Regression to the Mean, Explained with Examples

What it is

Regression to the mean means that after an unusually high or low result, the next one is usually closer to average, even if nothing changed. "The mean" is just another word for the average.¹

It happens because any measurement involves some luck. An extreme result is usually extreme partly because of luck. Next time, the luck is unlikely to be as extreme, so the result tends to drift back towards the average.¹

The idea goes back to the scientist Francis Galton, who described it in 1886 while studying the heights of parents and their children.²

Why it matters

Regression to the mean is one of the most common ways we fool ourselves into thinking something worked.

Here's how. We tend to act when things are at their most extreme: when we feel worst, when results are worst, or when a problem seems to be at its peak. Afterwards, things usually get better anyway. So whatever we did gets the credit.

It doesn't only fool individuals. It can lead doctors, health officials, and managers to conclude that a treatment or a policy worked, when the change was really due to chance.³

The Placebo effect entry shows how this explains part of why people "get better" on fake treatments, and its dice "cure" lets you see it for yourself. The Signal vs noise entry shows how it hides in everyday measurements.

What it is not

It's not a force. Nothing pushes results back towards the average. The extreme result was simply partly luck, and luck doesn't usually repeat itself in the same way.
It's not "being due" for a change. After a bad run, a good run isn't owed to you. Each new result is not pulled towards the average. That mistaken belief is called the gambler's fallacy.
It doesn't mean everyone ends up average. People still vary just as much as before. It's only the most extreme results that tend not to repeat.

The fix: a comparison group

The best protection is a comparison group: a similar group, picked in the same way, that gets no treatment. If people chosen for their extreme scores "improve" even without treatment, comparing against them reveals how much of the change was just regression.¹ This is one of the main reasons that randomized controlled trials include a control group. See the Randomized controlled trial entry.

In everyday life

All of these are imaginary examples:

Speed cameras. Imagine a council puts a speed camera at a junction right after an unusually bad year for crashes. The next year, crashes fall. The camera may have helped. But crashes at that junction might have fallen anyway, because the bad year was partly bad luck.
The rookie slump. Imagine a sports player who has an outstanding first season. In the second season, they do less well. Commentators call it a slump. But a first season that stood out was probably partly luck.
Praise and criticism. Imagine a teacher who criticises pupils after an unusually bad test and praises them after an unusually good one. The criticised pupils tend to do better next time, and the praised ones worse. The teacher may wrongly conclude that criticism works and praise doesn't.

The common trap

The trap is giving credit, or blame, to whatever you did right after an extreme result.

Some ways out:

Ask "compared with what?" What would have happened if you'd done nothing?
Be careful when acting at extremes. If you only step in when things are at their worst, almost anything will seem to help.
Look for a comparison group that was picked the same way but didn't get the treatment.

Try it

You need about 20 people and a coin each. Everyone flips their coin 10 times and counts the heads. Pick the three people with the most heads and "coach" them by saying "Well done, keep it up!" Then everyone flips 10 more times.

The top three will usually score closer to 5 the second time, though not always. Did the coaching fail, or was it regression to the mean?

Related concepts

Placebo effect · Signal vs noise · Randomized controlled trial · Sample size · Cognitive shortcuts

Sources

Barnett, A. G., van der Pols, J. C., & Dobson, A. J. (2005). Regression to the mean: What it is and how to deal with it. International Journal of Epidemiology, 34(1), 215–220. https://doi.org/10.1093/ije/dyh299
Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15. https://doi.org/10.2307/2841583
Morton, V., & Torgerson, D. J. (2003). Effect of regression to the mean on decision making in health care. BMJ, 326(7398), 1083–1084. https://doi.org/10.1136/bmj.326.7398.1083