30.46
PETROSIAN 1976 47 8289 62.54 21.16 27.38 30.11
PETROSIAN 1977 48 8479 62.10 21.34 27.99 30.98
PETROSIAN 1978 49 8289 61.36 21.58 28.51 31.82
PETROSIAN 1979 50 8332 61.89 21.85 28.69 31.88
PETROSIAN 1980 51 8101 62.26 21.59 28.29 31.17
PETROSIAN 1981 52 8086 62.81 21.36 27.81 30.39
PETROSIAN 1982 53 7807 61.62 20.91 27.35 30.36
PETROSIAN 1983 54 7766 60.67 20.99 27.81 31.59
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
SMYSLOV 1948 27 5487 63.59 22.22 26.06 30.20
SMYSLOV 1949 28 5837 65.65 22.46 26.11 29.80
SMYSLOV 1950 29 6367 65.23 22.29 26.07 29.73
SMYSLOV 1951 30 6642 67.21 22.56 26.25 29.48
SMYSLOV 1952 31 7005 66.16 21.94 26.03 29.49
SMYSLOV 1953 32 7389 66.33 21.71 26.14 29.19
SMYSLOV 1954 33 8016 65.85 21.53 25.97 29.11
SMYSLOV 1955 34 8264 66.22 21.49 26.18 28.99
SMYSLOV 1956 35 8196 66.41 20.69 25.39 27.70
SMYSLOV 1957 36 7577 66.03 20.72 25.74 28.46
SMYSLOV 1958 37 7842 65.82 20.55 25.49 28.49
SMYSLOV 1959 38 8172 64.49 20.31 25.12 28.20
SMYSLOV 1960 39 8124 65.18 19.94 24.79 27.68
SMYSLOV 1961 40 8725 64.23 20.43 25.23 27.93
SMYSLOV 1962 41 8605 64.52 20.38 25.44 27.69
SMYSLOV 1963 42 8635 65.39 21.02 26.41 28.83
SMYSLOV 1964 43 8868 66.77 21.19 26.59 28.80
SMYSLOV 1965 44 8800 67.22 20.65 25.48 27.79
SMYSLOV 1966 45 8944 66.87 20.87 25.90 28.60
SMYSLOV 1967 46 9690 67.71 21.00 25.64 27.91
SMYSLOV 1968 47 9928 69.13 22.08 27.03 28.75
SMYSLOV 1969 48 9736 69.59 22.33 27.57 29.28
SMYSLOV 1970 49 10053 68.61 22.43 28.18 30.22
SMYSLOV 1971 50 9515 68.59 21.89 28.35 30.44
SMYSLOV 1972 51 9817 67.75 21.54 27.59 30.06
SMYSLOV 1973 52 10028 66.67 20.95 26.64 29.29
SMYSLOV 1974 53 9573 65.91 21.42 27.20 30.10
SMYSLOV 1975 54 9301 65.02 21.63 28.07 30.98
SMYSLOV 1976 55 9093 64.27 21.41 27.94 30.70
SMYSLOV 1977 56 8596 62.46 21.29 28.26 31.78
SMYSLOV 1978 57 8360 61.15 19.80 26.22 30.30
SMYSLOV 1979 58 8074 60.23 19.30 25.45 29.83
SMYSLOV 1980 59 7289 60.84 19.58 25.15 29.10
SMYSLOV 1981 60 7123 60.22 19.40 24.46 28.51
SMYSLOV 1982 61 6394 60.07 19.60 24.68 28.70
SMYSLOV 1983 62 6017 59.64 19.24 24.82 28.97
SMYSLOV 1984 63 6032 57.29 18.08 23.47 28.17
SMYSLOV 1985 64 6115 56.16 17.79 22.47 27.39
SMYSLOV 1986 65 5863 55.51 17.60 22.30 27.60
SMYSLOV 1987 66 5619 55.71 17.65 21.52 26.50
SMYSLOV 1988 67 5632 54.95 18.16 22.36 27.05
SMYSLOV 1989 68 5983 55.53 18.02 21.98 25.93
SMYSLOV 1990 69 6271 54.00 17.81 21.93 26.46
SMYSLOV 1991 70 6070 54.51 18.15 22.39 27.19
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
SPASSKY 1962 25 7672 67.45 25.49 30.66 34.50
SPASSKY 1963 26 7764 67.33 25.31 30.85 34.45
SPASSKY 1964 27 8974 67.47 24.57 30.21 33.81
SPASSKY 1965 28 9147 67.50 24.59 30.80 33.95
SPASSKY 1966 29 9511 66.97 23.38 30.17 33.43
SPASSKY 1967 30 9498 66.93 23.45 29.91 33.05
SPASSKY 1968 31 10045 67.54 23.74 30.08 33.00
SPASSKY 1969 32 10011 66.72 23.15 30.02 33.13
SPASSKY 1970 33 9806 66.58 22.33 29.05 31.88
SPASSKY 1971 34 9650 66.50 22.81 29.70 32.37
SPASSKY 1972 35 9144 64.48 22.00 28.89 32.23
SPASSKY 1973 36 9998 64.29 22.04 29.38 32.86
SPASSKY 1974 37 9050 63.23 22.38 30.33 34.20
