08/30/2023
GM Larry Kaufman just sent me this very interesting and in depth article. I hope you will take time to read it. It is very unfair to compare players’ ratings from different generations.
Accuracy, Ratings, and GOATs
There have been many attempts to estimate ratings of chess players, both past and present, by looking at their game scores and comparing the moves with a top engine's choices, including one notable study here on Chess.com in 2017.
These attempts have been generally correct in showing the steady advance of chess skill over time, but they have mostly been rather unconvincing at actually comparing individual players; one study even ranked Jose Capablanca as the objectively best player of all time! He may have been the best of all time relative to his peers or had the most talent (though that is not my conclusion), but to suggest that he actually played as well as GM Garry Kasparov or GM Vladimir Kramnik at peak (this study was done before GM Magnus Carlsen arrived on the scene), even after the opening, is just not plausible; chess knowledge has advanced tremendously since 1920.
The main reason for the difficulty in comparing players is that those who prioritize not losing and excel in endgames (Capablanca, GM Tigran Petrosian, GM Anatoly Karpov, perhaps Carlsen) get more draws than those who prioritize winning and excel in attacking (Alexander Alekhine, GM Mikhail Tal, Kasparov, GM Veselin Topalov), and draws show much higher accuracy (or lower error rates) than decisive games in general.
In fact, strong players generally show a higher Chess.com accuracy on average for draws than they do for wins! This creates a huge bias for the cautious/endgame players if you derive ratings from accuracy scores or error rates. My solution to this major problem is simple—just exclude draws from the data! This appears to put wild and cautious players on an equal footing.
The second issue is the opponents' strength. It is easier to get a high accuracy (low error rate) against a weaker opponent than against a stronger one; the stronger opponent will pose problems that are not easy for a weaker player to solve. Players who generally play much weaker opponents will look better on accuracy than similar players who normally play equal or stronger opponents.
Full article here: https://www.chess.com/article/view/chess-accuracy-ratings-goat