Regression to the mean: extremes don't repeat

An unusually good or bad result tends to be followed by a more average one, for purely statistical reasons that have nothing to do with cause and effect.

Established Supported by convergent, high-quality evidence.

Plain-language answer

Whenever a measurement combines a real underlying ability or tendency with some amount of randomness or measurement error, an unusually extreme result is disproportionately likely to have been boosted by good luck (if high) or bad luck (if low) — and that luck does not carry over to the next measurement. So an extreme result tends to be followed by a more ordinary one, on average, purely from the statistics of how random noise combines with a stable underlying trait. This is regression to the mean, and it happens even when no cause — no punishment, no reward, no intervention — is doing anything at all.

Why it matters

Regression to the mean is one of the most reliable generators of false causal stories, because it produces a pattern (extreme results followed by more average ones) that looks exactly like the pattern a real causal mechanism would produce, and it happens constantly in ordinary life: sports performance, medical symptoms, business results, students’ test scores. Anyone who intervenes right after an extreme result (praising a great performance, treating a bad symptom, coaching a slump) will tend to see improvement or reversion afterward — and will be tempted to credit the intervention, when a fair share of that “improvement” was going to happen regardless.

Worked example: the flight instructors

Israeli air force flight instructors observed that trainees who were praised after an exceptionally smooth landing tended to perform worse on their very next landing, while trainees who were criticized after a rough landing tended to perform better next time. The instructors concluded, reasonably from their experience, that criticism works and praise backfires.

Kahneman and Tversky’s analysis points out that this pattern is exactly what regression to the mean predicts on its own, without praise or criticism doing anything causal at all: landing quality combines real skill with substantial moment-to-moment variability, so an exceptionally good or bad landing is partly luck, and luck (unlike skill) does not repeat. The very best landings are disproportionately followed by more ordinary ones, and the very worst landings are disproportionately followed by more ordinary ones — regardless of what an instructor says in between.(Kahneman & Tversky, 1973)

Common misconception

“The pattern was so consistent that it must have been the intervention” mistakes a wide, general statistical phenomenon for evidence of a specific cause. Regression to the mean is not a rare side effect that occasionally sneaks into data — it is the default expected pattern any time a measurement combines a stable component with real variability, which describes most measurements of human performance, health, and behavior. A causal claim needs to show an effect beyond what regression to the mean already predicts, for example via a controlled comparison against people who received no intervention.

Limits and open questions

Regression to the mean explains why an extreme result tends to move back toward average — it does not tell you the size of that effect for a specific measurement without knowing how much of the observed variation is real signal versus noise. Distinguishing “some regression, plus a genuine additional effect” from “regression alone, no genuine effect” for a specific real-world claim usually requires a proper comparison (a control group, a larger sample, or repeated measurement), not just noting that regression to the mean exists.

  • Base rates works through the flight-instructor example as part of a broader look at how people misjudge over-time patterns.
  • The law of large numbers covers the related but distinct idea of how averages behave over many repeated trials.

Key takeaways

  • After an unusually extreme result, a more ordinary result tends to follow — for purely statistical reasons, not because anything changed in between.
  • This pattern is easy to mistake for evidence that an intervention (praise, criticism, treatment) worked, when the reversion would likely have happened regardless.
  • Confirming a real effect beyond regression to the mean requires a proper comparison against what would have happened without the intervention.

Sources

  1. Kahneman, Tversky (1973). On the Psychology of Prediction. Psychological Review, 80(4), 237-251. https://doi.org/10.1037/h0034747 ↩