The Hot Hand Fallacy II

I thought it might be useful to create in a simple, model situation in which hot hands do indeed exist but which yields results totally consist with the finding of Tversky, Gilovich, and Vallone on the phenomenon.

Let us assume there is a player, Smith, who has genuine hot streaks when she is "in the zone."* She is ordinarily a 50% shooter, but during those times, she shoots 70%. However, how long she will stay in the zone is random, and on every new shot she has a 50% chance of "losing" the hot hand. At the moment she loses the flow, since she loses through some sort of disruption in her concentration,** she only has a 30% chance of making her next shot.

It should be obvious that even when Smith genuinely has a hot hand at time x, for any shot at x + 1 there is a 50% chance the shot will go in, which is exactly her normal shooting average. Applying the method and the criterion of Tversky et al. to Smith would yield their conclusion, "the hot hand is an illusion." But we have deliberately set up a model situation in which the hot hand is real, and their criterion has mistakenly concluded it is not real. QED, they used a flawed criterion for deciding if the hot hand is real.

Two notes: I am dealing in this and in the previous post with the main criterion that I have seen written up for how Tversky et al. reached their conclusion. As I recall from my reading of the original paper this was their key argument against the hot hand; it is certainly how everyone else describes their argument. If, in fact, they have another argument against the existence of the hot hand, that argument is untouched by what I write here! If this were an academic paper, I would certainly be checking up on this further before submitting it; but it is not, it is a blog post, which for me means it is my writer's notebook entry.

Secondly, the above is certainly not, and certainly not offered as, a proof that the hot hand does exist! What I am contending is that Tversky et al. certainly did not show that it is a "fallacy." (Why in the world are people using the term "fallacy" for an empirical proposition? We don't speak of the phlogiston "fallacy" or the Ptolemaic "fallacy"!)

* Amazingly, Kahneman acknowledges this phenomenon as real and well-established in psychology in areas other than basketball (see page 40-41 in Thinking, Fast and Slow): apparently he thinks it is only basketball players who can't get into the "flow."

** This disruption, of course, is no part of the formal model, but a way of showing that this choice of percentage is not prima facie absurd.


  1. Steve Landsburg writes in: "I am nearly sure --- though without checking the literature to be sure --- that "hot hand" is taken to *mean* that your recent performance is a useful predictor of what will happen on your next attempt. In your model, you've got a 50% chance of making your next attempt regardless of whether or not you are "in the zone". Therefore, I think, being in the zone (in your sense) does not constitute having a hot hand (in the usual sense).

    Well, yes... if we take hot hand to mean that, then of course Tversky et al. have proved their point. But... Kahneman and many others certainly seem to think they have proved that "hot streaks" simply don't exist, and are simply a clustering error. If their conclusion had been "the hot hand is not predictive," their paper would have been far less famous, and we wouldn't hear things like "When a player thinks he is hot, that is simply a statistical illusion." There is equivocation between the purely predictive interpretation and the broader conclusion. And that is my point!

  2. I think you err here Gene, as discussed in my email. But in 1940 Stravinsky was really on a roll. Just after the Symphony in C he wrote ...

    1. Ken, OK, I don't understand how you think I am wrong here, since to me, what you wrote in your email is the very point I am trying to make! So *that* can't be my error! Perhaps you can clarify here.

  3. My point in the email is that the chances of the next shot are the same regardless of what condition I was in before the shot. Which is Landsburg's point too. The 'hot hand' is a period diagnosable solely from recent performance where a higher than customary success rate can be predicted. Your model doesn't do that. The predicted success rate is the same whether I am in .7 state or .3 state internally. The pst success are not predictive in your model.

    I'm not denying there could be an internal hidden variable. I put my glasses on, or not with 50% frequency. No-one can tell, and I follow no pattern, just coin tosses. But that's not what the 'hot hand' is. The hot hand is a claim about the likelihood of a basket considering the last few shots.

    1. "My point in the email is that the chances of the next shot are the same regardless of what condition I was in before the shot."

      Yes. The model was *deliberately* designed to yield that result.

      "The hot hand is a claim about the likelihood of a basket considering the last few shots."

      No, that is just plain wrong. I watch sports all the time, play them sometimes, have played music. The "hot hand" is TWO separable claims:

      1) Players (musicians, etc.) enter certain states where they are "in the flow" and perform better than they usually do.

      2) When someone has the hot hand, it is a good idea to feed them the ball.

      Tversky et al. proved that 2 is wrong (to my satisfaction): the hot hand is not predictive. But they then used that disproof of 2 to claim that 1 is just an illusion.

      But disproving 2 does not justify that further conclusion.

    2. I'm saying the same thing Landsburg did though Gene.
      (Maybe we should write him and ask!)

      As for flow, yes I think I agree there are such cases. My bridge example. But that is what makes up my customary success rate amd pattern. If you could detect my flow state independently -- you see me put on my glasses with a strap to hold them on and hear me mutter, 'enough with the coin toss' -- then bet on me. That would be a good bet. But you can't get that reliably from just the recent past success rate alone. Which is the hot hand claim.

  4. I used to play duplicate Bridge very seriously. And there were days when I was definitely in the flow, with enormous concentration. On those days I learned to press, confident that I would find the small hints and chances better than other players with my cards, better than I would on average days. Now that's not quite the basketball hot hand, as I am basing my actions on more than my success rate, but also on observation and introspection.

    1. "Now that's not quite the basketball hot hand, as I am basing my actions on more than my success rate, but also on observation and introspection"

      But so are basketball players who claim to be "in the zone"!


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