The hot hand fallacy in sports, gambling, and finance

Reading time: 4 minutes

You are sitting on the couch and you are watching a football game. On the pitch, there is a striker that has scored in each of the ten previous games. Each match in football, as we all know, is always a unique case, and yet you have the impression that the probability for that specific striker to score again is higher than usual. Why does this happen? First of all, let us go overseas, in the United States, to find where this illusion has been first discovered and studied.

“He’s on fire”

This phenomenon is called the hot hand fallacy and it is born in the world of American basketball. In 1985, a study was conducted with the aim to verify if a player, after having scored several shots in a row, had a higher probability of making successful shots, compared to the situation in which he hadn’t scored any points in the same game. As a matter of fact, there was this feeling, among professional players and the audience, that a player had a hot hand, and it was almost impossible for him to miss a shot.

However, despite a great number of analyses, no correlation between the “hot hand” and the probability of success of a shot arose. Rather, it seemed that the opposite was true: the players, who were feeling confident and sure of themselves, tried to take shots with a higher difficulty, therefore with a higher risk of missing them.

The hot hand fallacy is therefore that effect that makes us think that, after a series of successes, other positive results will occur (and vice versa).

When hot hands become a risk

The hot hand fallacy is present not only in sports. It is found in fact even in finance and in gambling.

In the finance world, this phenomenon can lead to the investment strategy known as averaging up. This technique consists in buying more shares of a stock you already own, as soon as you see their price increasing. The investor erroneously thinks that the price is going to skyrocket and that he has hit the jackpot, while it may be only a temporary increase, followed by a physiological decrease. The average price of the shares that have been bought therefore increases, with less economic gain for the investor.

The averaging up is not necessarily wrong, but it involves great risks if it is influence by the hot hand fallacy and not by financial studies and analyses.

To be precise, unlike sports and gambling, which we’ll deal with soon, market trends are not completely predictable with statistical data of the past, and this partially justifies the trust of investors and the use of the averaging up strategy.

L’illusione della mano calda è quindi quell’effetto secondo il quale dopo aver ottenuto una serie di successi, vi è la tendenza a pensare che verranno ottenuti altri risultati positivi (e viceversa).

The human component and the gambler’s fallacy

In gambling instead, the hot hand fallacy leads the gambler to bet his money based only on his perception of his own fortune or self-confidence. “This is my lucky day” is the sentence we often say when there is a series of events that favors us. If we had to guess if a coin lands on heads or tails, we tend to consider our choice as more probable if it is our lucky day, or if we had the right guess three times in a row. But the probability for heads or tails is always 50%.

A really interesting study from 2004 shows how, in predicting an event, the component of the choice is fundamental in the hot hand fallacy. In the first experiment, which consisted in choosing between two results with the same probability (exactly like heads or tails), the subjects tended to make their decision based on their series of successes (or failures).

“If I guessed right four times in a row while always choosing heads, it’s impossible that I make a mistake, so I’ll choose heads again”.

Basing your guess on the series of successes does not change the probability for heads or tails.

On the contrary, if we eliminate the component of the choice and we base the decision only on the concept of randomness, we fall for the opposite bias: the gambler’s fallacy. In the second experiment, a two-colored roulette was used. In this way, if red was the result three times in a row, the subjects tended to think that it was impossible if black wasn’t the following result, it wouldn’t be random.

This illusion leads us to think that if an event happens repeatedly, it’s impossible that it will happen again, rather the opposite must occur. Or we don’t perceive it as truly random. And this happens only if we eliminate the human component in the decision: self-confidence or fortune.

How to avoid ignoring the logic

Going back to the hot hand fallacy, the problem is now to understand why this phenomenon occurs, the reason for its existence. Why don’t we base some of our choices on the cold logic? Why do we avoid rationality, in favor of irrationality?

At the base of everything, there are probably our failures in predicting events during all of our life, which has led us to this fallacious reasoning. The cause of these failures is therefore to attribute to our inability to understand the concept of randomness. It’s a matter of representativeness: we tend to consider a small sample size as generalizable to the whole population. Therefore, in a series of random events, we either consider the following event too improbable (gambler’s fallacy), or we don’t consider it truly random, because it is influenced by human factors (hot hand fallacy).

Someone could claim that subjects in their later years could be less influenced by these types of biases, since they have more experience, and yet there are studies that show that age is not a determining factor.

So, how can we avoid these cognitive errors? Castel, Rossi and McGillivray, with a study from 2012, have analysed the procedural characteristics related to the hot hand fallacy, and they discovered that the effect of these illusions on the subjects disappeared as they spent more time undergoing their experiments. The more you are exposed to it, the faster you adapt. These subjects, regarding these specific biases, have learned from their experience. And that is what we have to do too.

A first step for everyone is being aware of how our mind works. Knowing it better, we can learn how to use it, without being overwhelmed.

Carlo Sordini

– Tversky, A, Gilovich, T. & Vallone, R. (1985). The hot hand in basketball: On the misperception of random sequences. In Cognitive Psychology, 17(3), 295-314. https://doi.org/10.1016/0010-0285(85)90010-6

– Ayton, P., & Fischer, I. (2004). The hot hand fallacy and the gambler’s fallacy: Two faces of subjective randomness? In Memory & Cognition, 32(8), 1369-1378. https://doi.org/10.3758/bf03206327

– Castel, A. D., Rossi, A. D., & McGillivray, S. (2012). Beliefs about the “hot hand” in basketball across the adult life span. In Psychology and Aging, 27(3), 601-605. https://doi.org/10.1037/a0026991