Regression to the Mean
Extreme results are usually followed by more typical ones—even without any real change.
Author
Francis Galton (1886); modern statistics and epidemiology
Model type
About
Regression to the mean is a statistical tendency: when outcomes vary and today’s result is unusually high or low, the next measurement is likely to be closer to average simply because luck/noise won’t be extreme twice in a row. Galton noticed tall parents had tall—but less extreme—children on average. It’s not a force pushing outcomes; it’s a sampling effect that fools us into seeing causation (e.g., “the cure worked!”) where none exists.
How it works
Conditions – there’s genuine variability and the correlation between time-1 and time-2 is imperfect (r < 1).
Expectation – E[X_{2}\,|\,X_{1}=x] \approx \mu + r\,(x-\mu); with 0<r<1, the expected follow-up is nearer the mean \mu.
Selection on extremes – if you pick the worst performers or the best funds, their later scores will look better/worse even without intervention.
Illusory improvement – any programme targeted at extreme cases will appear to “work” unless you control for this effect.
Use-cases
Performance & sport – “hot hands”, “SI jinx”, star funds; extreme runs cool naturally.
Product & ops – teams targeted after a bad month will often rebound anyway.
Medicine & policy – treat only the highest BP/lowest scores and you’ll overstate treatment effects.
A/B testing & analytics – picking variants after a lucky spike leads to disappointment on reruns.
Quality control – outlier weeks drift back without any process change.
Step-by-step
Use proper controls – randomise or add a matched control group so both groups regress similarly.
Measure multiple baselines – average several pre-tests to reduce noise before intervening.
Analyse deltas, not levels – difference-in-differences or ANCOVA (post adjusted for pre) rather than raw post.
Shrink extreme estimates – use Bayesian/hierarchical models or empirical Bayes to temper outliers.
Beware “coach effect” stories – if you intervene because results were extreme, expect improvement even if the intervention is useless.
Report uncertainty – show intervals, reliability (r), and rerun on new samples.
Forecast sanely – temper peaks/troughs toward typical levels unless you have a causal reason not to.
Pitfalls & Cautions
Mistaking reversion for remedy – crediting training, penalties or bonuses for natural bounce-backs.
One-group pre/post – classic trap; without controls you mostly measure regression.
Overfitting – picking the best model/creator/fund from many ensures a later slide.
Changing variance – if measurement noise or mix shifts, the amount of regression changes.
Punishing extremes – regression makes “punishment works, praise fails” look true (Kahneman note); design fair feedback loops.
Related Mental Models
Click below to learn other mental models
Principal-Agent Problem
When decision rights are delegated, agents optimise their own payoff under information asymmetry. Without smart contracts and governance, effort, risk and horizon drift away from the principal’s goals.
Circle of Competence
Operate where you truly understand cause and effect; stay inside the circle, expand it deliberately, and partner outside it.
Second Order Thinking
Consider the long-term and indirect consequences of decisions, rather than just the immediate or obvious ones.