- One implication of a theory I have written about before is that a best of 5 set match confers a greater advantage on the stronger player than a best of 3 set match. (The basic idea is that the 5 sets gives the stronger player more flexibility in timing his bursts of effort.) Here are some data that would shed light: compare men’s versus women’s Grand Slam matches in terms of the probability that a higher-seeded player will win. Even better: divide the data into non-Grand Slam and Grand Slam matches. Ask how much more likely a higher-seeded player wins a Grand Slam match versus a non-Grand Slam match. Do this for both women and men. Then do the difference-in-differences. This gives you a nice control because women play 3 sets whether its a Grand Slam or not. Men play 5 sets in Grand Slams and 3 sets in almost all non-Grand-Slam events.
- Four Grand Slams, only three surfaces. It’s time the US Open switched to ice. (with skates.)

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May 28, 2011 at 7:38 am

JohnVariance is a function of $n$. Small variance is better for the stronger player. Occam. QED.

May 28, 2011 at 9:15 am

jeffWell yes. (That Occam dude is such a square.) So the question is how to factor out the two reasons. I think that a 3 set match is already pretty long so that the variance factor is going to be negligible. (In practice the law of large numbers is usually the law of numbers larger than about twelve.)

May 28, 2011 at 9:43 am

JohnYou confuse me. I’ve never heard anyone state that we can do experiments with n=3:) This would be the case if a 3 set match was sufficiently long…

The law of large numbers holds when $n$ is large (you state 12) so that as long as n<12 we are still approximating. The larger $n$ is the better the approximation. Hence 5 is a much better approximation than 3 which will then mean that strong players will win more 5-sets than 3-sets.

As for teasing out multiple factors *if* they exist it is pretty easy to quantify the effect of experiment size and hence if anything remains it is fair game. The sample size (this time in terms of number of matches) is likely to be huge though.

Not being a fan of tennis I do not know if such a sample exists.

May 28, 2011 at 10:40 am

jeffA set is already the first to 7 games (with some contingencies) and a game is the first to 4 points (again with contingencies). So n is way more than 3.

Another thought coming soon.

May 28, 2011 at 5:31 pm

AnshMaybe what I’m gonna say is identical to John has said, but here goes: The probability of an upset in an NBA series is much higher if it’s a one shot game, a bit lower if it’s a five game series and a lot lower if it’s a seven game series. This is because luck plays a smaller role in a seven game series. The odds of rolling a 6 on a die is higher than the odds of rolling a 6 three times out of five or four times out of seven. This is why longer contests favor better teams or players.

May 29, 2011 at 12:34 am

More French Open Notes « Cheap Talk[…] does the additional length of a 5 set match help the stronger player? Commenters to my previous post point out the direct way: it lowers the chance of a fluke in which the weaker player wins with a […]