Regression to the Mean
Extreme results are partly luck. On the next measurement, luck is unlikely to be as extreme, so results tend to move back toward the typical level.
author
Francis Galton (observed in 1886)
Model type
About
Galton noticed that very tall parents had children who were tall but closer to average height. The general rule: whenever outcomes mix skill with noise, extreme observations are likely to be followed by less extreme ones. If you reward or punish after an extreme, you can misattribute the natural drift toward average to your intervention.
How it works – what to map
Two ingredients: a stable underlying level (skill, true rate) + random variability (noise).
Selection effect: picking on highs/lows captures extra luck; next time luck is more average.
Persistence (autocorrelation): with coefficient ρ between 0 and 1, the forecast shrinks toward the mean by (1−ρ).
Stationarity matters: regression to the mean assumes the process has a roughly stable mean and variance.
Selection effect: picking on highs/lows captures extra luck; next time luck is more average.
Persistence (autocorrelation): with coefficient ρ between 0 and 1, the forecast shrinks toward the mean by (1−ρ).
Stationarity matters: regression to the mean assumes the process has a roughly stable mean and variance.
Use cases
Performance management – after an unusually good or bad quarter, expect partial bounce back without changing people.
Investing – sectors or managers with extreme recent returns often cool toward long-run averages; beware chasing performance.
Sales & quotas – rockstar or struggling reps tend to drift toward their true productivity; design comp and coaching accordingly.
A/B testing – early spikes from small samples fade as data accumulates; wait for sufficient power.
Quality & ops – after a rare outage or a perfect week, expect metrics to move back toward normal control limits.
Hiring & admissions – super high test scores include luck; combine with broader signals and use shrinkage forecasts.
Investing – sectors or managers with extreme recent returns often cool toward long-run averages; beware chasing performance.
Sales & quotas – rockstar or struggling reps tend to drift toward their true productivity; design comp and coaching accordingly.
A/B testing – early spikes from small samples fade as data accumulates; wait for sufficient power.
Quality & ops – after a rare outage or a perfect week, expect metrics to move back toward normal control limits.
Hiring & admissions – super high test scores include luck; combine with broader signals and use shrinkage forecasts.
How to apply
Define the baseline – estimate the typical level (mean/median) for the person, team, or metric.
Estimate persistence (ρ) – from history or similar cohorts; low ρ means heavy reversion, high ρ means stickier performance.
Shrink forecasts – Next = Mean + ρ × (Last − Mean). Use ranges, not points.
Use controls – when judging interventions after extremes, compare to a similar untouched group or to time series controls.
Set guardrails – SPC limits or pre-declared A/B stopping rules to avoid overreacting to noise.
Estimate persistence (ρ) – from history or similar cohorts; low ρ means heavy reversion, high ρ means stickier performance.
Shrink forecasts – Next = Mean + ρ × (Last − Mean). Use ranges, not points.
Use controls – when judging interventions after extremes, compare to a similar untouched group or to time series controls.
Set guardrails – SPC limits or pre-declared A/B stopping rules to avoid overreacting to noise.
pitfalls and cautions
Confusing reversion with trend – if the mean itself is moving (new strategy, seasonality), do not expect bounce back.
Attribution errors – crediting coaching or punishment for natural reversion after an extreme.
Selection bias – analysing only the top/bottom performers exaggerates reversion effects.
Over-shrinking – using too low a persistence and erasing real changes in skill or process.
Small samples – early results swing wildly; wait for enough observations before acting.
Attribution errors – crediting coaching or punishment for natural reversion after an extreme.
Selection bias – analysing only the top/bottom performers exaggerates reversion effects.
Over-shrinking – using too low a persistence and erasing real changes in skill or process.
Small samples – early results swing wildly; wait for enough observations before acting.