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,aplayer 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.