Instrument 5 · regression to the mean

The jinx that isn't

The best one year is mediocre the next. The worst school improves after an intervention. Both look like causes and neither is: any score is skill plus luck, and luck does not repeat. Wherever you selected on an extreme, the next measurement drifts back on its own.

This year against next year

What the top ten per cent did next

everyone the top ten per cent no change line

The same statement, with the numbers in it

E[x2∣x1] =μ+ρ(x1−μ) , ρ= σskill2 σskill2+ σluck2
ρ=0.50 , E[x2∣x1= +2σ]=+1.0σ

ρ is the share of the spread that is real. At ρ = 1 nothing regresses — the score is all skill. At ρ = 0 the first score tells you nothing and the second lands on the average, every time.

Fine tune