Regression to the mean
Extreme measurements tend to be followed by more average ones, purely by chance.
What it means
Regression to the mean is a statistical phenomenon in which an extreme value on a noisy measure tends to be closer to the average when measured again, simply because the extreme reading was partly the product of random fluctuation that is unlikely to recur. The mechanism is that any observed score combines a stable true component with random error; when a score is extreme, error has probably contributed heavily to its extremity, so the next, independent measurement will tend to drift back toward the underlying mean. The phenomenon is not caused by any force pulling values toward the center — it is a necessary consequence of imperfect correlation between repeated measures. Its great practical danger is that it masquerades as a causal effect: because people intervene precisely when things are at their worst (or reward and study things at their best), the natural drift back toward average gets misattributed to the intervention, the punishment, or the praise. This produces illusory beliefs that treatments work and that praise spoils while criticism improves performance. It matters because failing to account for it leads to crediting or blaming interventions for changes that would have happened anyway, which only a proper control group can rule out.
Examples
A sports team's worst month is often followed by a better one — with or without the new 'turnaround' plan that gets the credit.
Israeli flight instructors saw that praise after a good landing was followed by a worse one, and shouting after a bad one by a better one, and concluded criticism works. Neither did anything.
Patients join a back-pain trial when the pain is at its very worst, so most feel better a fortnight later — improvement any treatment, or none at all, will appear to have caused.
First described in Francis Galton (1886).