Best Chess Players

The best chess player in the 18^th century was François-Andre Danican Philidor (1726-1795).  Before Philidor, the best player was Legall de Mermeur (1702-1792).  Legall was perhaps the strongest player in the world from 1730 to 1755.  By 1755, Philidor could beat Legall and dominated chess until he died in 1795.

In the early 19^th century, Alexandre Deschapelles (1780-1847) was perhaps the strongest player in the world from 1800 to 1821.  

Louis-Charles Mahle de La Bourdonnais (1795-1840) was perhaps the strongest player in the world after Deschapelles   He ruled chess from 1821 (when he defeated Alexandre Deschapelles) to 1840.

From 1843 to 1851, the strongest player in the world was Howard Staunton (1810-1874).  Perhaps the second strongest player at the time was Pierre Charles Fournier de Saint-Amant, who Staunton beat in 1843.

From 1851 to 1857, Adolf Anderssen (1818-1879) was the strongest player in the world.  He was the winner of the great international tournament of 1851.  Staunton was perhaps the 2^nd strongest player in the world during this time.

From 1857 to 1860, Paul Morphy (1837-1884) dominated the chess world and was considered the unofficial world champion during this period.  In 1857, he won the first American Chess Congress.  In 1858, he defeated Adolf Anderssen in a match.  He defeated virtually all serious opposition except for Staunton, who refused do play Morphy.  Morphy retired from chess in 1860.

From 1861 to 1866, Anderssen was the strongest player in the world after Morphy retired.  In London 1862, Anderssen took 1^st place with the score of 11 out of 13.   Louis Paulsen (1833-1891) was perhaps the second strongest player during this time.  He took 2^nd at London 1862.

From 1866 to 1894, Wilhelm (William) Steinitz (1836-1900) was the strongest player in the world.  In 1866, he defeated Adolf Anderssen.  In 1872, he defeated Johannes Zukertort (1842-1888) in a match.  In 1872, Steinitz scored 7 out of 7 in the 3^rd British Chess Association (BCA), ahead of Blackburne and Zukertort.  In 1876, he defeated Blackburne in a match.  In 1886, he defeated Johannes Zukertort in the first official world chess championship.  Steinitz successfully defended his world title against Mikhail Chigorin (twice) and against Isidor Gunsberg.  He finally lost the world title to Emanuel Lasker in 1894. 

From 1894 to 1921, Emanuel Lasker (1868-1941) was the world chess champion and the strongest player in the world.  In 1894, he defeated an aging William Steinitz for the world chess championship.  He defeated Frank Marshall, Siegbert Tarrasch, David Janowski, and Carl Schlechter in world championship matches.  He finally lost to Jose Capablanca in the world championship match.

From 1921 to 1927, Jose Capablanca (1888-1942) was the world chess champion.  Capablanca was undefeated in any serious game of chess from February 10, 1916 to Match 21, 1924.  This included the world championship match with Lasker.  Capablanca did not lose a single game.  In 1927, Capablanca won the powerful New York International, ahead of Alekhine and Nimzowitsch.  Capablanca remained one of the top players in the world, tying for 1^st in the Strong Nottingham 1936 chess tournament with Mikhail Botvinnik.

From 1927 to his death in 1946, Alexander Alekhine (1892-1946) was the strongest player in the world and world champion except for 1935 to 1937, when he was beaten by Max Euwe.  During that time, he defeated Efim Bogoljubov twice in world championship matches.

For a short time, from 1935 to 1937, Max Euwe (1901-1981) was world chess champion.  Euwe’s win was regarded as a major upset to become the 5^th official world chess champion.  Several stories attributed Euwe’s wins to Alekhine’s alcoholism, but it may have just been overconfidence by Alekhine. 

From 1948 to 1963, with a few breaks, Mikhail Botvinnik (1911-1995) was world chess champion.  In 1948, he won the world championship match-tournament at the Hague and Moscow, ahead of Smyslov, Keres, Reshevsky, and Euwe.  In 1951, he defeated David Bronstein for the world title.  In 1954, he defeated Vasily Smyslov for the title.  In 1957, he lost the title to Smyslov, but won it back in 1958.  In 1960, he lost the title to Mikhail Tall, but gained it back by defeating Tal in 1961.  He finally lost the title for good against Tigran Petrosian.

From 1963 to 1969, Tigran Petrosian (1929-1984) was world champion after winning the 1962 Candidates Tournament and beating Botvinnik in the world championship match.  In 1966, he defeated Boris Spassky, who was the world championship challenger that year.  In 1969, he lost to Boris Spassky,

From 1969 to 1972, Boris Spassky (1937- ) was the 10^th world chess champion.  He first had to beat Efim Geller, Bent Larson, and Viktor Korchnoi in the Candidates’s matches to qualify to play Petrosian.  In 1972, he lost his title to Bobby Fischer in their world championship match in Reykjavik, Iceland.

