"Better player" vs. "one who wins"?

An interview with Kramnik about the Anand-Topalov match has had excerpts translated in English. Nothing he said is surprising or new, but I thought it would as good a time as any to revisit a serious philosophical question, which every sports fan or stock market trader grapples with regularly: in a competitive enterprise, what is the nature of the distinction between someone who is "better" and someone who "wins" often (the implication being that someone could "just" be "lucky")?

Kramnik says that Anand is the "better" player, while Topalov "still has good results even when he doesn't play well." This is a somewhat biased, provocative way of summarizing the objective reality of the records of these two fine, top-level chess players. With computer-aided analysis of chess moves that occur in a game, it is easy to note the number of moments when someone has made a move that is so "bad" that with perfect responses by the opponent, the player should lose where the game should not have been lost otherwise. For example, round 9 was an ideal example of a game in which Topalov repeatedly made errors such that if Anand had played perfectly, Topalov would have lost. This is one way of expressing what it means for someone to not play "well" but still achieve a good result (in this case, a draw). But this is a biased criterion, because one could also say that in this game, it was Anand who did not play "well", because he failed to win when he could have.

A more "objective" criterion could be, summarize the computer-scored evaluations of the positions after each player's moves, and see who has the smallest average evaluation score deviation from the computer's "best" move. By this criterion, Anand might come out the better player in this game, or might not (I have not bothered to do any such computation). But this criterion is still flawed. In many of the games in which Anand drew as Black with the Slav, his "average" deviation might still be lower than Topalov's, because of the use of the passive, defensive opening whose entire goal is to try to "safely" ensure a draw while clawing back from an inferior endgame the whole way; various opening moves would be penalized, even if after the opening phase, Anand started playing many perfect moves. To use a criterion of "deviation" blindly would be to violate the whole spirit of chess, which is that computer scores are not a reflection of some kind of Platonic reality but are a tool for driving choice of a move, a strategy; and different computer engines assign interestingly different scores to the same moves. Different openings result in a different rhythm of how Black deals with White's initial "advantage". Since chess is undoubtedly a draw with best play anyway, the numbers are only a reflection of how well one can see the rest of the game at a given point. Changing the computer's evaluation depth and time limit results in different numbers.

In the end, chess is a sport, a "struggle", as David Bronstein put it. To speak of someone being a "better" player outside the context of proved competitive results again and again does not make sense. Kramnik knows this, of course, so what he is really saying is simply that he prefers to play in a particular way, minimizing the risk of forced loss (against any competitor, including a computer), while Topalov is willing to achieve good results by whatever means necessary, including being more physically and emotionally resilient, playing "bad" moves in order to confuse his human component and hope to swindle a draw or win, avoiding getting into time trouble. This is all part of the struggle.

All of us who play chess know this. I cannot count how many games I have won even though I "should" not have, simply because I stubbornly played on in a lost position and swindled a win. I also cannot count how many games I have lost even though I was winning the whole way and then made errors. Kramnik is basically implying that somehow there should be a notion of "justice" in the chess universe, such that there should be a limit to how much one gets "lucky", and somehow players like Topalov get "lucky" more than they should. I think he is in error in implying that there has to be this notion of justice. Was it fair that the dinosaurs went extinct on the earth while tiny little mammals survived what is thought to have been an asteroid collision? The question does not objectively make that much sense.

My final comment is that I personally prefer the Kramnik or Anand style of chess play to Topalov's. I did not always have this preference, but I grew into it. My best argument for my preference is simply that years ago, when I began appreciating it and adopting it in my own play (toning down the speculative attacks), I not only improved my results but also improved my enjoyment and "understanding" of chess.

There are two more rounds to go for Anand-Topalov. I hope Anand accepts the Nimzo-Indian challenge again as White.