Predicting the Improbable

One natural human bias is that we tend to draw strong conclusions based on few observations. This bias, misconceptions of chance, shows itself in many ways including the gambler and hot hand fallacies. Such biases may induce public opinion and the media to call for dramatic swings in policies or regulation in response to highly improbable events. These biases are made even worse by our natural tendency to “do something.”


An event like an earthquake happens, making it more available in our mind.

We think the event is more probable than evidence would support so we run out and buy earthquake insurance. Over many years as the earthquake fades from our mind (making it less available) we believe, paradoxically, that the risk is lower (based on recent evidence) so we cancel our policy. …

Some events are hard to predict. This becomes even more complicated when you consider not only predicting the event but the timing of the event as well. This article below points out that experts, like the rest of us, base their predictions on inference from observing the past and are just as prone to biases as the rest of us.

Why do people over infer from recent events?

There are two plausible but apparently contradicting intuitions about how people over-infer from observing recent events.

The gambler's fallacy claims that people expect rapid reversion to the mean.

For example, upon observing three outcomes of red in roulette, gamblers tend to think that black is now due and tend to bet more on black (Croson and Sundali 2005).

The hot hand fallacy claims that upon observing an unusual streak of events, people tend to predict that the streak will continue. (See Misconceptions of Chance)

The hot hand fallacy term originates from basketball where players who scored several times in a row are believed to have a “hot hand”, i.e. are more likely to score at their next attempt.

Recent behavioural theory has proposed a foundation to reconcile the apparent contradiction between the two types of over-inference. The intuition behind the theory can be explained with reference to the example of roulette play.

A person believing in the law of small numbers thinks that small samples should look like the parent distribution, i.e. that the sample should be representative of the parent distribution. Thus, the person believes that out of, say 6, spins 3 should be red and 3 should be black (ignoring green). If observed outcomes in the small sample differ from the 50:50 ratio, immediate reversal is expected. Thus, somebody observing 2 times red in 6 consecutive spins believes that black is “due” on the 3rd spin to restore the 50:50 ratio.

Now suppose such person is uncertain about the fairness of the roulette wheel. Upon observing an improbable event (6 times red in 6 spins, say), the person starts to doubt about the fairness of the roulette wheel because a long streak does not correspond to what he believes a random sequence should look like. The person then revises his model of the data generating process and starts to believe the event on streak is more likely. The upshot of the theory is that the same person may at first (when the streak is short) believe in reversion of the trend (the gambler’s fallacy) and later – when the streak is long – in continuation of the trend (the hot hand fallacy).

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