Subconsciously, Athletes May Play Like Statisticians

January 20, 2004
 By DAVID LEONHARDT 


When Justine Henin-Hardenne rips a cross-court forehand at
the Australian Open or Tom Brady, the New England Patriots
quarterback, dodges an onrushing defender, each looks like
the very definition of living in the moment. Like other
great athletes, they often appear to rely on speed,
strength and lightning-fast reactions. 

There seems to be little time for highly advanced
quantitative analysis that weighs current observations
against past experiences to suggest a plan of attack. 

But this kind of analysis is precisely what the human brain
does when facing a physical challenge, according to a study
by two European scientists published in the current issue
of Nature. 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. 

Among researchers, the combining of new information with
conventional wisdom is known as Bayesian analysis, and it
has become increasingly popular in recent years. Once
controversial, because it muddies supposedly pure
scientific data with subjective opinion about which prior
research is relevant to a particular study, it has gained
adherents as the explosion of computing power has allowed
the method's complex formulas to be performed on a basic
laptop computer. 

With the encouragement of the Food and Drug Administration,
medical-device makers use the method to test new devices
that are only slightly different from their predecessors.
Computer companies use Bayesian methods to build spam
filters for e-mail, said Dr. Michael Lynch, the chief
executive of Autonomy, a British software company, and
governments use it to try to prevent terrorism, combining
data from security cameras and X-ray machines with criminal
profiles. 

"In academia, the Bayesian revolution is on the verge of
becoming the majority viewpoint, which would have been
unthinkable 10 years ago," said Bradley P. Carlin, a
professor of public health at the University of Minnesota
and a Bayesian specialist. 

Stephen M. Stigler, a professor of statistics at the
University of Chicago who considers himself to be roughly
in the middle of the spectrum in the Bayesian debate,
added: "It's not a controversial subject. Twenty years ago,
it was." 

In everyday life, of course, people have been using the
ideas underlying Bayesian analysis since well before it
became the vogue in science labs, or even before Thomas
Bayes, an 18th-century British minister and mathematician,
formalized the method in a paper that was published two
years after he died. When crossing a street, people rely on
both what they see and what they remember about the speed
of cars on similar roads. When deciding whether to take a
sick child to a doctor, parents consider the current
symptoms as well as the child's history and their general
knowledge of illness. 

"The human brain knows about Bayes's rule," said Konrad P.
Körding, a postdoctoral researcher at the Institute of
Neurology in London, who conducted the study published in
Nature along with Daniel M. Wolpert, a professor at the
institute. 

The new research stands out because it offers a detailed
window into how the Bayesian thought process works, showing
the point when uncertainty becomes great enough to give
past experience an edge over current observation. 

Each participant in the experiment sat down and placed a
hand on a tabletop. A projection of a computer screen
blocked their view of the hand. The goal was to guide a
cursor, which followed the movement of the hand, from one
side of the screen to a target on the other side. 

Adding to the uncertainty, the cursor usually appeared
slightly to the right of the hand, and the participants
caught at most a quick glimpse of it when it was halfway
across the screen. Sometimes, the cursor appeared as a
discrete point; other times, it was an ill-defined cloud. 

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. 

http://www.nytimes.com/2004/01/20/health/20TENN.html?ex=1075792047&ei=1&en=328b2646c7112a38