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went to a nail-biting seventh game, the home team came away empty-handed 62 percent of the time. Since 1983, however, the trend has shifted somewhat. Between 1983 and 1999 the home team won 54 percent of the first two games, but in series that went five games or more the home team won 62 percent of the remaining games, and 80 percent of the deciding seventh game. It is possible that in some instances overly zealous fans become fanatics (from whence the term comes) in the final stretch, driving their charges into a frenzied state of unrealistic expectations that stymies performance. But clearly there are teams that thrive on such pressure and respond accordingly.

Science has also illuminated (and in one case debunked) another aspect of the psychology of sport known technically as Zones of Optimal Function, but colloquially called peak performance, or flow. This is “runner’s high.” It is one of those fuzzy concepts athletes talk about in equally fuzzy expressions such as being “in sync,” “floating,” “letting go,” “playing in a trance,” “in the cocoon,” “in the groove,” or ‘going on autopilot.” Psychologists describe it with such adjectives as relaxed, optimistic, focused, energized, aware, absorbed, and controlled. It is a matching of skills with the challenge at hand. And it is called peak performance because, supposedly, the athlete’s performance hits a peak in this state of flow. The golf ball drops into the cup instead of skirting the edge. The bat hits the ball with that crisp crack and it always seems to fall where they ain’t. Basketballs drop one after another, swish, swish, swish. When you’re hot, you’re hot.

Maybe not. Streaks in sports can be subjected to the tests of statisticians who consider the probability of such trends in any given task. Intuitively we believe hot streaks are real, and everyone from casino operators to sports bookies counts on us to act on this belief. But in a fascinating 1985 study of “hot hands” in basketball, Thomas Gilovich, Richard Vallone, and Amos Tversky analyzed every basket shot by the Philadelphia 76ers for an entire season and discovered that the probability of a player hitting a second shot did not increase following an initial successful basket, beyond what one would expect by chance and the average shooting percentage of the player. In fact, what they found is so counterintuitive that it is jarring to the sensibilities: the number of streaks, or successful baskets in sequence, did not exceed the predictions of a statistical coin-flip model. That is, if you conduct a coin-flipping experiment and record heads or tails, you will shortly encounter streaks. How many streaks and how long? On average and in the long run, you will flip five heads or tails in a row once in every thirty-two sequences of five tosses. Since we are dealing with professional basketball players instead of coins, however, adjustments in the formula had to be made. If a player’s shooting percentage was 60 percent, for example, we would expect, by chance, that he will sink six baskets in a row once for every twenty sequences of six shots attempted. What Gilovich, Vallone, and Tversky found was that there were no shooting sequences beyond what was expected by chance. Players may feel “hot,” and when they have games that fall into the high range of chance expectations they feel “in flow,” but science shows that nothing happens beyond what probability says should happen. (The exception is Joe DiMaggio’s fifty-six-game hitting streak, a feat so many standard deviations away from the mean that, in the words of the scientists who calculated its probability, Ed Purcell and Stephen Jay Gould, it “should not have happened at all” and ranks as perhaps “the greatest achievement in modern sports.” Every once in a while individual greatness defies scientific theory.)

The Art of Sports Psychology

The fortunes and failures of sports psychology match those of the social sciences in general: we are much better at understanding behavior than we are in predicting or controlling it. It is one thing to model all the variables