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Mathematics, probability & statisticsPart III

Regression to the mean

Extreme results drift back toward average. Don't confuse reversion with causation.

Regression to the mean illustration

Galton's discovery: extreme observations are mostly followed by less extreme ones, not because of any intervention, just because randomness is mostly somewhere near the mean and extremes are rare.

This creates a famous family of mistakes. The herbal remedy "cured" the patient (they'd recover anyway, regression toward health). The new coach "turned around" the team (the team had a terrible season, the next one was bound to be closer to average). The Sports Illustrated cover "jinx" (you only make the cover after an extraordinary streak; the next stretch is bound to look worse).

For operators, the warning is: when a department or salesperson or business unit has an unusually bad period, much of the next period's improvement will be regression, not your interventions. Same goes the other way for unusually good periods.

Examples in the wild

Operating

CEOs hired after a terrible year frequently get credit for "turnarounds" that were mostly regression to the mean. Boards reward themselves for prescient hiring decisions that were really just statistical reversion.

Investing

Last year's best-performing fund is usually not next year's best. Mean reversion in fund returns is one of the most reliable patterns in finance.

Everyday life

Praising kids only when they do extraordinarily well and punishing them only when they do extraordinarily badly: the next time, both groups regress, making praise look ineffective and punishment look effective. Pure illusion.

Regression to the mean is one of the mental models we apply through real cases inside the Pareto MBA — a part-time program for professionals who want to think clearly about business.