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The researchers found that when no cursor flashed, people relied
on what they had learned during 1,000 practice runs before the
experiment: namely that the cursor was, on average, one centimeter
to the right of the hand. When a cloud flashed, they considered it,
but only somewhat, in a pattern that followed what Bayes's formula
predicted. When a distinct cursor flashed, they relied on it and not
past experience.
"Most decisions in our lives are done in the presence of
uncertainty," Dr. Körding said. "In all these cases, the prior
knowledge we have can be very helpful. If the brain works in the
Bayesian way, it would optimally use the prior knowledge."
The researchers drew the analogy to tennis in their paper, and it
is not the first study to suggest that athletes have a more
sophisticated understanding of mathematics than even they may
realize.
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.
Some researchers remain skeptical that the human mind works like
the coldly rational Bayesian machine suggested by the Nature paper.
Consider the self-destructive mistakes drivers make in their
behavior, from turning a steering wheel the wrong way on a patch of
ice to buying sport-utility vehicles that are less safe than their
owners believe.
"I'm quite comfortable with the idea that people use
probability," said Dr. Stigler, the Chicago statistician. "The idea
that it's associated with a Bayesian approach is not quite
clear."
The most likely explanation may be that some people are quite
good at subconsciously using statistical techniques and others are
far less so. As the Super Bowl and Australian Open play out over the
next two weeks, the athletes holding trophies at the end might be
the Bayesians.
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