Are athletes Bayesians?

Mark A. Walker and John C. Wooders, economists at the University of Arizona, recently studied old videotapes of tennis matches involving stars like Bjorn Borg, Ivan Lendl and Pete Sampras. The economists looked at the serves in each match to see how well players randomly altered playing the ball to an opponent's forehand or backhand.

Many people do poorly on similar tests when they are conducted in a laboratory. Ask somebody to write down a list of hypothetical coin-flip outcomes, for example, and the result will probably contain too few streaks of heads or tails. Because people know that the overall odds are 50-50, they underestimate how often three straight tails or four straight heads turn up.

But professional tennis players realize, on some level, that their opponent will have an advantage if he knows that a serve to the forehand is likely to be followed by one to the backhand. They do a relatively good job of mixing serves, though still not as randomly as a computer program would, Professors Walker and Wooders reported in a 2001 paper.

Controlled experiments yield similar results, read this account from The New York Times.

Here is the bottom line:

The more uncertainty that people face — be it caused by wind on a tennis court, snow on a football field or darkness on a country highway — the more they make decisions based on their subconscious memory and the less they depend on what they see.

Related research by Doru Cojoc of Clemson shows that chess players play mixed strategies to keep their opponents off balance. Furthermore they are more likely to play such sophisticated strategies, the higher the rewards on the line.

By the way, even plants seem to perform implicit calculations when they breathe, read this recent account. Armen Alchian, of course, once postulated a similar conjecture, namely that plants maximize sunlight without any conscious awareness of such a process.