Who is the strongest chess player in the world? We can assume that it is Viswanathan Anand after he won the 2008 world chess championship, followed by Vladimir Kramnik, his challenger. But on the official world chess federation (FIDE) rating for October, 2008, there are four other chess players rated higher than these two players. The highest ranked player is Veselin Topalov (2791), followed by Alexander Morozevich (2787), Vassily Ivanchuk (2786), and Magnus Carlsen (2786). Anand is rated at 2783 and Kramnik is rated at 2772.
Over the years, Garry Kasparov has been ranked #1 on the official FIDE rating list 23 times.
The best-ever Elo ratings are Kasparov (2851), Topalov (2813), Kramnik (2809), Anand (2803), Morozevioch (2788), Ivanchuk (2787), Carlsen (2786), Fischer (2785), and Karpov (2780).
The Live Top List, a provisional world chess rankings list by Hans Runde, lists the top 6 players as Anand (2796), Topalov (2791), Ivanchuk (2789), Morozevich (2779), Carlsen (2778), and Kramnik (2759).
The Chessmetrics database by Jeff Sonas listed the top 10 players for 3 year peak range as Kasparov (2874), Fischer (2867), Capablanca (2857), Lasker (2855), Botvinnik (2852), Alekhine (2841), Karpov (2833), Anand (2822), Kramnik (2815), and Pillsbury (2806). Over a one-year period, the top players in Sonas’s list are Fischer, Kasparov, Botvinnik, Capablanca, Lasker, and Alekhine. In a 20-year span, the top players are Kasparov, Karpov, Lasker, Alekhine, Korchnoi, and Smyslov
The Bratko and Guid method of strongest player was calculated using computers and the best chess programs to look at the quality of play, regardless of game score. The top world champion that showed the lowest average error was Capablanca, followed by Kramnik, Karpov, Kasparov, Spassky, Petrosian, Lasker, Fischer, Alekhine, Smyslov, Tal, Botvinnik, Euwe, and Steinitz. The top world champion that had the lowest percentage of blunders was Capablanca, followed by Petrosian, Karpov, Kramnik, Smyslov, Kasparov, Spassky, Alekhine, Lasker, Fischer, Tal, Botvinnik, Euwe, and Steinitz. The world champion that best performed when facing complex postions was Kramnik, followed by Capablanca, Karpov, Kasparov, Petrosian, Fischer, Lasker, Alekhine, Spassky, Smyslov, Tal, Botvinnik, Euwe, and Steinitz. The world champion that played the best moves was Fischer, followed by Euwe, Kramnik, Alekhine, Kasparov, Lasker, Steinitz, Karpov, Tal, Spassky, Botvinnik, Petrosian, and Steinitz.
Charles Sullivan at TrueChess.com has compared chess champions based on best year. His ranking is Fischer, Anand, Smyslov, Kramnik, Spassky, Botvinnik, Euwe, Capablanca, Petrosian, Kasparov, Karpov, Talk, 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.
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).
In 1978, Arpad Elo listed his top players over the best five-year span of their career. The top players were Capablanca (2725), Botvinnik and Lasker (2720), Tal (2700), and Alekhine, Morphy, and Smyslov (2690).
In 1989, Keene and Divinksy ranked the top players when considering games between the top 64 players in the world. The top players were Kasparov, Karpov, Fischer, Botvinnik, Capablanca, Lasker, Korchnoi, Spassky, Smyslov, and Petrosian.
In 2008, after Fischer’s death, Anand ranked Kasparov as the strongest player ever, followed by Fischer.
Historically, the top 19th 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 (1900). This is according to the Edo ratings by Rod Edwards.
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.
If we look at world champions and how long they reigned, the list is as follows: Lasker (27 years), Alekhine (17 years), Karpov (16 years), Kasparov (15 years), Botvinnik (13 years), Steinitz (8 years), Kramnik (6 years), Capablanca (6 years), Petrosian (6 years), Fischer (3 years), Spassky (3 years), Anand (2 years), Euwe (2 years), Ponomariov (2 years), Smyslov (1 year), Tal (1 year), Khalifman (1 year), Kasimdzhanov (1 year), and Topalov (1 year).
Kramnik, Anand, Kasparov, etc have all been beaten by chess computer programs. The top chess programs are Rybka (3009) which is the current world compter chess champion, Naum (2863), Hiarcs (2853), Fritz 11 (2857), Shredder 11 (2848), Zap (2823), and Fritz 10 (2800).