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:

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?

You can click here to return to the Truechess.com homepage

Truechess.com Compares the Champions

Who was the greatest chess player of all time?

The Project's FAQ

The Project

Calculating "Raw Error" and "Complexity"

Ranking a Player's Relative Accuracy of Play

Verifying the "Blunders"

Percent of Points Scored

Data Used in the Analysis

Complexity Scores

A Test Case

Kasparov-Karpov Matches, All 144 Games

Kasparov-Karpov Matches, Decisive Games Only

Examine the "raw" data

Summarized Statistical Rankings

Ranking of Champions Based on Best Year [ Excluding Draws ]

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

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

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

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

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

Who Was "The Greatest"?

Paul Morphy (born 1837, died 1884)

Wilhelm Steinitz (born 1836, died 1900)

Emanuel Lasker (born 1868, died 1941)

José Raúl Capablanca (born 1888, died 1942)

Alexander Alekhine (born 1892, died 1946)

Max Euwe (born 1901, died 1981)

Mikhail Botvinnik (born 1911, died 1995)

Vasily Smyslov (born 1921)

Mikhail Tal (born 1936, died 1992)

Tigran Petrosian (born 1929, died 1984)

Boris Spassky (born 1937)

Bobby Fischer (born 1943, died 2008)

Anatoly Karpov (born 1951)

Garry Kasparov (born 1963)

Vladimir Kramnik (born 1975)

Vishy Anand (born 1969)

The Greatest Was ...