SPASSKY 1975 38 8559 62.94 22.54 30.38 34.32
SPASSKY 1976 39 7536 63.49 23.53 30.95 34.80
SPASSKY 1977 40 7839 61.80 22.66 30.17 34.70
SPASSKY 1978 41 7467 60.77 22.23 30.00 34.95
SPASSKY 1979 42 7240 60.04 23.08 31.02 36.37
SPASSKY 1980 43 7314 59.15 22.60 30.31 35.58
SPASSKY 1981 44 7250 58.76 21.89 29.81 35.29
SPASSKY 1982 45 7745 59.35 22.24 30.45 35.39
SPASSKY 1983 46 7424 58.29 22.40 29.55 34.70
SPASSKY 1984 47 7256 58.24 22.00 28.45 33.10
SPASSKY 1985 48 7543 58.12 21.66 27.94 32.80
SPASSKY 1986 49 8283 58.65 21.95 28.90 33.50
SPASSKY 1987 50 7437 59.18 22.16 29.25 33.39
SPASSKY 1988 51 7591 58.78 21.96 29.22 33.50
SPASSKY 1989 52 7581 58.12 21.11 27.60 32.13
SPASSKY 1990 53 7525 58.03 21.07 27.67 32.77
SPASSKY 1991 54 7468 58.13 20.96 27.75 32.63
SPASSKY 1992 55 7025 57.32 20.87 27.35 32.48
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
STEINITZ 1868 32 1792 73.17 34.47 38.00 42.29
STEINITZ 1869 33 1723 72.27 34.76 38.50 43.21
STEINITZ 1870 34 1900 70.00 36.18 41.70 46.94
STEINITZ 1871 35 1900 70.00 36.18 41.70 46.94
STEINITZ 1872 36 1908 71.55 36.11 42.20 45.86
STEINITZ 1873 37 2225 73.53 35.77 40.84 43.42
STEINITZ 1874 38 2106 72.27 34.89 39.59 42.01
STEINITZ 1875 39 2025 71.55 35.35 40.12 42.79
STEINITZ 1876 40 1716 78.28 34.79 39.60 39.41
STEINITZ 1877 41 1164 78.46 36.28 41.10 41.45
STEINITZ 1878 42 1164 78.46 36.28 41.10 41.45
STEINITZ 1879 43 1164 78.46 36.28 41.10 41.45
STEINITZ 1880 44 834 83.70 32.28 34.11 34.77
STEINITZ 1881 45 834 83.70 32.28 34.11 34.77
STEINITZ 1882 46 1515 77.44 31.11 34.25 34.82
STEINITZ 1883 47 1848 72.11 27.05 30.76 33.13
STEINITZ 1884 48 1848 72.11 27.05 30.76 33.13
STEINITZ 1885 49 1848 72.11 27.05 30.76 33.13
STEINITZ 1886 50 2091 68.52 26.05 29.62 33.27
STEINITZ 1887 51 2091 68.52 26.05 29.62 33.27
STEINITZ 1888 52 2153 69.64 26.96 30.76 34.62
STEINITZ 1889 53 2443 68.61 27.88 31.49 35.82
STEINITZ 1890 54 2579 67.75 27.41 31.34 35.66
STEINITZ 1891 55 2766 66.89 26.23 30.50 34.44
STEINITZ 1892 56 2262 63.01 25.97 30.08 35.44
STEINITZ 1893 57 1481 60.24 27.49 32.11 38.36
STEINITZ 1894 58 2051 58.48 26.72 30.46 37.27
STEINITZ 1895 59 2768 58.00 26.50 30.05 34.77
STEINITZ 1896 60 2376 57.63 27.08 30.90 35.17
PLAYER 10-YEAR PERIOD ENDING AGE NUMBER OF MOVES ANALYZED (MOVES 16-40) PERCENT OF TOTAL POINTS SCORED COMPLEXITY SCORE, ALL GAMES COMPLEXITY SCORE, DECISIVE GAMES COMPLEXITY SCORE, WINNING GAMES
TAL 1965 28 10703 68.77 25.56 30.89 34.85
TAL 1966 29 10939 69.33 26.06 31.13 35.13
TAL 1967 30 11016 69.08 25.82 30.97 34.76
TAL 1968 31 10509 67.33 25.75 30.89 34.88
TAL 1969 32 10036 65.80 24.55 29.83 33.96
TAL 1970 33 9748 65.66 24.72 29.61 33.83
TAL 1971 34 9552 66.52 24.77 30.53 34.46
TAL 1972 35 9327 68.46 25.55 31.10 34.36
TAL 1973 36 9889 66.86 25.24 31.10 34.80
TAL 1974 37 9601 66.69 25.67 31.49 35.53
TAL 1975 38 10169 66.23 25.59 31.36 34.92
TAL 1976 39 10194 64.55 24.50 31.05 34.60
TAL 1977 40 10784 64.60 24.87 30.83 34.51
TAL 1978 41 10423 64.85 24.74 31.06 34.58
TAL 1979 42 10736 65.95 24.23 30.88 33.91
TAL 1980 43 10962 64.38 23.85 30.82 34.34
