Children of tall parents are, on average, shorter than their parents.

This is a simple example of a common phenomenon: regression to the mean or the tendency for extremes to be pulled back towards the average. And for the same reason children of short parents are, on average, taller than their parents.

In the case of heights, regression to the mean is just a fact and nobody worries too much about it. However, there are many other cases in which regression to the mean is seriously misunderstood.

One famous example is the Sports Illustrated ‘jinx’.

Appearing on the cover of Sports Illustrated is said to be a ‘kiss of death’: it is frequently followed by a loss of form, by failure of some sort. But of course the jinx is just regression to the mean. You only get to be on the cover if you are doing exceptionally well. And if you are doing exceptionally well now, then when regression to the mean kicks in you will be doing worse. All good runs come to an end. If Sports Illustrated started to feature those who were doing exceptionally badly on the front cover then people would be queuing up to appear, because if you are having a bad run then you will improve when regression to the mean occurs. (Of course good and bad runs don’t come to an end in a predictable way and some runs last longer than others. As ever in statistics we are talking about averages and randomness here.)

The Sports Illustrated ‘jinx’ is a case of mistaking correlation for causation. Appearing on the cover may be correlated with a loss of form but it is not the cause of a loss of form. This misinterpretation is much more worrying when it affects serious areas such as health, where the fallacious reasoning can appear to defend quackery.

“I was seriously ill and tried all sorts of things to no avail. But then I tried psychic surgery and I recovered. Therefore psychic surgery works.”

No, many people who are seriously ill get better eventually. It’s regression to the mean which is responsible.

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