From 1972 to 1975, Bobby Fischer (1943-2008) was world chess champion.  When the first official FIDE rating list was published in July 1971, Fischer was the highest rated player by a wide margin.  His FIDE rating was 2760 and his USCF rating was 2801.  He had been US chess champion since January, 1964, at age 14 years and 9 months.  In 1958, Fischer’s USCF rating was 2722 and he was ranked #1 in the US until 1975, when he was no longer active in competitive chess. 

From 1975 to 1985, Anatoly Karpov (1951- ) was world chess champion.  From 1993 to 1999, he was FIDE world chess champion.  He did not have to play Fischer as Fischer forfeited his world championship match.  In 1978 and 1981, he defeated Viktor Korchnoi, the candidate for the world championship matches.  In 1985, he was defeated by Garry Kasparov.  In 1993, the world chess championship was split between FIDE and the Profession Chess Association (PCA).  Karpov won the FIDE world championship by defeating Jan Timman.  In 1996, he defeated challenger Gata Kamsky for the world championship.  In 1998, he defeated Viswanathan Anand, the challenger that year. 

From 1995 to 2000, Garry Kasparov (1963- ) was world chess champion.  He defeated Karpov in world chess championship matches in 1985, 1986, 1987, and 1990.   He defeated Nigel Short in 1993 and Vishy Anand in 1995.  In 2000, he lost to Vladimir Kramnik in the PCA world championship match. 

From 2000 to 2007, Vladimir Kramnik (1975- ) was world chess champion.  In 2000, he defeated Kasparov.  In 2004, he defeated Peter Leko.  In 2006, he defeated Veselin Topalov.  He finally lost his tile in 2007 to Anand. 

In 1996, FIDE changed its rules and the incumbent world chess champion was no longer automatically qualified for the final match.  The world champion was the winner of single-elimination matches. In 1999, Alexander Khalifman became world champion by winning a tournament in Las Vegas.  In 2000, Vishy Anand became world champion by winning a tournament in India and Iran.  In 2002, Rustan Ponomariov became world champion by winning a tournament in Moscow.  In 2004, Rustam Kasimdzhanov became world champion by winning a tournament in Tripoli.  In 2005, Veselin Topalov became world champion by winning a tournament in Argentina. 

From 2000 to 2002, and from 2007 to 2013, Viswanathan Anand (1969- ) was world chess champion.  In 2000, he won the 100-player single-elimination tournament in New Delhi and Tehran.  He had to play a tiebreaker, and defeated Alexei Shirov in the final match.  In 2007, he won an 8-player double round-robin held in Mexico City, ahead of Kramnik, Gelfand, Leko, and Svidler.  In 2008, he defeated Kramnik in a match for the world championship in Bonn, Germany.  In 2010, he defeated Topalov in Sofia, Bulgaria.  In 2012, he defeated Boris Gelfand in Moscow.  He finally lost his title to Magnus Carlsen in 2013.

From 2013 to the present, Magus Carlsen (1990- ) has been world chess champion.  In 2013, he defeated Vishy Anand in Chennai.  In 2014, he beat Anand in Sochi, Russia.  In 2016, he defeated Sergei Karjakin for the title in New York City.  In 2018, he defeated Fabiano Caruana for the title in London. 

So who are the best chess players in the USA and the world?  In 1950, FIDE gave the first grandmaster titles to 27 players: Bernstein, Boleslavsky, Bondarevsky, Botvinnik, Bronstein, Duras, Euwe, Fine, Flohr, Gruenfeld, Keres, Kostic, Kotov, Levenfish, Lilienthal, Maroczy, Mieses, Najdorf, Ragozin, Reshevsky, Rubinstein, Saemisch, Smyslov, Stahlberg, Szabo, Tartakower, and Vidmar. 

The first United States Chess Federation (USCF) National Rating List was published in Chess Life magazine on November 20, 1950.  The first list had nine classifications and rated 2,306 players.  The first list had Reuben Fine rated as an active Grandmaster with a rating of 2817.  Sam Reshevsky was rated as an inactive Grandmaster with a rating of 2770.  Players listed as inactive had not competed in any rated tournaments since January 1, 1947.  The active Senior Masters were A. Kevitz (2610), Arthur Dake (2598), Arnold Denker (2575), Isaac Kashdan (2574), and I.A. Horowitz (2558).  The inactive Senior Masters included A. Simonson (2596), Fred Reinfeld (2593), A. Kupchik (2538), D. Polland (2521), and G. Treysman (2521).  There were 26 active masters.  Those over 2400 included Larry Evans (2484), Herb Seidman (2451), Max Pavey (2442), G. Shainswit (2442), Albert Pinkus (2422).  They were followed by Arthur Bisguier (2394), George Kramer (2394), Herman Steiner (2394), Donald Byrne (2392), and Weaver Adams (2383).  There were 10 inactive masters.

