Regression to the Mean, explained.
Regression to the mean is the tendency for an unusually high or low measurement to be followed by a less extreme one when repeated measurements are imperfectly correlated.
Why it happens
A standout result often combines a persistent component with temporary luck or measurement noise. Selecting the extremes also selects unusual noise. On a later measurement, that temporary component need not repeat.
In the experiment, each person has an unchanged underlying ability. Their two scores add fresh, independent noise to that same ability. Selecting the highest first scores also selects people whose first measurement was unusually favorable.
The next measurement usually removes some of that advantage at the group level. Nobody had to become less capable. Selecting on an unusually bad first result creates the opposite tendency.
Read the result
Compare first and second scores for the selected extreme group. Lower correlation produces more movement toward the population average; it does not force every individual point to move in that direction.
A worked example
A team rebounds after a bad week
Choose teams because their first-week results were unusually poor.
Some had bad luck as well as weak performance. A second week with different luck may look better without any intervention.
A comparison group helps distinguish this selection effect from an improvement caused by a new policy.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Ability is normally distributed with mean 50 and standard deviation 10. Both scores add normally distributed noise with mean zero and the standard deviation you choose.
The model’s correlation between repeated scores is 100 / (100 + noise²). With no noise the correlation is 1 and scores match exactly. With noise, the conditional expected second score is 50 + correlation × (first score − 50). Scores are unbounded units.
Where this idea is useful
A change following an unusually good or bad result does not by itself identify a cause. A comparison group can help distinguish a real intervention from selection and noise.
A common misconception
“Every extreme score must move toward the average next time.”
Regression describes a conditional tendency across observations, not a rule that determines the next result for one person.
What this explanation leaves out
- The model has stable ability and independent errors. Learning, fatigue, shared conditions, and real trends can change the pattern.
- Regression is a conditional average tendency, not a force that guarantees the next individual score will be closer to 50.
Is regression to the mean the same as genuine improvement?
No. Improvement changes an underlying process; regression can happen with stable ability and fresh noise. Both may occur together, so the before-and-after difference alone is insufficient.
Was a group chosen because its first result was extreme? How would that affect a before-and-after comparison?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
For a broader treatment of regression, measurement, and inference, see the authors’ resources for Regression and Other Stories.