What is regression to the mean, and why does it fool us?

Regression to the mean is a statistical phenomenon in which unusually large or small measurements tend to be followed by measurements closer to the average. An epidemiology paper describes it as something that can make natural variation in repeated data look like real change. It fools us because we tend to look for a cause of the change, when chance alone can account for it. The idea is usually credited to Sir Francis Galton. [1] [2]

Many measurements combine something stable, such as skill or preparation, with chance. A student's exam score depends on preparation, but also on sleep, distractions, stress and similar factors. Chance is unbiased, so it is as likely to push a score up as down across a whole group. But the very highest scores were probably helped by unusually good luck, and the lowest were probably hurt by unusually bad luck. [3]

On a retest, the stable part carries over but the lucky or unlucky part does not. The Statistics LibreTexts text puts it this way: people with high scores tend to be above average in both skill and luck, and only the skill is relevant to future performance. This does not mean every high scorer was lucky, only that on average they were. The effect grows with measurement error, and it is most visible when follow-up is examined only for a subgroup chosen by its baseline value. [4] [1]

Mistaking this drift for a real cause is called the regression fallacy. A classic example, described by Tversky and Kahneman in 1974, involved Israeli Air Force flight training. Trainees who were praised after a good landing tended to do worse next time, and those reprimanded after a bad landing tended to do better. That can look like proof that praise hurts and reprimands help. But landings depend partly on chance, so exceptionally good ones tend to be followed by worse ones and exceptionally poor ones by better ones, whatever the instructor says. [3]

The same trap affects research. It can lead researchers to believe an intervention caused a change when the cause was chance, especially when they focus on people, cases or organizations at the extremes. One writer notes that policymakers might spend heavily on a program at scale and later find they were measuring statistical noise. [5] [3]

A Cambridge University Press article illustrates how selection creates the illusion using lung-function data (FEV1) for 150 patients. Only the 43 patients with extremely poor first readings, below 1.5 litres, were retained for a second measurement. Six of them were no longer extremely poor, and none moved the other way, so the group seemed to improve. This was because patients above the cutoff had been excluded by design. The article shows that selecting on the second period instead would produce an apparent deterioration, which reflects only how the data were cut. [6]

Clinical trials are exposed because they often require extreme baseline values, such as a diastolic blood pressure of at least 95 mmHg, so some spontaneous improvement is expected. The remedy described is a control group: patients are chosen on baseline readings, then randomly assigned to treatment or control, so the effect is similar in both. Treatment is judged by comparing the groups at the end, not by comparing the end result to baseline. The epidemiology paper adds that better study design and suitable statistical methods can also reduce the problem. [6] [1]