Any one-off measurement is part real signal, part luck of the day. An extreme result needed both to line up — so when you measure again, the luck won't repeat and the score drifts back toward the average, all by itself. Regression to the meanThe pull is set entirely by the correlation between the two measurements: the weaker the link (more luck), the harder a score snaps back to the mean. is no force acting on anything — it's just what randomness looks like. Feed in a score and how repeatable the measure is, and see where the next one lands.
A score of 130 sits +30 from the mean of 100. Expect the next one near 118 — it gives back 40% of the gap, no change in true ability required.
Every line slopes the same way — toward the mean — and by the same fraction, 40% of its gap. The further out a score starts, the more it has to give back. Crank the correlation to 1 and the lines go flat (perfectly repeatable, no regression); drop it to 0 and they all collapse onto the mean (pure luck).
| First score | Expected next |
|---|---|
| 130+2 SDnow | 118 −12 |
| 115+1 SD | 109 −6 |
| 1000 SD | 100 0 |
| 85−1 SD | 91 +6 |
| 70−2 SD | 82 +12 |
This is the trap behind "praise made them worse, criticism made them better." Praise tends to follow a great result; criticism a poor one. Both are usually followed by something nearer average — so the praise looks like it backfired and the criticism looks like it worked, when neither did anything at all.