Bayesian logic is a type of analysis that violates old-school logic — because it incorporates conventional wisdom. For example, when a doctor examines a patient, she’s analysing not just the symptoms of that particular person. She’s also drawing on a pile of previous experience: Her interactions with other, similar patients, her knowledge of the disease in general, and the life history of that particular patient. Old-school logic doesn’t like using things like previous history because it seems muddy and subjective. But these days, everyone’s using it. Most spam filters use Bayesian logic to deduce whether your incoming mail is likely to be spam or not, based on its previous experience of observing not just your mailbox — but often the mailboxes of the world. Ultimately, Bayesian logic works so well because it seems eerily human-like.

And in fact, there’s evidence that our brains may in fact be performing Bayesian analysis. A story in today’s New York Times discusses a few economists who studied pro tennis players and how they choose which way to serve and volley. Since tennis is a very fast sport, the athletes aren’t making entirely conscious choices about what to do; their brains are doing a lot of sophisticated preconscious on-the-fly crunching. The economists found that the athlete’s brains may be doing explicitly Bayesian math:

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.