May 2, 2009 — The NBA playoffs are underway, and for a Boston Celtics fan like myself, it has been an exciting first-round matchup against the Chicago Bulls. As I write this, the Bulls have pushed the defending champs to a deciding seventh game in a series that has already seen an unprecedented four of the first six games go to overtime. In Game 6, which was only decided in triple overtime, the Celtics’ Ray Allen scored 51 points, including a playoff record-tying nine hree-pointers. Despite his hot hand, the Celtics lost by a single point.
But wait a minute. Did Allen really have a “hot hand”? Was he in “the zone”?
Those nine threes were made on 18 attempts, and 50 percent shooting from beyond the arc is certainly excellent, even for an NBA star. There is no question, after the fact, that he had a stellar game. The question is, when a basketball player starts to “get hot”—that is, hit more shots than his typical hit-miss ratio would predict—should his teammates make an extra effort to feed him the ball, confident that his streak will continue? Conversely, when a player is “cold,” should he pass up shots, or even take a seat on the bench? Belief in the “hot hand” is almost universal among fans, players themselves, and even coaches. Alas, it has not stood up to statistical scrutiny. As we shall see, the fact that many people continue to believe in it anyway has some serious repercussions.
The “hot hand” superstition is certainly seductive. A simple demonstration, however, should at least give us pause. According to the online Skeptic’s Dictionary
, if you flip a coin 20 times, there is a 50 percent chance that you will get four heads in a row. Flip it 30 times and you’re likely to get a run of five or six. We do not expect there to be such streaks of heads or tails since coin flips are random, but that is the point: random events commonly do produce streaks or clusters. It would be more surprising if the heads or tails were evenly spaced, alternating regularly from one to the other. Our propensity to assign meaning to random clusters is called the clustering illusion
Of course, the fact that clusters occur in random sequences does not prove that clusters of hits or misses in basketball are random (taking into account players’ typical hit-miss ratios). For that, we must turn to statistical examination of those hits or misses themselves. The Skeptic’s Dictionary sums up the basic research that has been done, which shows that while players do have streaks of hits and misses during game play, they are no more common than would be expected by pure chance. Researchers “also analyzed free throws by the Boston Celtics over two seasons and found that when a player made his first shot, he made the second shot 75% of the time and when he missed the first shot he made the second shot 75% of the time.”
Critics, though, have charged that these kinds of studies are flawed, failing to account for the fact that “hot” shooters may attempt more difficult shots or attract more defensive attention during game play. Free throws attempts, for their part, are often spaced too far apart to capture any “in the zone” effect. A study by researchers Jonathan Koehler and Caryn Conley took these concerns seriously by examining the NBA’s Long Distance Shootout contest
. In that contest, players take five uncontested shots from each of five predetermined spots just beyond the three-point arc. They have 60 seconds to take all 25 shots.
Despite addressing the critics’ concerns, the researchers still found no evidence of hotness. For instance, “shooters made 57.3% of shots (122 of 213) following streaks of three or more hits, and 57.5% of shots (73 of 127) following streaks of three or more misses.” Intuitive though it seems, the “hot hand” is a myth. Announcers’ exclamations that certain players are “on fire” should be taken for what they really are: simple descriptions of the past, not reliable predictions of the future.
Why It Matters
We imagine that when a player is “hot” he is more likely to keep hitting his shots. As sports myths go, this one is quite plausible—much more so than superstitious playoff beards or fans who think watching or not watching will affect the outcome of a game. But plausible or not, as far as we can tell, it is still a myth.
What this myth illustrates is that we humans are very prone to seeing patterns where there is only randomness. This may be harmless for a sports fan qua sports fan, but it may have important consequences for others. It may lead coaches, for instance, to deviate from their game plans and sit their best players down when they should instead encourage them to play through streaks of misses.
More seriously, it is not easy to cordon off this irrationality and keep it from affecting other areas of our lives. Hence, when we see cancer clusters in a particular community, we search for a reason where there is none to be found, and end up blaming power lines. When we observe that a common cold gets better after visiting the alternative health shaman, we forget that common colds do tend to go away with time and rest, and we give credit where none is due. And when we notice that the dice are hot—or that the stock market is—we place bigger bets and end up losing our shirts.
The Rational Animal
Are we doomed to act irrationally, succumbing to the cluster illusion and other cognitive mistakes? Not at all. In fact, reason is our birthright. It is our means of survival and flourishing. It is what separates us from the rest of the animal kingdom. But reason is not automatic. We have free will, and we must choose to use our brains. To think or not to think is the most fundamental question we face, after the decision to live or not to live. If we are to live—if we are to survive and thrive—then we must learn to think straight. We must exercise our faculties of reason, train them to work properly and be on guard for common fallacies and foibles. And precisely because we are neither infallible nor all-knowing, we need a philosophy like Objectivism
that celebrates reason as a paramount value, and rationality as the foremost virtue to be cultivated.
Playing and watching sports can be a valuable part of life. Aside from the health benefits of actively participating, sports is a microcosm in which effort and skill and strength of character are dramatized for all to see. But we must not allow its popular misconceptions to reinforce our cognitive shortcomings. We need to educate ourselves, and our children, about randomness, and about statistics more generally. If we do, we’ll be equipped to put health scares, purported cures, and stock market trends in their proper place—and we’ll live happier, healthier lives as a result.