A USCF rating list was published in December, 1962.  The top players included Fischer (2687), Benko (2608), Reshevsky (2597), Evans (2568), Lombardy (2565), Robert Byrne (2529), Bisguier (2503), Donald Byrne (2503), Rossolimo (2485), and Steinmeyer (2463). 

In 1964, Bobby Fischer listed the top 10 chess players in the world (excluding himself) as follows: Morphy, Staunton, Steinitz, Tarrasch, Chigorin, Alekhine, Capablanca, Spassky, Tal, and Reshevsky.  In 1970, he revised as list to as follows: Morphy, Steinitz, Capablanca, Botvinnik, Petrosian, Tal, Spassky, Reshevsky, Gligoric, and Larsen. 

In 1968, Arpad Elo rated the best chess players in history.  His list of top players were: Jose Capablanca (2725), Emanuel Lasker (2720), Mikhail Botvinnik (2720), Mikhail Tal (2700), Alexander Alekhine (2690), Paul Morphy (2690), and Vasily Smyslov (2690).  

In 1969, Elo listed the top contemporary players to be: Fischer, Spassky, Korchnoi, Botvinnik, Petrosian, Larsen, Smyslov, Portisch, Geller, Polugaevaky, Stein, Keres, and Tal.

In 1970, the first official FIDE list was published.  The top five players were Bobby Fischer (2720), Boris Spassky (2670), Viktor Korchnoi (2670), Efim Geller (2660), and Paul Keres (2650). 

In 1971, the top three players were still Fischer (2760), Spassky (2690), and Korchnoi (2670).  Bent Larsen also tied with Korchnoi (2670), followed by Petrosian (2640). 

 In 1972, Fischer topped the ratings (2785), followed by Spassky (2660), Petrosian (2645), Polugaevsky (2645), and Korchnoi (2640). 

In 1973, Fischer remained in top with a 2780 rating (he lost 5 rating points after the Fischer-Spassky world championship match).  Karpov and Tal were the 2nd and 3rd ranked with 2660, followed by Spassky at 2655 and Portisch at 2650. 

 In 1974, Fischer was inactive (and would remain inactive until 1992, but not for a FIDE rating).  The top player was Karpov (2700), followed by Korchnoi (2670), Spassky (2650), and Portisch (2645).

 In 1975, Karpov was rated 2705, followed by Korchnoi at 2655, Petrosian and Polugaevsky at 2645.

 In 1976, after Karpov played Korchnoi, Karpov’s rating was 2695, followed by Korchnoi at 2670.  Petrosian and Polugaevsky were rated at 2635, followed by Spassky at 2630. 

In 1976, chess author Irving Chernev listed the world’s greatest chess players as follows: Capablanca, Alekhine, Lasker, Fischer, Botvinnik, Petrosian, Tal, Smyslov, Spassky, Bronstein, Rubinstein, and Nimzowitsch. 

 In 1977, Karpov was rated 2690.  Korchnoi and Petrosian were rated at 2645.  Mecking came next at 2635, followed by Portisch at 2625. 

 In 1978, Karpov was rated 2725, followed by Korchnoi at 2665.  Mecking, Portisch, and Spassky were rated 2630. 

In 1978, Arpad Elo listed the top players ever as: Capablanca (2725), Botvinnik (2720), Lasker (2720), Tal (2700), Alekhine (2690), Morphy (2690), Smyslov (2690), Petrosian, Reshevsky, Spassky, Bronstein, Keres, Korchnoi, Fine, Geller, Boleslavsky, Euwe, Steinitz, Rubinstein, Najdorf, Pillsbury, Portisch, Timman, Flohr, Gligoric, Kholmov, Kotov, Larsen, Maroczy, Stein, Averbakh, Nimzowitsch, Anderssen, Bogoljubov, Furman, Ljubojevic, Szabo, Tarrasch, Mecking, Polugaevsky, Anderssen, Chigorin, Schlechter, Taimanov, Vidmar, von der Lasa, Zukertort 

 In 1979, after the world championship match between Karpov and Korchnoi, Karpov was rated 2705.  Korchnoi was rated at 2695.  Spassky and Portisch were rated 2640, followed by Polugaevsky at 2625.

 In 1980, Karpov was rated 2725.  Tal came 2nd with 2705, followed by Korchnoi at 2695.  Portisch was rated 655.  Polugaevsky was rated 2635.

 In 1981, Karpov was rated 2690.  Korchnoi and Portisch were rated 2650.  Huebner and Spassky were rated 2635.

 In January 1982, Karpov was rated 2700, followed by Jan Timman at 2655.  Korchnoi was rated 2645.  Kasparov was 4th with 2640, followed by Portisch at 2630.  By July 1982, Kasparov was 2nd with 2675, followed by Korchnoi at 2635, Huebner at 2630, and Portisch at 2625.

