Baseball and Luck in Competition

22:30 Thu 26 Aug 2010
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Aptly-named Yankees blog It’s About the Money has an excellent post up about luck and competitive balance in the baseball post-season. One of its key points concerns how likely a given team is to win a particular series, and how that translates into their odds of winning the whole thing.

Using methodology I won’t go into here, they use the 2009 Yankees (who did win it all) as an example and give them winning chances of about 70% against the Twins, 60% against the Angels, and 65% against the Phillies. The Yankees were thus favored in every series… but by multiplying those chances against each other, you come up with about 27%, which was their chance of winning everything in the post-season. Thus even the mighty Yankees, with baseball’s best record, had to get “lucky” to win the World Series.

In other words, there’s a lot of luck in a baseball series—otherwise the likelihood of the Yankees beating one of those other teams would have been higher.

If there were less luck in a baseball series, there would be a lot less variation in who’s won titles, as the better team would win more often—and the postseason would also be significantly more predictable. The article compares baseball to basketball in this regard, as basketball is significantly more predictable and also has a smaller pool of teams that have won championships.

I’d be interested in seeing a comparison of sports that have both regular seasons and post-season championships, to compare the differential between winning percentages in the regular season and elimination rounds. Such a comparison could be used to determine the amount of luck (for want of a better term) in the sport. One problem with this is that some setups may allow teams to “coast” in the regular season; it’s often claimed that the NBA has this problem, as shown by the performance of the Boston Celtics last year.

I’m also curious about how this applies to tennis. Tennis doesn’t have a lot of luck in it, and is structured very well to increase the chances of the better player winning. Applying the same math as above, the individual match winning likelihoods for Federer and Nadal during the last several years must really be outrageously high. To win a Grand Slam, a player has to beat seven opponents; if they have a 90% chance against each opponent, their chance of winning the tournament is still only around 48%. A 91% chance of winning each match brings them over the 50% mark, just. Clearly it’s a lot more complicated than that, and the model needs to account for much higher chances of winning (usually) in the early rounds and then lower chances later.

Another area I’m interested in is whether repeat champions in high-variance competition are merely getting lucky, or are so good that they can transcend the luck—and if there’s any way to figure that out.

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