2. The Hot Hand
Do athletes ever have a “hot hand”? Sometimes it seemed that the Boston
Celtics’ Larry Bird could never miss a basket, or the New York Rangers’ Wayne Gretzky or Argentina’s Diego Maradona a shot on goal. Sporting
commentators see these long streaks of consecutive successes and proclaim
that the athlete has a “hot hand.” Yet according to psychology professors
Thomas Gilovich, Robert Vallone, and the late Amos Tversky, this is a
misperception of reality. They point out that if you flip a coin long enough,
you will find some very long series of consecutive heads. The psychologists
suspect that sporting commentators, short on insightful things to say, are just
finding patterns in what amounts to a long series of coin tosses over a long
playing season. They propose a more rigorous test. In basketball, they look
at all the instances of a player’s baskets, and observe the percentage of times
that player’s next shot is also a basket. A similar calculation is made for the
shots immediately following misses. If a basket is more likely to follow a
basket than to follow a miss, then there really is something to the theory of
the hot hand.
They conducted this test on the Philadelphia 76ers basketball team.
The results contradicted the “hot hand” view. When a player made his last
shot, he was less likely to make his next; when he missed his previous
attempt, he was more likely to make his next. This was true even for Andrew
Toney, a player with the reputation for being a streak shooter. Does this
mean we should be talking of the “strobe hand,” like the strobe light that
alternates between on and off?
Game theory suggests a different interpretation. While the statistical
evidence denies the presence of streak shooting, it does not refute the
possibility that a “hot” player might warm up the game in some other way.
The difference between streak shooting and a hot hand arises because of the
interaction between the offensive and the defensive strategies. Suppose
Andrew Toney does have a truly hot hand. Surely, the other side would start
to crowd him. This could easily lower his shooting percentage.
That is not all. When the defence focuses on Toney, one of his
teammates is left unguarded and is more likely to shoot successfully. In other
words, Toney’s hot hand leads to an improvement in the 76ers’ team
performance, although there may be a deterioration in Toney’s individual
performance. Thus, we might test for hot hands by looking for streaks in
team success.
Similar phenomena are observed in many other team sports. A
brilliant running-back on a gridiron team improves its passing game and a
great pass-receiver helps the running game, as the opposition is forced to
allocate more of its defensive resources to guard the stars. In the 1986 soccer
World Cup final, the Argentine star Diego Maradona did not score a goal, but
his passes through a ring of West German defenders led to two Argentine
goals. The value of a star cannot be assessed by looking only at his scoring
performance; his contribution to his teammates’ performance is crucial, and
assist statistics help measure this contribution. In ice hockey, assists and
goals are given equal weight for ranking individual performance.
A player may even assist himself when one hot hand warms up the
other. The Boston Celtics’ star, Larry Bird, preferred shooting with his right
hand (though his left hand was still better than most). The defence knew
that Bird was right-handed, so they concentrated on defending against right-
handed shots. But they did not do so exclusively, since Bird’s left-handed
shots were too effective to be left unguarded.
What happens when Bird spends his off season working to improve his
left-handed shooting? The defence responds by spending more time covering
his left-handed shots. The result is that this frees his right hand more often.
A better left-handed shot results in a more effective right-handed shot. In
this case not only does the left hand know what the right hand is doing, it’s
helping it out.
It is also true that when the left hand is stronger it may even be used
less often. Many of you will have experienced this seemingly strange
phenomenon when playing tennis. If your backhand is much weaker than
your forehand, your opponents will learn to play to your backhand.
Eventually, as a result of all this backhand practice, your backhand will
improve. As your two strokes become more equal, opponents can no longer
exploit your weak backhand. You will play more evenly between forehands
and backhands. You get to use your better forehand more often; this could be
the real advantage of improving your backhand.