 In 1983, Karpov was rated 2710, followed by Kasparov at 2690.  Ljubojevic was rated 2645, followed by Ulf Andersson at 2640 and Huebner at 2625.

 In 1984, Kasparov led the list with a 2710 rating, followed by Karpov at 2700.  Korchnoi and Ljubojevic were rated 2635, followed by Andersson at 2630. 

 In January 1985, Kasparov was rated 2715, followed by Karpov at 2705.  Timman was rated 2650, followed by Vaganian at 2640 and Beliavsky at 2635.  By July 1985, Karpov moved up with a 2720 rating, followed by Kasparov at 2700,  Beliavsky and Timman were at 2640, followed by Korchnoi at 2630. 

In 1986, Kasparov was rated 2740, followed by Karpov at 2705.  Yusupov was 3rd with 2660, followed by Korchnoi at 2650, Timman at 2645, and Huebner at 2620. 

In 1987, Kasparov topped the list with 2740.  Karpov was rated at 2710.  Yusupov and Sokolov were rated 2645, followed by Korchnoi at 2630. 

In 1988, Kasparov was at 2760 and Karpov was at 2725.  Timman was rated 2675.  Short and Beliavsky were at 2665.  Korchnoi was rated 2640. 

In 1989, Kasparov was rated 2775, followed by Karpov at 2755.  Ivanchuk and Short were rated 2660, followed by Korchnoi at 2655. 

In 1989, mathematician Dr. Nathan Divinsky and grandmaster Raymond Keene, in their book Warriors of the Mind, attempted to establish a rating system comparing the strength of players active in different eras to determine the strongest player of all time.  Their top 10 list included: Kasparov (3096), Karpov (2876), Fischer (2690), Botvinnik (2616), Capablanca (2552),  Lasker (2550), Korchnoi (2535), Spassky (2480), Smyslov (2413), and Petrosian (2363). 

In 1990, Kasparov was at 2800, followed by Karpov at 2730.  Gelfand and Ivanchuk were rated 2680, followed by Timman at 2660. 

In 1991, Kasparov was rated 2800 at the beginning of the year.  Ivanchuk was rated 2735, followed by Karpov at 2730.  Bareev was rated 2680, followed by Salov at 2665.

In 1992, Kasparov was rated 2790.  Karpov was rated at 2725.  Ivanchuk was rated at 2720.  Shirov was rated 2710, followed by Anand at 2690.

In 1993, Kasparov was rated 2815, followed by Karpov at 2760.  Anand moved up to 2725, followed by Ivanchuk and Kramnik at 2710.  Gelfand was rated 2690. 

In 1994, Kasparov remained at 2815, followed by Karpov at 2780.  Shirov was rated at 2740, followed by Kramnik at 2725 and Anand at 2720.  Ivanchuk was at 2710. 

In 1994,  the Professional Chess Association (PCA) listed the current 50  best players as:  Kasparov, Karpov, Kamsky, Anand, Ivanchuk, Salov, Piket, Shirov, Kramnik, Gelfand, Yusupov, Lautier, Sokolov, Ehlvest, J Polgar, Timman, Short, Akopian, Vaganian, Korchnoi, Adams, Bareev, Tiviakov, Nikolic, Huebner, Georgiev, Dreev, Topalov, Hodgson, Epishin, Kaidanov, Beliavsky, Gulko, Nunn, Hansen, Speelman, Dolmatov, Dautov, Malaniuk, Azmaiparashvili, Vladimirov, Nenashev, Illescas, Magerramov, Khalifman, Romanishin, Gurevich, Oll, Fischer, Andersson 

In 1995, Kasparov was rated at 2805 at the beginning of the year.  Karpov was at 2775.  Ivanchuk was at 2740, followed by Kamsky at 2735 and Kramnik at 2730. 

In January 1996, Kasparov and Kramnik were both rated 2775, followed by Karpov at 2770.  Ivanchuk and Kamsky were rated 2735.  By July 1996, Kasparov moved up to 2785, followed by Karpov at 2775, Kramnik at 2765, Topalov at 2750, and Kamsky at 2745.

In 1997, Kasparov was at 2820.  Kramnik was next at 2770, followed by Anand at 2765, Karpov at 2760, Topalov at 2745, and Ivanchuk at 2740. 

In 1998, Kasparov was at 2825.  Anand was at 2795, followed by Kramnik at 2790.  Ivanchuk and Topalov were rated at 2740, followed by Karpov at 2725.

In 1999, Kasparov’s rating went up to 2851 (the highest ever).  Anand was 2781, followed by Kramnik at 2760.  Shirov and Morozevich were rated 2726.

In 2000 the FIDE ratings came out three times a year. Kasparov was rated 2851 in January 2000, followed by Anand at 2774 and Kramnik at 2770.  Morozevich was rated 2756, followed by Adams at 2755 and Shirov at 2751.  Leko was rated 2748. 