TAL 1981 44 10738 64.60 24.05 30.94 34.09
TAL 1982 45 10844 63.94 23.85 30.60 34.27
TAL 1983 46 9892 63.15 23.26 30.14 33.64
TAL 1984 47 9631 61.16 22.39 29.09 32.91
TAL 1985 48 9550 61.22 22.08 28.73 32.69
TAL 1986 49 8757 61.84 22.41 28.42 32.22
TAL 1987 50 8151 61.35 22.07 28.49 32.20
TAL 1988 51 8373 60.49 22.65 29.19 33.33
TAL 1989 52 7559 59.14 22.79 29.26 33.83
TAL 1990 53 7338 60.09 22.71 29.44 33.50
TAL 1991 54 6992 58.72 22.49 29.23 33.80
TAL 1992 55 6067 57.07 22.27 29.41 34.14

Summarized Statistical Rankings
anking 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:
Paul Morphy (born 1837, died 1884)
Although not usually recognized as World Champion, Morphy belongs on this list.
Pro: Morphy was clearly way ahead of his time: the numbers indicate he would easily have beaten Steinitz. Had he kept playing, Morphy surely would have been the strongest player in the world from 1857 until his death at age 47 -- a span of 27 years. Had he lived, he might have been the best player until the beginning of the 20th century!
Con: Judged by today's standards, Morphy's accuracy was just average. Also, his career in top-flight chess lasted only 3 years.
Wilhelm Steinitz (born 1836, died 1900)
Steinitz was universally acknowledged to be the first World Champion after defeating Zukertort in 1886.
Pro: Steinitz had a complex style, won a high percentage of games, was successful as a match player, and was probably the best active player for about 20 years (although he was "official" Champion for only 8 years).
Con: Most of Steinitz's numbers place him at the bottom -- nobody else is even close!
Emanuel Lasker (born 1868, died 1941)
Lasker was World Champion for a record 27 years.
Pro: Although Lasker played in an era which had relatively few great players, it is still remarkable that he was one of the very top competitors for more than 40 years (he won the strong New York tournament of 1924 by 1½ points over World Champion Capablanca)! According to the numbers, Lasker is the first chessplayer who could have held his own against the great champions of history.
Con: Lasker was absent for years at a time from competition, so it is difficult to get a fully reliable fix on his ability.
José Raúl Capablanca (born 1888, died 1942)
Capablanca awed all those who saw him because of his extremely rapid comprehension of the position on the board. Lasker famously said, "I have known many chess players, but only one chess genius, Capablanca."
Pro: Capablanca's numbers are universally excellent. He played with great accuracy, committed relatively few blunders, and won a high proportion of games.
Con: He suffered an unexpected loss to Alekhine in 1927.
Alexander Alekhine (born 1892, died 1946)
Alekhine was not born with the Capablanca's natural talent, but he showed what an unparalleled love of chess and a fanatical will to win can do. He played several of the most-admired games of all time.
Pro: He defeated the "invincible" Capablanca in 1927 and decisively defeated the underappreciated Euwe in a match in 1937.
