Can someone explain to me why hot hand phenomenon is considered a fallacy?

Hot hands refers to the idea that a player who has scored a basket (therefore, has "hot hands") is more likely to score the next basket.

It is suggested that this is a fallacy because apparently scoring is considered a random event (as far as I understand it). It is the equivalent of flipping coins. And just as when you flip coins, you might get three heads in a row by chance, the same applies to scoring in basketball. So players probably remember those sequences when they scores several baskets in a row and think it had something to do with them.

Now I can not shake the feeling that this explanation is incomplete. Let me compare scoring with my efforts to learn probability on my own, which I have been doing for a while.

When I get some question right, I become more energized and confident, and am more likely to work on the following question because I feel more hopeful that I will figure it out.

But when I try several probability questions and get them all wrong, I am quite unlikely to try my best on the next one. I have sometimes later returned to questions that I had failed at, noting that they were quite easy but that earlier I had simply lost the will to put in any effort.

Anyhow, so to go back to the basketball example, why is each shot is assumed to be completely independent of the previous shots. Why doesn't a player's effort or confidence level is irrelevant? I can imagine hot hands applying to someone blindingly throwing the ball and once in a while getting lucky, but the same thing applies to professional players even? Yes, the ball has no memory but the person throwing the ball does. No?

• I think calling it a fallacy is a little mistaken simply because they assume that events are uncorrelated which I am very much not convinced that they are. Consider the Rockets in game 7 against the Warriors. They had one of the worst streaks in the league for 3s. They missed.. 27 in a row, ended up missing 33 of 40 or something? At some point, it seems to me that the events aren't necessarily uncorrelated but that there is something Markovian (or possibly non-Markovian) going on. In that context, hot hand (or its inverse) seems less fallacious. Jun 12, 2018 at 0:01
• Players can be exhausted or mentally demolished to the point where they can't shoot at all and there's no real way to account for that. Basketball is probably the most questionable regarding hot hand (or its inverse). Other sports are MUCH more heavily team sports and I think hot hand is probably more fallacious there. Jun 12, 2018 at 0:05
• en.wikipedia.org/wiki/… Jun 12, 2018 at 0:17
• The idea that repeated attempts at something skill-based are independent and random seems on its face to be itself a fallacy to me. For roulette, dice or other games of pure chance, yes; even for games of mixed chance like poker, which involves large amounts of psychology and strategy, the hypothesis that the outcome of each hand is independent of the previous hands seems to me less plausible than the "hot hand" hypothesis... Jun 12, 2018 at 0:21
• Related: Gambler's Fallacy which might be what other people who refer to the hot hand fallacy are intending to refer to. The point being that if the events are in fact independent, then knowledge of past events has no influence over future outcomes. As mentioned elsewhere in the comments, the independence assumption is in reality not perfectly valid in games such as basketball. Jun 12, 2018 at 1:08

The Hot Hand is no longer considered a fallacy. There's a growing body of evidence to show that it is indeed real. Furthermore, there was a mathematical mistake in the original 1985 paper that, when corrected for, actually supported the existence of a hot hand.

This is known as the Hot Hand Fallacy Fallacy.

This blog article explains the original paper's mistake. I'll do my best to summarize:

Say we flip a fair coin 100 times, and we would like to know the outcome that typically follows heads. So, whenever we flip a head, we get our pen and paper ready and write down the result of the following flip.

Question: What is the expected proportion of heads written on this piece of paper? Obviously one-half, right?

Crazy right? But it's true. The mistake is that when you get many successes (heads, in the case of the blog) in a row, you get a very high proportion, but it misses the fact that it should be "more important" than other samples.

(Using the example from the blog article, HHH is counted as having a proportion of 1, which is the same weight it gives to the sequence THH. But this is wrong because HHH should really be counted as 2/2 while THH should be counted as 1/1.)

Now there's some pretty plausible reasons why the hot hand exists (like you said, one could get more energized and confident), but I don't think much research has been done so far as to WHY it exists, only that it does...

