The Hot Hand Fallacy

The_Hot_Hand_Fallacy_LargeThe Hot Hand Fallacy is the assumption that wins or losses in games of chance exist in streaks.

While gambling, some people will feel they are having an ‘cold night’ or that ‘someone is really on tonight’, assuming luck exists as an etherial vein you can tap into as opposed to a series of independent events.

Humans are excellent at seeing patterns in what is really just noise. This is known as the ‘clustering illusion.’ Randomness is clumpy er clustery.

In basketball it is a common belief that when a player makes a basket, they will be more likely to make another basket, and another and another. This is untrue. Each basket a player makes is a statistically distinct event and thus has no effect on future baskets. Sports = arbitrary :)

This fallacy is the cousin of the ‘Gambler’s Fallacy’ which also preys on peoples misunderstanding of statistical independence.


7 thoughts on “The Hot Hand Fallacy

  1. I love this site, so thanks for making it! I do have a comment about your description of this fallacy. There may be good reasons why the clumpiness of repetitive human endeavors is causally streaky. Your example of the basketball player is a prime example. Since the psychology of the player affects his\her performance, and his\her psychology is affected by past performance, a given clump can be extended by the interaction of the clump, as an historical “trend”, with the player’s psychology. E.g., a few bad performances in a row can cause the player to second guess their abilities\mechanics\choices\etc., which disrupts the patterns they have built up, throwing off their game even more. So, each basket is not a statistically distinct event. What do you think?

    The fallacy applies to anything that is purely random.

  2. I know this is a much debated subject for the reasons you outlined(and others). It does stand to reason that there may be negatively or positively reinforced trends when it comes to athletic performance. I knew there was some contention over the issue particularly in basketball so did some detective work.

    Apparently streaks are a big deal in the world of basketball, so there have been studies attempting to look for them. The most well known study I could find on the matter did conclude that each basket IS in fact statistically distinct.

    Check out:

    Gilovich, T., Vallone, R., & Tversky, A. (1985). The hot hand in basketball: On the misperception of random sequences. Cognitive Psychology, 17, 295-314.

    and his book where he lays it out pretty cleanly.
    There are a number of interesting side notes in the book and various interpretations of why people are so inclined to think they see causally linked streaks.

    The Wikipedia entry on the Hot Hand Fallacy refers to a number of other studies confirming that finding, however most are behind a paywall so I didn’t link to them. If you find any documented info to the contrary please let me know! I have a vague recollection of a news item about it a few years ago it but can’t recall the context nor if the findings refuted this study.

    Thanks for the comment! Keep them coming!

  3. Interesting…I read the first study, and the text of it focuses more on people’s beliefs in the Hot Hand, not due to a causal link such as psychology, but just due to “irrational” beliefs, most likely due to mistakes in perception and relative weighting of phenomena. The data itself is interesting, especially the ’76ers data, which seems to show a consistent trend across players of bias toward making the shot after several misses…a Cold Hand affect if you will ;). Could be due to lots of variables, or pure chance, or it might be due to psychology: several consecutive misses increases concentration, or perhaps better shot selection, affecting the probability of a subsequent, successful shot. However, I wouldn’t want to interpret this single data set as evidence of a causal link.

    Maybe the term, “statistically distinct” is problematic for me, and I’m also thinking beyond Hot Hand. Hot Hand refers to one kind of linkage: a history of successful shots creates a higher chance of more successful shots. Player psychology could affect future outcomes in either direction. Statistically distinct means that there is no statistical evidence of a general Hot Hand trend across events when aggregated over a statistically relevant data set. Since psychology is such a personal, malleable thing, the general aggregated effect across players might not be visible because not everyone responds in the same way. I do think that the chances of a successful shot are affected by psychology acting on history, so the outcome of such events in a series are linked through psychology, but maybe I can’t say that they are causally linked, since psychology is just one factor. I think I can safely say that if a player’s psychology is at all at work in their success rate, and if their psychology is affected by past performance, then future events are affected by historical ones.

    Does that make sense? I may have over-thought a possibly minor point.

  4. Yes, it absolutely makes sense. I appreciate the feedback. I agree that since there are so many variables that influence these kind of results that calling them completely independent might not be quite correct. Baskets appear to be generally regarded as statistically independent, at least as far as what I could find. On the other hand, it makes sense that over time, from say a young kid to an adult professional player, that the number of streaks would increase and lends to the idea that an aggregate of more baskets leads to more baskets in the future or that a set of circumstances could set off some kind of chain like that in someone. I also know there has been some startling research on ‘priming’, exposing people to certain information or a feeling and observing a predictable result based on that( e.g. Dan Ariely’s “Predictable Irrationality”). I will do some more research and see what I can dig up. At very least, I will change the description at some point to better describe the problem how people have attempted to detect whether or not the phenomena exists in the example as well as reference any controversy surrounding it. Thanks again!

  5. Would a person responding to your declaration that a celebrity has died with “these things come in threes” be the same phenomenon you are describing with this card?

  6. Genevieve,

    Great question! The classification of logical fallacies is often a bit slippery, so everything I say completely up for debate, but here is my answer.

    I would say no(with and asterisk). The reason is that the Hot Hand Fallacy is a misunderstanding of probability. Where someone assumes that because something happened, that something else in the same vein is likely to happen. Luck and bad luck exist as etherial streaks that once hit are some how self-reinforcing. Think, a bad night at the poker table or a great week for your investments on the stock market.

    My understanding of ‘celebrities die in threes’ is that there is some preordained list in the hands on the grim reaper. A super-natural force with nefarious intentions. I imagine this interpretation might not be consistent with everyone so it is possible that people ascribe the same forces in lucky streaks as they do in celebrity death streaks. However since these celebrity death streaks are limited to 3, it is likely another force would be used to explain it.

    Now for the asterisk. *

    Both of these beliefs rely on a mix of pattern seeking and confirmation bias. Our brains are constantly looking for and recognizing patterns. which is super helpful when making sense the world. But quite often these patterns are completely meaningless which is the case with both the Hot Hand Fallacy and ‘Celebrities die in 3s’. Confirmation bias is when we count the hits but forget the misses, like all the time when celebrities die in 1s and 2s, or when you do okay and just break even in the casino. These times don’t stand out as much. Here are a couple articles that do a great job of making sense of the ‘Celebrities die in 3s’ idea.

    Also check out Michael Shermer’s ‘The Believing Brain’ which is referenced in the above article.

    Thanks again for the great question!!

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