## Sunday, January 06, 2008

### Some evidence of streakiness in tennis

There is some evidence of streakiness in tennis, according to a study linked to in a post by Alan Reisman, of "Volleymetrics" and "The Hot Hand."

Reisman started by trying to figure out if momentum means anything heading into the fifth game of a best-of-five series in volleyball. He found that it probably didn't. When team A won the first two games, and team B won the second two games, the team with momentum – B – won the fifth game less than half the time. When the first four games went ABBA, the team with the little bit of momentum – this time, A – did win 15 out of 23. But that wasn't statistically significant. Reisman's full results:

AABB: B won 15 out of 34
ABAB: B won 16 out of 33
ABBA: A won 15 out of 23

Total: the team with momentum won 46 out of 90, almost exactly what you'd expect by chance. (Interestingly, a commenter notes that in all three cases, the team that won game 1 actually wins the majority of game 5s.)

However, in tennis, the player with momentum won substantially more than half the fifth sets:

AABB: B won 188 out of 339 (p = .025)
ABBA: A won 186 out of 324 (p = .004)
ABAB: B won 156 out of 291 (p = .120)

One explanation for these results is that it's not really momentum that matters, but the conditions of the two players. If a player gets tired over the course of the match, that should affect the fourth and fifth sets more than the others, so the fourth set is predictive of what will happen in the fifth set. Or, if one player finally figures out a strategy for beating the other, again, that will affect the fourth and fifth sets more than the others.

These may not be as true for volleyball, because the various players on the team would tire at different rates, so the effect would be smaller. As well, a strategy that works against one player would not be as useful when there are six on the court.

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