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

Question

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?

Answer 1

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?

Answer: Less than one-half.

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.)

There's also some good stuff in vadim's link in the comments: https://en.wikipedia.org/wiki/Hot_hand#Recent_research_in_support_of_hot_hand

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...

Answer 2

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! :)