• I don't understand the table from the paper, linked in the blog article. They show all 8 equally likely sequences of coin flips. We see H 8 times in the first or second flip, giving us 8 observations for what follows H. In 4 of those observations, we get H, and in 4 we get T. So, the odds of seeing H after H is exactly 1/2. How do they get 5/12? Apr 21, 2020 at 17:35
• @ Timidpuedo: great answer! I gave a shot at it as well - check it out! Dec 12, 2022 at 7:24
• using coin flips to illustrate the hot hand phenomenon is grossly incorrect. each flip of the coin is iid and does not depend on whether heads or tails occurred beforehand. shooting basketballs is completely different becasue the moral of the player, which affects accuracy, is affected by previous results. Dec 12, 2022 at 8:26
• @ryry well, the point is that we KNOW that coins don't get hot hands, so the math should calculate to 1/2, but it doesn't, so that points to the math in the original paper being wrong. Dec 13, 2022 at 15:12
• I should also add that there's a pretty plausible explanation for why hot hands is a thing. consider cold hands. maybe the player is sick, playing through a minor injury, etc. then the player's performance will bring down his average performance. that means the player's performance when he is healthy will be above is average performance, and thus will look like he has a hot hand. Dec 13, 2022 at 15:16

I have also struggled to understand a similar problem. Here is some context:

My friend and I have long argued about this problem - suppose I flip a coin 10 times, and all 10 flips come up as heads. Seeing this, I think of two things:

• The coin is probably rigged! It is extremely unlikely that a fair coin will come up 10 heads in a row!
• But let's assume for a second that maybe this coin is not rigged, and it actually came up 10 heads in a row - the next flip has to be a tails ..... correct?

Well the thing is - not necessarily! Why?

Well the obvious reason is that in a fair coin, the result of the previous flip should in no way, shape or form influence the results of the next flip. In my opinion, the confusion comes from more of a semantics problem : 10 consecutive heads sounds very "perfect" - my brain has an easier time imagining 10 coins on a table all facing heads, compared to 10 coins on a table with some arbitrary sequence. But for some reason, our brains tend to think that "10 consecutive heads" is somehow more "special and unique" compared to some arbitrary sequence of coins.

What this means is, a sequence of "H, H, H, H, H, H, H, H, H, H" is in reality just as "unique and special" as some arbitrary sequence such as "T, T, H, T, H, H, H, T, H, T" - in reality, both of these two sequences are equally "special and arbitrary". Both sequences are equally likely or unlikely to manifest themselves! It's just that we tend to consider the "uniformity" of the first sequence to be more "eyebrow raising" than the second sequence - when in reality, given a fair coin, there is nothing special about "streaks" -"streaks" are equally likely to form and break in the long run.

Now, the "Hot Hand Fallacy" becomes more of an issue in real world examples - in which the probability of the previous event might influence the probability of the next event.

As an example, after successfully scoring a few consecutive baskets, a basketball player might start to get into a "groove" and some muscle memory might tend to subconsciously activate ... somehow resulting in an overall higher accuracy. However, when the player misses a shot and breaks the streak - the player might feel a bit unnerved and feel jittery, the player might go through a phase of reduced accuracy, and will need to get back into their groove before returning back to their phase of improved accuracy. Thus explaining the "Hot Hand Fallacy".

In the end, it all boils down to the following points:

• When a process (e.g. coin flips) is not influenced by its history, the "Hot Hand Fallacy" is irrelevant

• When a process (e.g. shooting baskets) might be influenced by its history, the "Hot Hand Fallacy" might be relevant

In Probability and Statistics, we often use words such as "Independent and Identically Distributed" (IID) to describe a process which is not influenced by its history - and "Markovian" (e.g. Markov Chains) to describe a process which is influenced by its history.

Let me know if you have any questions! :)

• There is nothing special about any particular sequence of heads or tails as all are indeed equally likely. However, if you flip a coin say 10 times, not all proportions of heads or tails are equally likely, and it is indeed "special" to get all heads. This is because there is only one sequence that corresponds to geting all heads, but there are many sequences that correspond to getting 5 heads out of 10 flips. In any case, the probability of heads or tails is not influenced by previous results because each flip is iid. Dec 12, 2022 at 8:48