Friday, November 8, 2013

Luck and the World Chess Championship

"I don't believe in luck. I make it, and I take it, but I don't stand around waiting for it to happen."--Vinnie Terranova, "Wiseguy"

Like fictional Organized Crime Bureau undercover agent Vinnie Terranova, I do not believe in luck--particularly in arenas where skill can and should prevail. Matthew Wilson's three part series for titled Are the chess World Champions just lucky? examines the margins of victory of various World Championship matches and attempts to ascertain whether the championship winners displayed statistically significant dominance or if the winners were "lucky" (meaning that there is at least a reasonable probability that the objectively weaker player won the match).

Max Euwe's 15.5-14.5 victory over Alexander Alekhine in the 1935 World Chess Championship does not look decisive either to a casual chess fan or to a statistically-minded observer, particularly considering that Alekhine prevailed 15.5-9.5 in the 1937 rematch. Wilson reaffirms the widely held view that "it is unlikely that Euwe is his equal."

Wilson concludes that Bobby Fischer's 12.5-8.5 victory over Boris Spassky in the 1972 World Chess Championship is statistically significant; based on the players' pre-match ratings, Wilson calculates that there was only an 8.3% chance for Fischer to win so decisively (Wilson actually used 12.5-7.5 in his analysis, disregarding the unplayed game that Fischer forfeited). In marked contrast, the official FIDE World Championship titles won in knockout-style tournaments by Alexander Khalifman, Ruslan Ponomariov and Rustam Kasimdzhanov in the late 1990s and early 2000s "were denounced as being little more than lotteries and FIDE overhauled the championship cycle." The big difference is that the short knockout-style matches introduced tremendous randomness into the results; the best player will almost certainly win a lengthy match but a weaker player has a puncher's chance in a short match with fast time controls, much like a recreational basketball player is highly unlikely to beat LeBron James in a one on one game played to 21 points but the amateur could prevail in a game played under the condition that the first made basket wins.

What about the epic Garry Kasparov-Anatoly Karpov duels from the 1980s and 1990s? Kasparov only enjoys a slight overall edge in terms of the aggregate score but Wilson looks at the matchup from a different statistical perspective: "Starting from 1985, what is the probability of winning 3.5 matches out of four against Karpov?" Wilson says that this probability is less than 20%, a number that "is still not statistically significant. But if we combine this information with Kasparov's numerous tournament victories and his long reign as the #1 rated player (there are only two rating lists from 1985-2004 that do not have him at the top), then it is easy to persuade yourself that Kasparov truly was the best player in the world at his time."

The next World Chess Championship match begins on Saturday, with World Champion Viswanathan Anand defending his title against Magnus Carlsen, who sports the highest rating in chess history.
Carlsen outrates Anand by more than 80 points. Wilson ran thousands of simulations under various conditions but no matter how the numbers are tweaked Carlsen emerges as a huge favorite; even if generous statistical assumptions are made on Anand's behalf, Carlsen wins more than 77% of the simulations. The probability that Carlsen triumphs by a statistically significant margin--defined by Wilson as 7-3 or greater--is much larger than the probability that Anand prevails at all. Of course, rating differences and statistical simulations do not take into account match experience and other psychological factors that can be very important in any high level competition.

The Anand-Carlsen match is scheduled for 12 standard length games and if the match ends in a 6-6 tie then the championship will be decided by the outcome of successively faster tiebreak matches, starting with four rapid games. Is this the ideal format to prove who is the world's best chess player? Wilson suggests that the length of World Chess Championship matches should be determined by what he calls "The 50 Point Principle," namely "If one player's strength is 50 rating points above his opponent's, then the match has to be designed so that the better player wins 90% of the time...The shortest way to satisfy the 50 point principle is a 26 game match with a two game tiebreaker if the match is drawn 13-13. Fortunately, the traditional 24 game matches were very close to respecting the 50 point principle...So to answer the question asked in the beginning, most of the world champions are not just lucky, since the better player will prevail in a large majority of the standard 24 game matches."

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