In 2000, Anand listed his to 10 as follows: Fischer, Morphy, Lasker, Capablanca, Steinitz, Tal, Korchnoi, Keres, Karpov, and Kasparov. 

In 2001, the FIDE ratings came out 4 times a year.  Kasparov’s highest rating during that year was 2849.  Kramnik maxed out at 2809.  Anand was rated 2794.  Adams was at 2750.  Morozevich was rated at 2749.  Leko was rated 2745.

In 2001, Chess Informant readers listed the best chess players ever as follows: Fischer, Kasparov, Alekhine, Capablanca, Botvinnik, Karpov, Tal, Lasker, Anand, and Korchnoi. 

In 2002, Kasparov was 2838 throughout the year.  Kramnik peaked at 2809.  Anand was 2757, followed by Adams at 2752.  Topalov’s rating was 2745.  Morozevich was at 2742. 

In 2002, the Professional Chess Association (PCA) listed the current 50  best players as: Kasparov, Kramnik, Topalov, Ponomariov, Anand, Bareev, Leko, Adams, Ivanchuk, Gelfand, Grischuk, Khalifman, Shirov, Morozevich, Svidler, Azmaiparashvili, Malakhov, Zvjaginsev, J Polgar, Karpov, Bacrot, Dreev, Short, Lautier, Krasenkov, Smirin, Sutovsky, Van Wely, Sakaev, Ye Jiangchuan, Akopian, Sokolov, Nikolic, Vallejo Pons, Vaganian, Lputian, Radjabov, Rublevsky, Tkachiev, Graf-Nenashev, Goldin, Kasimdzhanov, Georgiev, Volkov, Lutz, Almasi, Macieja, Piket, Pigusov, Tiviakov. 

In 2003, Kasparov was rated 2847 at the beginning of the year.  Kramnik was rated 2807, followed by Anand at 2774 and Leko at 2746.  Adams was at 2745.  Topalov was at 2743.  Bareev was at 2739 and Shirov was at 2737. 

In 2004, Kasparov topped the list at 2831.  Anand was 2nd at 2782.  Kramnik was 2777, followed by Morozevich at 2758.  Topalov’s rating was 2757.  Svidler was rated 2747, followed by Leko at 2741 and Shirov at 2736.

In 2004, another rating system, the Edo Historical Chess Ratings system, was created by Rod Edwards.  This was an attempt to retroactively rate chess players over time.  It uses an iterative method (Bradley-Terry).    It top peak Edo ratings were: Steinitz (2803), Morphy (2796), Lasker (2752), Kolisch (2710), Tarrasch (2699), Zukertort (2678), von der Lasa (2676), Anderssen (2673), Neumann (2671), and Maroczy (2665).  According to Edwards, historically, the top 19^th century chess players were Morphy (2802), Steinitz (2798), Lasker (2753), Kolisch (2709), Tarrasch (2685), Paulsen (2677), Neumann (2676), Zukertort (2675), von der Lasa (2659), and Pillsbury. By 1914, the top 10 players were: Lasker (2750), Capablanca (2736), Alekhine (2653), Rubinstein (2610), Marshall (2606), Nimzowitsch (2589), Teichmann (2582), Vidmar (2579), Tarrasch (2574), and Bernstein (2571).  The top 50 list from 1809 to 1902  included:: Morphy, Steinitz, Emanuel Lasker, Kolisch, Tarrasch, Paulsen, Neumann, Zukertort, von der Lasa, Pillsbury, Anderssen, Chigorin, Winawer, Suhle, Staunton, Blackburne, Maroczy, Dubois, Bauer, de Vere, Makovetz, Lipshutz, Gunsberg, Weiss, Janowski, Mackenzie, Schlecther, Mason, Harrwitz, Charousek, von Bardeleben, de Labourdonnais, Buckle, Burn, Englisch, Rosenthal, Petrov, B Lasker, Potter, Moehle, Atkins, Goetz, Lipke, Schwarz, Alapin, Bird, Riemann, Hirschfeld, Lange (source: http://www.edochess.ca/)

In 2005, Kasparov was at 2812, followed by Anand and Topalov at 2788.  Leko was rated 2763, Kramnik at 2754, and Ivanchuk at 2752.

