The hot-hand effect

Anyone interested in sports has heard of the hot-hand effect: players who score well are more likely to score on their next shot. On the court, most players tend to believe in the ‘mystical powers’ of the hot-hand, turning it into a self-fulfilling prophecy. A person scoring gets passed the ball more and thus has more opportunities to score, reinforcing the idea of the hot-hand effect.

Another rationale offered is that scoring boosts confidence, subconsciously improving the player’s scoring chances. Until recently, statisticians had denied the existence of the hot-hand effect, but their consensus appears to be shifting.

This belief in a ‘hot streak’ was first empirically reported in 1985 by a group of psychologists (Gilovich, Vallone, and Tversk). They found that 91% of basketball fans believed that a player had “a better chance of making a shot after having just made his last two or three shots than he [would] after having just missed his last two or three shots.” To back this, they obtained and analyzed records of every shot taken by the 1980-81 Philadelphia 76ers in their 48 home games. No statistically significant presence of score-streaks (i.e. the hot-hand effect) was observed.

On a similar vein, Albright (1993) analyzed streakiness in batting by examining 501 season records of professional baseball players through four seasons (1987–1990) and found no evidence of a hot-streak.

Recently, however, a paper by Miller & Sanjurjo shed new light on these studies. The paper reveals a subtle — but substantial — bias in previous experiments that may have skewed their results. This can be illustrated quite simply.

For instance, let’s consider flipping coins. We know that each toss is independent, i.e., the probability of obtaining a head is 0.5 irrelevant to what was obtained in the previous or next toss. However, when the same analysis is carried out on a large number of tosses, the probability of obtaining a head immediately following a head comes out to be 0.4. This illustrates that even independent events may appear anti-streaky with the bias.
The bias appears due to the fact that when we observe the toss following a head, we effectively remove the obtained head from the sample. This means that the number of heads appearing in the sample gets distorted, thus giving an anti-streaky bias.

The conclusions of the previous studies had a similar bias and therefore understated the existence of a hot-hand. Correcting for this bias has shown evidence for the existence of hot streaks. In fact, another paper by Miller & Sanjurjo authors analyzed the data in an NBA three point contest, and found evidence suggesting the existence of the hot-hand effect.

Cornell psychologist Tom Gilovich, a co-author of the 1985 paper, said the argument of the new study appears to be accurate and opens up the possibility for future research, but it remains to be seen if this overturns the hot-hand fallacy.

Miller says their results reflect both traditional and behavioral economics and suggest that professional basketball players do indeed know from experience that the hot-hand effect isn’t nonsense. Additionally, their results illustrate how faulty intuition can lead even experienced researchers astray.This discovery is shocking academics around the globe as they come to terms with its implications on the accuracy of human intuition, modeling of human behavior, subtle bias in statistics, and their consequences on sport strategy. Meanwhile, our very own student body here at Northwestern is hedging its hopes on the hot-hand effect to pull the ‘Cats to victories in not only the last of the B1G 10 games, but also in the Bowl game.

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