Comparison of Top Chess Players Throughout History - Statistical Methods - Elo System

Elo System

Perhaps the best-known statistical model is that devised by Arpad Elo. In his 1978 book The Rating of Chessplayers, Past and Present, he gave ratings to players corresponding to their performance over the best five-year span of their career. According to this system the highest ratings achieved were:

• 2725 – José Raúl Capablanca
• 2720 – Mikhail Botvinnik, Emanuel Lasker
• 2700 – Mikhail Tal
• 2690 – Alexander Alekhine, Paul Morphy, Vasily Smyslov.

(Though published in 1978, Elo's list did not include five-year averages for Bobby Fischer and Anatoly Karpov. It did list January 1978 ratings of 2780 for Fischer and 2725 for Karpov.)

In 1970, FIDE adopted Elo's system for rating current players, so one way to compare players of different eras is to compare their Elo ratings. The best-ever Elo ratings are tabulated below.

As of March 2012, there were 85 chess grandmasters in history who broke the 2700 limit and only 6 of them were capable of overcoming the 2800 line. Particularly notable are performances by players like Fischer, Karpov and Kasparov, who achieved their peak ratings in earlier years (1972, 1994, and 1999 respectively).

Table of top 20 rated players ever, with date their best ratings were first achieved

Rank	Rating	Player	Year-month
1	2851	Garry Kasparov	1999-07
2	2848	Magnus Carlsen	2012-11
3	2825	Levon Aronian	2012-05
4	2817	Viswanathan Anand	2011-03
5	2813	Veselin Topalov	2006-07
6	2809	Vladimir Kramnik	2001-10
7	2793	Teimour Radjabov	2012-11
8	2788	Alexander Morozevich	2008-07
9	2788	Sergey Karjakin	2011-07
10	2787	Vassily Ivanchuk	2007-10
11	2786	Hikaru Nakamura	2012-10
12	2786	Fabiano Caruana	2012-11
13	2785	Bobby Fischer	1972-04
14	2780	Anatoly Karpov	1994-07
15	2773	Alexander Grischuk	2011-01
16	2772	Shakhriyar Mamedyarov	2011-01
17	2768	Ruslan Ponomariov	2011-07
18	2765	Peter Svidler	2011-07
19	2763	Peter Leko	2005-04
20	2762	Gata Kamsky	2012-11