In 2005, Statistician Jeff Sonas developed a rating system called “Chessmetrics.”    He claims that it takes into account rating inflation, as well as frequency of play.  His top 1-year peak list is: Fischer (2881), Kasparov (2879), Botvinnik (2871), Capablanca (2866), Lasker (2863), and Alekhine (2851).  For a 10-year peak, his list is the following: Kasparov (2863), Lasker (2847), Karpov (2821), Capablanca (2813), Fischer (2810), and Botvinnik (2810).   For a 20-year peak, the top players were: Kasparov (2856), Karpov (2818), Lasker (2809), Alekhine (2781), Korchnoi (2766), Smyslov (2759), Keres (2755), Petrosian (2754), Botvinnik (2748), and Spassky (2747).  If we did it by age, such as peak rating at age 30, the list would be: Kasparov (2884), Fischer (2858), Lasker (2829), Karpov (2816), and Anand (2814).  In 2005, his ranking of the highest rated players in the world were: Fischer (2895), Kasparov (2886), Botvinnik (2885), Lasker (2878),  Capablanca (2877), Alekhine (2860), Karpov (2848), Anand (2833), Kramnik (2826), and Steinitz (2826).  The top 50 list of all time included: Kasparov, Lasker, Capablanca, Botvinnik, Fischer, Karpov, Alekhine, Anand, Kramnik, Pillsbury, Ivanchuk, Korchnoi, Steinitz, Smyslov, Tarrasch, Maroczy, Petrosian, Rubinstein, Tal, Reshevsky, Keres, Najdorf, Nimzovich, Spassky, Zukertort, Bronstein, Chigorin, Marshall, Kamsky, Leko, Gelfand, Salov, Bogoljubow, Beliavsky, Shirov, Geller, Timman, Adams, Fine, Janowsky, Polugaevsky, Topalov, Schlechter, Portisch, Stein, Euwe, Flohr, Morozevich, Larsen, Bareev  (source: http://www.chessmetrics.com/cm/) 

In 2006, Kasparov was no longer active, having retired.  Kasparov was ranked #1 in the world 54 times, or 255 months.  Topalov was rated the highest at 2813.  Anand was 2803, followed by Svidler at 2675.  Aronian was rated 2756.  Leko was at 2751.  Ivanchuk was rated 2748.   Morozevich’s rating was 2747.  Kramnik’s rating was 2743.  

In 2007, Anand’s rating was 2801, followed by  Ivanchuk at 2787.  Topalov was rated at 2783.  Kramnik was rated at 2785.  Morozevich was at 2762, then Aronian at 2759, then Leko at 2755, and Mamedyarov at 2754.

In 2007, Majej Guid and Ivan Bratko used a computer-based method of analyzing chess abilities.  They used Rybka 2 and compared the average number of errors in the player’s game.  The best player ever with the least number of errors was Bobby Fischer.  The other players, in order of least errors, were: Kramnik, Kasparov, Botvinnik, Capablanca, Karpov, Smyslov, Tal, Petrosian, Euwe, Spassky, Alekhine, Anand, Lasker, Morphy, and Steinitz.  Another criterion was the average difference between moves played and best evaluated moves by computer analysis.  The world champions with the least number of errors were, in order: Capablanca, Kramnik, Karpov, Kasparov, Spassky, Petrosian, Lasker, Fischer, Alekhine, Smyslov, Tal, Botvinnik, Euwe, and Steinitz. (source: http://en.chessbase.com/news/2006/world_champions2006.pdf)

In 2008, Anand’s rating was 2803, followed by Kramnik at 2799.  Topalov was rated 2791.  Morozevich was rated at 2788 and Ivanchuk and Magnus Carlsen were rated at 2786.  Anand fell to 2783.  Svidler was rated at 2763.  

Stefan Fischl was done some chess statistics and listed the top Elo performance from 2000 to 2008 as Kasparov (2812), Anand (2780), Kramnik (2773), Topalov (2770), Leko (2742), Ivanchuk (2737), Morozevich (2737), and Svidler (2726).  His top players for the last 12 months (09/2007 to 08/2008) include Anand (2808), Morozevich (2786), Carlsen (2785), Topalov (2783), Kramnik (2774), and Ivanchuk (2764).   Stefan Fischl’s historic players’ statistics for 1851 to 1890 include Steinitz, Anderssen, Morphy, Mackenzie, Winawer, Zukertort, Paulsen, Englisch, Blackburne, and E. Williams as the top players. (source: http://members.aon.at/sfischl/stat.html)

In 2009, Topalov topped the list with 2813.  Carlsen was at 2801.  Anand was rated at 2791.  Aronnian was rated 2786.  Ivanchuk was rated 2779.  Kramnik was rated 2772.  Morozevich was rated at 2771.  Yakovenko was rated 2760, followed by Radjabov at 2756.

Another computer study in 2009 by Julian Alejandro of Argentina, using Rybka 3 and using 3 minutes per moves, came up with a list of fewest errors in their chess games.  The man with the fewest errors, according to the computer analysis was Bobby Fischer, followed by Kramnik, Svidler, Topalov, Karjakin, Tal, Anand, Kasparov, Morphy, Leko, Shirov, Ivanchuk, Lasker, Euwe, Beliavsky, Khalifman, Matulovic, Uhlmann, Pillsbury, Karpov, Alekhine, Ponomariov, Aronian, Botvinnik, Smyslov, Capablanca, Ivkov, Kasimdzhanov, Spassky, Geller, Petrosian, Rubinstein, Kolisch, Steinitz, Korchnoi, Eichborn, Stean, Zukertort, Anderssen, Greco, La Bourdonnais, Staunton, and Philidor. (source: http://www.chess.com/forum/view/chess-players/greatest-player-according-rybka-3-3-min-quad)

