William M. Briggs

Statistician to the Stars!

The Hot Hand: Statistical Fluke Or Genuine Article?

My hand does not appear aflame.

My hand does not appear aflame.

I’ll save you hunting through the text. It’s a real thing. If you want to know why, read on. If not, you just tell ’em W.M. Briggs sez so, which is enough to stop any argument (though perhaps not in your favor).

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.

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A Twitter follower pointed me to this article some time ago, but I neglected to write down who. I apologize for that.

7 Comments

  1. The hot streak doesn’t really relate to Chamberlin or Kobe’s high scoring games. The “hot streak” is a specific, very short duration phenomenon that some times takes place in a game.

    Example: Player A scores a beautiful (and this is important) shot from, say, the three point line. The next time he comes down the court, he scores again! The crowd – and the player – begin to think “are we seeing the start of a hot streak”!? The next time down the court, the player takes a quick and somewhat rash shot and misses, but the crowd discounts this because he may be on a hot streak! The next time he comes down he immediately shoots to see if the hot streak is real – and he scores, so that last miss must have been a fluke.

    This will go on for about three or four minutes over the course of 6 to 9 shots and is usually interrupted by a time out or stoppage in play. At the end of the “hot streak” it might turn out that, for a brief period of the game, the player made 60% to 80% of his shots (meaning may have missed made 3 of 8). However, the crowd takes away from the experience “wow, we just saw a hot streak” while discounting the fact that he was missing shots and that some of his shots were rash and it would have made more sense for him to pass the ball to an open player – especially since he started to be double teamed. The TEAM could have just as easily scored as many or more points in the same time frame, but it became all about the hot streak.

    On the flip side, and what the original research tried to address (and prevent) was the OPPOSITE effect where a player, egged on by the crowd thinks he’s on a hot streak when in fact he’s only shooting around 30% to 40% but the perception is that he’s making more shots that he is.

    It’s this second case that the research really tried to address and which is more common than the first, where, in fact, he was shooting at a higher (though not unprecedented) percentage for a brief period of time.

  2. Briggs

    April 14, 2014 at 10:29 am

    Jim S,

    Sounds like you’re invoking the No True Hot Hand fallacy by rejecting Bryant’s effort.

  3. The point I was trying to get across is that Bryant’s game-long performance is not what the studies were analyzing. The studies were analyzing brief scoring runs that only last a couple of minutes and only scores a few points relative to the final score.

  4. As a basketball player myself (albeit 30 years ago…) it always seemed crazy to me that the hot hand was discounted based on the assumptions stated. The subjective experience is what has been called ‘being in the zone’, a sensation of control and slowed-down time – everything seems clearer and slower. I suspect anyone who has played any sport long enough has had this experience. What happens is that you are able to better anticipate and execute – it’s a (slightly) altered mental state.

    Mechanically, being hot could merely mean having a lucky streak of made shots – sure, and anyone who has played much has seen those occasions. But it could also mean a period of improved physical and mental *execution*. That’s certainly what it feels like subjectively – “man, I was really feeling today.” In such a state of heightened execution, one would expect to make more shots than usual.

    The focus on the feedback loop – I just made a difficult shot, so I am more likely to take another difficult shot – neglects the existence of coaches, teammates and fans, and most importantly, of years and years of disciplined practice. While there are players who seem unaffected by these things – guys who will just keep shooting harder and harder shots – the more typical example of the hot hand among professionals would be a highly disciplined shooter – a Ray Allen or Jerry West – who could, effectively, get a good shot pretty much any time they wanted. They, when blazing hot, just take the same shots they normally take. The difference is that their *teammates*, not being stupid and wanting to win, keep feeding them the ball. Other times, players who are not ‘feeling it’ will, for that reason, pass up shots they might otherwise take. So, as you say, there’s nothing random about it – except for the few highly talented/highly undisciplined players good enough not to get benched immediately for dumb shot selection, any player’s next shot is the result of a confluence of planning, training, coaching and reacting to a constantly changing situation. Whether or not it goes in is due almost entirely (apart from blocked or otherwise altered shots) a result of a highly developed set of physical actions being properly executed.

  5. PAPER: “The Hot Hand: A New Approach to an Old ‘Fallacy’“

    When the research report is emblazoned with advertising (on every page…and from Ticketmaster in this case) you just know it has to be good…

  6. Listen, I play basketball a couple of times per week. The hot hand exists! We make use of it during games. If a player makes 2 or 3 shots in a row, his teammates will work to give him the open shot. It’s true that while one’s shooting percentage doesn’t vary much streaks are real and it’s stupid to not take advantage of them. It’s well understood by the folks I play with and apparently by commenter Joseph Moore. The more athletic, the more practiced that you are, the more likely you will have these streaks.

  7. Joseph Moore,
    regarding the zone… I don’t play basket ball. But I have had the sensation hitting a baseball that the ball looks really big. And they say that you cannot see the moment the ball makes contact with the bat, but I swear I saw the two make contact very clearly. Now, as I think about this “heightened perception,” did I really see everything more clearly, or did my brain hold onto a “richer memory”, and as I think back, I can see more detail.

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