Monday, February 12, 2007

The Novotna Rule

Steven Landsberg has this interesting, university-president career-destroying piece about how, in tennis women choke under pressure more often than men:

You can observe a lot of high achievers under pressure at a Grand Slam tennis tournament. Better yet, you can observe them under variable pressure: Things are a lot tenser when the score is 5-5 than when it's 0-0. Professor Daniele Paserman of Hebrew University made good use of this variability at the 2006 French Open, U.S. Open, and Wimbledon tournaments. First, he assigned an "importance" to each point in each match. He did this by assigning probabilities to every way the match might unfold, accounting for players' ratings, the surface they were playing on, and the identity of the server. That allowed him to say things like, "If Roger Federer wins this point, he has a 60 percent chance to win the match; if he loses the point, he has a 55 percent chance." The 5 percent difference measures the point's importance.

It turns out that by at least one measure—the number of unforced errors—men play equally well throughout the match. They make unforced errors on about 30 percent of the most important points, about 30 percent of the least important, and about 30 percent of all those in between. But women show a very different pattern: 34 percent unforced errors on the least important points, steadily rising to almost 40 percent on the most important. That's almost surely too big a difference to be mere coincidence.

What, besides choking, could explain those numbers? Maybe the closest games are usually played late in the match, when players are more fatigued; maybe more of those games involve weak players; maybe more of them occur at the French Open, where the court is harder to play. But professor Paserman tests all these theories, and none stands up to statistical analysis.

Another countertheory: Maybe women play more defensively when the score is tight. If both players just keep lobbing the ball back and forth, there can't be any forced errors, so all errors are recorded as unforced. In support of this theory, professor Paserman observes that women do play more defensively when the score is tight. (He measures defensive play by speed of serve, length of rallies, and so forth.) But, unfortunately for the countertheory, so do men. When the pressure's on, both men and women get more defensive (and by about the same amount)—but only women make more errors.

Get Larry Summers on line one!

1 comment:

Anonymous said...

I'm not a women's tennis watcher or a statistician, but isn't there something to be said for a larger sample size?

Moreover, all these matches have the Williamses in them, right? As far as I know, they don't really have a reputation for mental toughness.