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the hot-hand fallacy

Of all the things that people are terribly wrong about, sports may reign supreme. Perhaps because most have played a sport (at a terribly uncompetitive level), or because of the ubiquitous media commentary by fat, uneducated former players, the average American is thoroughly convinced he understands how their game of choice works, why a team is losing, why a player is struggling, etc. What’s more, the fan’s understanding will sound a lot like an ancient mystic reading tea leaves.  “Of course the Lakers won the NBA championship, did you see the look on Kobe’s face in the finals? He’s not smiling and has a meaner look than last year.” (While a made-up quote, that was indeed a real topic of discussion for those who missed it.)

Coaches choose whom to sit and start based on who’s “hot” and “cold,” and analysts explain every statistical hiccup in performance as the result of some minute, superficial change. Great players with 50 poor at-bats in the playoffs are deemed bad “clutch” performers, etc., etc.

Thankfully, little hangs on the common man’s understanding of sports, yet it does reinforce the practice of creating false non-random narratives to understand random patterns, effectively teaching young sports fans to understand the world in a wrong and unhelpful way. Leonard Mlodinow addresses one of my favorite misconceptions in The Drunkard’s Walk: How Randomness Rules Our Lives (which, on the contrary, provides a useful primer on understanding random and non-random patterns):

Interest in the hot-hand fallacy began around 1985, in particular with a paper by Tversky and his co-workers that was published in the journal Cognitive Psychology. In that paper, “The Hot Hand in Basketball: On the Misperception of Random Sequences,” Tversky and his colleagues investigated reams of basketball statistics. The players’ talent varied, of course. Some made half their shots, some more, some less. Each player also had occasional hot and cold streaks.

The paper’s authors asked the question, how do the number and length of the streaks compare with what you would observe if the result of each shot were determined by a random process? That is, how would things have turned out if rather than shooting baskets, the players had tossed coins weighted to reflect their observed shooting percentages?

The researchers found that despite the streaks, the floor shots of the Philadelphia 76ers, the free throws of the Boston Celtics, and the experimentally controlled floor shots of the Cornell University men’s and women’s varsity basketball teams exhibited no evidence of nonrandom behavior. In particular, one direct indicator of “streakiness” is the conditional probability of success (that is, making a basket) if on the prior attempt the player had achieved success. For a streaky player, the chance of a success on the heels of a prior success should be higher than his or her overall chance of success. But the authors found that for each player a success following a success was just as likely as a success following a failure (that is, a missed basket).

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Filed under: Cognition,

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