Another study, using Rybka 3, looked at the average expected error by thinking time.  The players with the least number of errors, in order, were: Deep Blue, Kramnik, Karpov, Fischer, Capablanca, Fine, Anand, Kasparov, Korchnoi, Smyslov, Botvinnik, Spassky, Petrosian, Keres, Nimzowitsch, Alekhine, Tal, Marshall, Tarrasch, Rubinstein, and Maroczy.  (source: http://www.scribd.com/doc/132380754/Chess-Player-Analysis-by-Rybka-3-14ply)

Charles Sullivan at TrueChess.com compared chess champions based on best year.  His ranking was: Fischer, Anand, Smyslov, Kramnik, Spassky, Botvinnik, Euwe, Capablanca, Petrosian, Kasparov, Karpov, Tal, Alekhine, Lasker, Morphy, and Steinitz.  The ranking based on the best 10-year period is: Fischer, Capablanca, Kasparov, Kramnik, Botvinnik, Smyslov, Karpov, Lasker, Spassky, Petrosian, Alekhine, Anand, Tal, Ewue, and Steinitz.

In 2009, listverse listed its 10 chess players in history.  They were, in order: Kasparov, Karpov, Lasker, Steinitz, Capablanca, Fischer, Alekhine, Botvinnik, Morphy, and Deep Blue. (source: http://listverse.com/2009/09/06/top-10-greatest-chess-players-in-history/) 

In 2010, Carlsen was number 1 ranked at 2826, followed by Topalov at 2805.  Anand was at 2800.  Kramnik was at 2790.  Aronian was rated 2783.  

Roman Krumsieck's top 50 list included: Eichborn, Kasparov, Anand, Kramnik, Ivanchuk, Karpov, Topalov, Svidler, Ponomariov, Leko, Shirov, Morozevich, Aronian, Grischuk, Adams, Kamsky, Milov, Bareev, Gelfand, Fischer, Radjabov, J Polgar, Salov, Bacrot, Kasimdzhanov, Mamedyarov, Short, Akopian, Sasikiran, Dreev, Smirin, M Gurevich, Malakhov, Van Wely, Sokolov, Khalifman, Azmaiparashvili, Georgiev, Rublevsky, Korchnoi, Nikolic, McShane, Piket, Yusupov, Beliavsky, Lautier, Nisipeanu, Nakamura, Naiditsch, and Timman.

In 2011,  Anand was 2817.  Carlsen was 2815.  Aronian was rated at 2808.  Kramnik was 2785.  Ivanchuk was 2779.  Karjakin was rated 2776.

In November 2012, the highest rated player was Magnus Carlsen at 2848.  For 2012, Aronian was rated at 2821, Kramnik at 2795, Radjabov at 2793, Caruana and Nakamura at 2786, Anand and Karjakin at 2780.

In January 2013, the top 10 players were Carlsen at 2861, Kramnik at 2810, Aronian at 2802, Radjabov at2793, Carauna at 2781, Karjakin at 2780, Anand at 2772, Topalov at 2771, Nakamura at 2769, and Mamedyarov at 2766. 

In January 2014, the top 10 players were Carlsen at 2872, Aronian at 2812, Nakamura at 2789, Kramnik at 2787, Topalov at 2785, Caruana at 2782, Grischuk at 2777, Gelfand at 2777, Anand at 2773, and Karjakin at 2759. 

In July 2015, the top 10 players were Carlsen (2853), Anand (2816), Topalov (2816), Nakamura (2814), Caruana (2797), Giri (2791), Kramnik (2783), So (2780). Grischuk (2771), and Aronian (2765). 

As of July 2015, the top US players are: Nakamura (2883), Caruana (2876), So (2840), Robson (2777), Kamksy (2755), Onischuk (2742), Shankland (2739), Lenderman (2731), Zherebukh (2724), Akobian (2716), and Naroditsky (2708). 

In May 2016, the top 10 players were Carlsen (2851), Caruana (2804), Kramnik (2801), Giri (2790), Vachier-Lagrave (2788), Nakamura (2787), Aronian (2784), Karjakin (2779), Ding (2778), and So (2775). 

In July 2017, the top 10 players were Carlsen (2822), Kramnik (2812), So (2810), Aronian (2809), Caruana (2807), Mamedyarov (2800), Nakamura (2792), Vachier-Lagrave (2791), Anand (2783), and Ding (2781). 

In January 2018, the top 10 players were Carlsen (2834), Caruana (2811), Mamedyarov (2804), Aronian (2797), Vachier-Lagrave (2793), So (2792), Kramnik (2787), Nakamura (2781), Ding (2769), and Svidler (2768). 

