I can't really answer who was the greatest chess player of all time, however, my simple-minded algorithm gives an indication of how the top players from the last 50 years compare.
It is widely believed that chess ratings have undergone significant inflation over the years. In 1979 there was only one player rated over 2700, whereas in 1994 there were six. Today in 2018, there are 46. It is not really known why ratings suffer from inflation, but it is probably due to a decrease in the rating floor, which means that more weak players enter the rating pool. This causes points to trickle up to the top.
Writing in 2009, Jeff Sonas made a careful study of rating inflation. He showed that the rating of the 10th player in the world was relatively constant during 1975-1985. Then ratings increased by about 8 points per year until 1997, when it became about 4 points per year. Sonas illustrated this graphically:
The upshot is that we cannot directly compare the ratings of players from different periods.
Since I agree with Sonas that the average strength of the top ten players has remained roughly constant, I decided to use his results to adjust the ratings of modern players to make them comparable to those of Fischer’s time.
My algorithm subtracts 8 points for each year from 1986 to 1997, and 4 points for each year from 1998 to 2018. During 2001 to 2018 inflation for the 100th player ran at 3.4 points per year. I have assumed 4 points per year inflation for 1998 to 2018. I have arbitrarily chosen 2625 as the cut-off point for inclusion. Ratings are not available for players before 1971, hence the absence of people like Alekhine and Capablanca.
I suspect that inflation became more severe recently. Of the twelve players who have passed 2800, except for Kasparov and Anand, they all did so during the last four years. Also, the adjusted ratings imply that eleven modern players are stronger than world champion Petrosian, which seems extremely unlikely. So even the adjusted ratings are probably inflated for recent players, such as Carlsen, Caruana, Aronian, Nakamura etc. My guess is that the adjusted ratings of the modern players should be reduced by something like 40 points.
Note that peak rating is only one measure of playing strength. In the last few years, a number of players have shot up over 2800, only to fall back again. Peak rating can surge after a single tournament and does not take into account consistency over years of play.
It is no surprise that Fischer comes out first, as no other player dominated the modern era the way that Fischer did in the lead-up to winning the world chess championship in 1972. Note that all the players over 2700 were world champions.
The table below lists each player, when they reached their peak, and their peak rating adjusted to the levels prevailing during 1971 to 1985. World champions are marked with an asterisk.
|
Player
|
Year
|
Adjusted rating
|
|
Fischer *
|
1972
|
2785
|
|
Kasparov *
|
1999
|
2751
|
|
Carlsen *
|
2014
|
2722
|
|
Karpov *
|
1994
|
2708
|
|
Tal *
|
1980
|
2705
|
|
Korchnoi
|
1979
|
2695
|
|
Spassky *
|
1971
|
2690
|
|
Caruana
|
2014
|
2684
|
|
Aronian
|
2014
|
2670
|
|
Anand *
|
2011
|
2669
|
|
Botvinnik *
|
1971
|
2660
|
|
Larsen
|
1971
|
2660
|
|
Ivanchuk
|
2007
|
2655
|
|
Morozevich
|
2008
|
2652
|
|
Topalov *
|
2015
|
2652
|
|
Nakamura
|
2015
|
2652
|
|
Grischuk
|
2014
|
2650
|
|
So
|
2017
|
2650
|
|
Kramnik *
|
2016
|
2649
|
|
Petrosian *
|
1972
|
2645
|
|
MVL
|
2016
|
2643
|
|
Radjabov
|
2012
|
2641
|
|
Karjakin
|
2011
|
2640
|
|
Leko
|
2005
|
2639
|
|
Mamedyarov
|
2018
|
2638
|
|
Geller
|
1971
|
2630
|
|
Giri
|
2015
|
2630
|
I hope I have not missed someone. Note that world champion Smislov does not even make the cut, giving further grounds to believe that modern players are over-rated. A curious fact is that of the 27 players, six reached their peak in 1971 or 1972 and seven in 2014 or 2015.
Postscript
Being dissatisfied with what I see as the over-valuation of modern players, I arbitrarily decided to subtract 39 points from all players who peaked after 1999. This has no statistical justification. However, I believe it gives more plausible results.
Post-Postscipt in January 2020
I saw a graph on chess.com showing the January ratings of the top players during 1971-2020. Using this graph, I estimate that the rating of the players rated 2 to 10 went up by about 40 points during 2005 to 2020. This adds credence to my subjective decision to subtract 39 points from players who peaked after 1999.
|
Player
|
Year
|
Subjectively adjusted rating
|
|
Fischer *
|
1972
|
2785
|
|
Kasparov *
|
1999
|
2751
|
|
Karpov *
|
1994
|
2708
|
|
Tal *
|
1980
|
2705
|
|
Korchnoi
|
1979
|
2695
|
|
Spassky *
|
1971
|
2690
|
|
Carlsen *
|
2014
|
2683
|
|
Botvinnik *
|
1971
|
2660
|
|
Larsen
|
1971
|
2660
|
|
Petrosian *
|
1972
|
2645
|
|
Caruana
|
2014
|
2645
|
|
Aronian
|
2014
|
2631
|
|
Geller
|
1971
|
2630
|
|
Anand *
|
2011
|
2630
|