Knockout Champions

While working on my post titled Calculating Collusion, a critique of Did the Soviets Collude? A Statistical Analysis of Championship Chess 1940-64 by Moul and Nye, a subject unrelated to collusion caught my attention.

More recently, Ryvkin (2005) has focused attention on the problem of how tournament design not only motivates effort but can also be structured to reveal the relative strengths of various players. In this light, the purpose of good tournament design is to maximize the probability that the result of the tournament will produce outcomes that conform to the "true," unobserved relative strengths of the participants. Many discussions of tournament structure have instead focused on "competitiveness." The latter goal actually values a large number of upsets or unlikely results -- such as seem likely to emerge from multi-round knockout tournaments which are common in tennis or collegiate sports.

In contrast, the chess community seems to put a very high value on competitions that accurately "reveal" the true strengths of players. Judging by the history of the world championship and its biases in favor of the incumbent world champion, there seems to be a revealed preference for a system that anoints the strongest player as World Champion. Periods when the official world champion was clearly not the strongest player -- as occurred when Garry Kasparov split from FIDE in the 1990s and created a parallel system for the championship -- have seen a loss of legitimacy for the systems that produced champions not widely viewed as the dominant players.

[Reference: Ryvkin, Dmitry (2005). "Tournaments: A Review." Unpublished working paper.]

The observation that, among chess players (is this unique to chess?), 'there seems to be a revealed preference for a system that anoints the strongest player as World Champion' is certainly true. The 'loss of legitimacy for the systems that produced champions not widely viewed as the dominant players' refers, of course, to the FIDE knockout tournaments, won successively by Khalifman (1999), Anand (2000), Ponomariov (2001), and Kasimdzhanov (2004). Excluding perhaps the event won by Anand, all of these knockout tournaments were criticized for producing a less-than-worthy World Champion.

As for the knockout event that produced a challenger -- Anand (1997) -- or the events that qualified players to the next stage of the championship -- Aronian (2005), Kamsky (2007), and Gelfand (2009) -- there was no criticism whatsoever. The chess world accepts the knockout format for identifying a challenger, but not for choosing a champion. Why should this be?