In April 2019, the top 10 players were Carlsen (2845), Caruana (2819), Ding (2809), Giri (2797), Mamedyarov (2793), Anand (2774), Nepomniachtchi (2773), Vachier-Lagrave (2773), Grischuk (2771), and Aronian (2763).

In January 2020, the top 10 players were Carlsen (2782), Caruana (2822), Ding (2805), Grischuk (2777), Nepomniachtchi (2774), Aronian (2773), Vachier-Lagrave (2770), Mamedyarov (2770), Giri (2768), and So (2765). 

In 2020, Colin Stapczynski, director of written content at chess.com listed the top chess players of all time.  His list, with the best being first includes: Garry Kasparov, Magnus Carlsen, Bobby Fischer, Jose Capablanca, Anatoly Karpov, Mikhail Botvinnik, Vladimir Kramnik, Emaneul Lasker, Alexander Alekhine, Paul Morphy, Tigran Petrosian, and Viswanathan Anand. 

In January 2021, the top 10 players were Carlsen (2865), Caruana (2821), Ding Liren (2791), Nepomniachtchi (2789), Vachier-Lagrave (2783), Aronian (2781), Grischuk (2777),  Mamedyarov (2770), So (2770), and Giri (2767). 

In January 2021, the top players in the United States Chess Federation (USCF) were Caruana (2891), So (2841), Dominguez (2829), Nakamura (2827), Xiong (2786), Shankland (2762), Robson (2749), Sevian (2733), Swiercz (2733), and Kamsky (2732). 

In January 2021, the top chess engines were Stockfish (3564) Leela Chess Zero (3467), Houdini (3444), Fire (3430), Ethereal (3386), Fizbo (3347), Andscacs (3337), Booot (3326), Deep Shredder (3324), and Xiphis (3193).

If we look at the total reign of world champions in years, the list is as follows: Lasker (27), Alekhine (17), Karpov (16), Kasparov (15), Botvinnik (13), Carlsen (8), Anand (8), Steinitz (8), Kramnik (7), Petrosian (6), Capablanca (6), Fischer (3), Spassky (3), Euwe (2), Ponomariov (2), Smyslov (1), Tal (1), Khalifman (1), Kasimdzhanov (1), and Topalov (1). 

If we look at peak Elo ratings, the top players are Carlsen (2882), Kasparov (2851), Caruana (2844), Aronian (2830), So (2822), Mamedyarov (2820), Vachier-Lagrave (2819). Anand (2817), Kramnik (2817), Topalov (2816), Nakamura (2816), Ding Liren (2816), and Grischuk (2810).

The top players to never have been world champion would be: Korchnoi, Keres, Bronstein, Tarrasch, Reshevsky, Chigorin, Pillsbury, Maroczy, Rubinstein, and Najdorf. 

Over the years, Kasparov has been ranked #1 in the world on the official FIDE rating list 23 times.  He was the world chess champion at age 22.  He was world chess champion for 15 years.  He was the highest rated player in the world almost continuously for 21 years, from 1984 until his retirement in 2005.  He held the all time record rating of 2851 for over 10 years until Magnus Carlsen broke his record in 2014.  He placed first or equal first in 15 tournaments from 1981 to 1990.  He won the Chess Oscar, given to the best player in a year, a record 11 times.  

Magnus Carlsen is the current World Chess Champion, World Rapid Champion, and World Blitz Chess Champion.  He has had the highest FIDE rating since 2010.  His peak classical chess rating was 2882, established in May 2014.  His FIDE rating is the highest in history.  He holds the record for the longest unbeaten run in chess.  He surpassed a FIDE rating of 2800 at age 18.  He reached the highest FIDE rating at age 19, becoming the youngest person ever to achieve those feats. 

For many, Bobby Fischer is considered the greatest chess player of all time.  He won the US championship ever time he played, a record 8 times, winning each by at least a point.  In 1956, he won the US Junior championship, scoring 8.5 out of 10, to become the youngest-ever Junior Champion at age 13.  He was a grandmaster at the age of 15.  He was the youngest Candidate for the World Championship at 15, a record that is yet to be broken and is probably never going to be broken.  At the age of 20, he won the 1963-64 US championship with a perfect 11-0 score, the only perfect score in the history of the tournament.  He won by a margin of 2.5 points to the 2^nd place finisher.  In US championship play, he won 61 games, drew 26, and lost 3.  He won the 1970 Interzonal by a record 3.5-point margin.  He won 20 consecutive games, including a 6-0 sweep of candidate Mark Taimanov (#5 in the world) and 6-0 sweep of candidate Bent Larsen (#4 in the world).  Fischer, as number one rated in the world, separated himself from #2 in the world by a larger rating margin than anyone in chess history.  In 1972, his 2785 Elo rating was 125 points than the #2 player, world champions Boris Spassky, rated at 2660.  Fischer was ranked 54 total months as number one in the world, and by that time, he had retired from chess.