The hot hand fell on hard times after Tom Gilovich and pals seemed to prove, via statistics, that the appearance of hot-handed shots were “due to chance” or that the shots were really “random.” Now that makes no sense. Every shot that makes and every shot that misses is caused to do so because of some reason and that reason can’t be chance. Chance is not a thing, nor is randomness—they are not physical entities—therefore it is impossible they can cause shots to make or miss.
ESPN’s Aaron McGuire “How the hot hand rose from the ashes” quoted the central premise of the original Gilovich paper: “Each player has an ensemble of shots that vary in difficulty [depending, for example, on the distance from the basket and on defensive pressure], and each shot is randomly selected from this ensemble.”
This makes no sense. Each player, taking into consideration the swarming bodies surrounding him, causes, in the moment he takes them, the shots he takes. He does not “select” the shots from some mysterious “ensemble.” The player himself, the physics of basketballs in flight, and the actions of the other players, even the behavior of the fans (as they affect the players), cause the shot to make or miss.
Now you in the stands watching the game won’t know when the player will take his next shot, nor whether it will go in, so to you, based on the information you have, the shot is “random”, which only means unknown, which is obvious. Emphasis: the shot is not random, only your understanding whether it makes or misses.
McGuire points to a new paper by Andrew Bocskocsky and others (“The Hot Hand: A New Approach to an Old ‘Fallacy’“, pdf) which uses different statistical methods than Gilovich. According to Bocskocsky his statistics prove the hot hand is real but small.
Bocskocsky makes the same mistakes in interpretation as Gilovich, however, and talks about shots being (or not being) “independent” from one another. It is impossible that shots are causally independent. Everything that happens in a game is contingent on what happened earlier in the game. Thus earlier shots must affect latter ones. If the opposition sees a man is “on fire”, and they see that because they have seen the majority of his (difficult?) shots go on, they are likely to increase guarding him. And so forth.
We may not be able to predict to reasonably accuracy what will happen from what came before, which only means our knowledge of (some) earlier shots is irrelevant to our predictions of future ones. Saying shots are “independent” or “random” is to mix up causal language with epistemological language, confusing why shots make or miss from with the level of our uncertainty in whether future shots will make or miss. It is “future” because we already know all about the past shots.
So just what is a hot hand? How about the kind of thing Wilt Chamberlain did when he scored 100 points? Which seems to be the same kind of thing Kobe Bryant did when he once scored 81.
Perhaps, as many argue. Chamberlin’s record isn’t as impressive as it first seems, but it’s still something special. And nobody poo-poos Bryant’s. Those two observations are all the instances we need to show that a hot hand exists. These don’t prove anybody else ever had it, or ever will. But these two single statistics, or data points, prove the hot hand is a reality.
Now it is rational to suppose, given these two extreme observations, that since the hot hand certainly exists on the large scale, that it probably does on the medium or small scale. And though Yours Truly is no expert on basketball statistics, we often hear of men scoring an unusual number of points in a game. So it appears the hot hand exists at the medium scale, too.
A Twitter follower pointed me to this article some time ago, but I neglected to write down who. I apologize for that.