Written by Dackohn; last reviewed November 2026.
Regression to the mean is the tendency of extreme measurements to be followed by less extreme ones. An unusually high score usually includes some good luck, which does not repeat. With a test-retest correlation of 0.5, someone 2 SDs above average is expected to be only 1 SD above next time, with no change in ability.
Why it happens
Any measurement is part signal, part noise. A student’s test score reflects their ability plus the luck of the day: which questions came up, how well they slept. Among the top scorers, more had good luck than bad. Next time their luck averages out, so as a group their scores fall. The same logic in reverse lifts the lowest scorers.
The formula
With both measurements on the same scale, the expected second score is:
expected = mean + r × (first score − mean)
Here r is the correlation between the two measurements. With r = 1 there is no noise and no regression. With r = 0 everyone is expected back at the mean.
Worked example
An IQ-style test has mean 100, SD 15 and a test-retest correlation of 0.5. A person scores 130, which is 2 SDs above the mean. The expected retest score is 100 + 0.5 × 30 = 115, or 1 SD above. Someone scoring 70 is expected to rise to 85. Half the distance to the mean disappears in both cases without anything having changed.
How it fools people
- Treatments that seem to work. People seek help when symptoms are at their worst. Many would improve anyway, so a remedy gets credit it did not earn.
- Remedial programmes. Choose the weakest students on one test, teach them anything, and their scores rise on the next.
- Praise and punishment. Performance tends to fall after praise for an unusually good result and to rise after criticism of an unusually bad one. This can make criticism look more effective than it is, a point Daniel Kahneman made about flight instructors.
- The “sophomore slump”. Outstanding debut seasons are usually followed by less outstanding ones.
Does everyone drift to average?
No. The overall spread of scores stays the same from one time to the next. Those who were extreme move inward, while others who had a typical first score have an extreme second one.
How to avoid being fooled
- Use a randomised control group. Both groups regress by the same amount, so any extra change belongs to the treatment.
- Do not select on the outcome. Selecting people because of an extreme baseline score guarantees apparent change.
- Take several baseline measurements. An average of repeated measurements contains less noise.
Try it yourself
Regression to the Mean Calculator →See how much change is expected by chance alone. Correlation Calculator →Estimate r from your own repeated measurements.Frequently asked questions
What is regression to the mean in simple terms?
Extreme results are partly luck. When you measure again, the luck usually does not repeat, so the next result tends to be closer to average.
Is regression to the mean the same as the gambler's fallacy?
No. The gambler's fallacy says outcomes are due to balance out, as if chance had a memory. Regression to the mean involves no memory: the next result is just drawn from the person's usual range.
How do I reduce it in a study?
Randomise to a control group, avoid choosing participants on extreme single scores, and average several baseline measurements.
Related reading: Correlation vs causation · Simpson’s paradox · P-hacking explained
Sources & further reading: NIST/SEMATECH e-Handbook of Statistical Methods · OpenStax Introductory Statistics. How we compute & validate: methodology. Written & reviewed by Dackohn; last reviewed August 2026.