Regression to the Mean

In statistical terms, regression to the mean appears when repeated measures are correlated but not perfectly correlated. If the correlation between first and second measurements is less than 1, the expected second score for someone selected on an extreme first score lies closer to the population mean than the initial score. The weaker the correlation, the stronger this pull toward a less-extreme expected follow-up.

The trap hides inside dramatic before-and-after stories

The easiest time to get fooled by regression to the mean is exactly when a story feels most convincing: my sleep was awful, I started magnesium glycinate, and three nights later I felt much better. That improvement may be partly real. But if you began during an unusually bad stretch, you also chose a moment that was statistically likely to be followed by something less extreme anyway.

That is why regression to the mean shows up everywhere from regression to the mean in psychology studies to sports “slumps,” blood pressure follow-ups, and supplement self-trials. Sir Francis Galton noticed it when very tall parents tended to have children who were still tall, but not usually quite as extreme as the parents.

The rubber-band picture

Picture a basketball tossed far above the crowd. The next bounce is usually still high, just not that high. Regression to the mean works like that with repeated measurements: when a result is extreme because of both a stable signal and a temporary wobble, the wobble is unlikely to be extreme in the same direction twice.

That “temporary wobble” can be many ordinary things: random biological fluctuation, measurement noise, a bad night of sleep, unusual stress, lucky guessing, or just having a weird day. The key surprise is this: regression to the mean is not a force pushing things back to average. It is what you expect when you re-measure something imperfectly stable after selecting an extreme result.

So what is meant by regression to the mean? In plain language: if you pick people, days, or scores because they were exceptionally high or low, the next measurement will usually be closer to typical. Not always. Not fully. Just closer on average.

Where the fallacy enters

The regression to the mean fallacy happens when people treat that ordinary softening as proof that some intervention worked or failed. A coach praises an athlete after a terrible game; the next game is better, so the coach thinks the speech caused it. A parent scolds a child after an unusually reckless day; the next day is calmer, so the scolding looks magically effective. Kahneman used a version of this training-story mistake to show how easy it is to confuse fluctuation with causation.

One decision that helps today

If you are testing a supplement, do not judge it from the week that made you desperate enough to start. Judge it against a longer baseline and, if possible, repeated weeks rather than one dramatic before-and-after swing. That single decision will protect you from a huge share of fake “wins” and fake “failures.”