Con: The numbers suggest that Alekhine was not quite as good as his reputation. He also suffered a most surprising defeat to Euwe in 1935.
Max Euwe (born 1901, died 1981)
Euwe had a successful life away from the chessboard, which cannot be said for most World Champions.
Pro: He convincingly defeated Alekhine in one of the biggest upsets in chess history. The numbers say that Euwe was better than his reputation.
Con: Euwe's reputation as a player who blundered often is, sadly, richly deserved.
Mikhail Botvinnik (born 1911, died 1995)
Botvinnik was so strong that he could have become World Champion as early as 1935. He finally become champion in 1948 and held the title for most of the next 15 years.
Pro: According to the numbers, Botvinnik was probably one of the five best players of all time. In addition, his fighting spirit must have been very resilient -- after losing matches to Smyslov and Tal, he won return matches a year later.
Con: After winning the title in 1948, Botvinnik became simply the first among equals and lost matches to Smyslov, Tal, and Petrosian.
Vasily Smyslov (born 1921)
One of those rare players who played almost as well in his sixties as he did in his thirties.
Pro: A player with impressive numbers -- he ranks 2nd behind Capablanca in the 15-Year Rankings (above). In 1984, he reached the Final of the Candidates' Matches in his 63rd year!
Con: There always seemed to be at least one player better (or luckier) than Smyslov: Bronstein, Botvinnik, Tal, Fischer, Kasparov.
Mikhail Tal (born 1936, died 1992)
Beloved by most everybody, Tal deserved a better fate: he was plagued by health problems throughout his life.
Pro: He had a sensational rise to the top in the late 1950's and early 1960's. He probably was an objectively better player in the 1970's.
Con: Although he was always among the handful of great players, he could never quite match his achievement of beating Botvinnik in 1960.
Tigran Petrosian (born 1929, died 1984)
In many ways, the anti-Tal: solid, possessor of a puzzling style, and widely unappreciated.
Pro: He won the Candidates in 1962 (over such great players as Keres, Geller, Fischer, Korchnoi, and Tal), handily defeated Botvinnik in 1963, and beat the great Spassky in 1966.
Con: His tournament results were usually mediocre and the numbers say he is not one of the greatest Champions.
Boris Spassky (born 1937)
World-famous because of his two matches with Fischer, Spassky was probably the best player for most of the 1960's.
Pro: Spassky proved his strength by winning the Candidates' Matches in both 1965 and 1968. He also proved his superiority in the 1966 Piatigorsky Cup where Fischer finished second. The numbers show that Spassky was an impressive player into his mid-forties.
Con: Spassky was not able to sustain the high level of brilliance he evidenced in the 1960's.
Bobby Fischer (born 1943, died 2008)
Like Morphy, "The Pride and Sorrow of Chess." Fischer coupled the precocious talent of Morphy and Capablanca with the obsession of Alekhine.
Pro: The sustained level of his play from 1967 through the 1972 match with Spassky is unmatched, as the numbers show.
Con: He quit too soon.
Anatoly Karpov (born 1951)
A steely competitor who, unlike most previous champions, was extremely active and competed successfully against the very best players of his time.
Pro: The numbers and the results show that Karpov was the best of his time.
Con: Karpov was not quite as good as either his predecessor or his successor.
Garry Kasparov (born 1963)
Kasparov showed that aggression pays on the chessobard. Also, he demonstrated the importance of the computer as a training aid.
Pro: The numbers confirm that Kasparov was one of the greatest players of all time.
Con: His blunder rate (as defined by this project), is surprisingly high. And, almost unbelievably, he lost a match to Kramnik without managing to win a game.
Vladimir Kramnik (born 1975)
Kramnik, at his best, is one of the most difficult players to defeat who ever played. He has had some health problems in the last few years.
Pro: In 2000, he defeated the truly great Kasparov (who was at or near his peak strength) in a match by two points without losing a game.
Con: Although he appears to have the talent to be the dominant player of his generation, he seems content to win by attrition. Also, perhaps because of his health issues, his form has been inconsistent.
Vishy Anand (born 1969)
As a youth, Anand shocked the chess world with his strong moves that were played at blitz speed. After several years of steady improvement (and learning to curtail his impulsiveness), he became Champion in 2007.
Pro: Anand's numbers have been outstanding in recent years -- his performance in 2006-2007 was almost flawless.
Con: Anand is at the top now, but he needs to sustain his current form for a few more years before he can be mentioned in the same breath with Capablanca, Fischer, and Kasparov.
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?