Regression to the Mean
Every performance is part skill, part luck — and luck does not carry over. This simulator gives each of N players a true skill drawn from a normal distribution and an observed score equal to skill plus fresh random luck, then plots season 1 against season 2. Highlight the top 10% of season 1 and watch their season-2 average fall back toward the population mean, while the bottom 10% climbs — nobody’s skill changed, only the luck was redrawn. Sliders for the skill spread and the luck spread recompute everything live, with a readout of the between-season correlation r = σ²_skill/(σ²_skill+σ²_luck) and the expected fall-back of the top group. Preset stories — the rookie of the year, star fund managers, and the flight instructors who concluded punishment beats praise — set the sliders and explain what regression to the mean does to each.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Selection on an extreme is selection on luck: the top group was picked partly for good luck, and since luck is redrawn next season, their expected score falls back — by exactly (1−r) of their distance from the mean.
- The between-season correlation equals the share of variance that is skill: r = σ²_skill / (σ²_skill + σ²_luck). All skill means no regression; all luck means complete regression.
- Kahneman’s flight instructors praised smooth landings and saw decline, punished bad ones and saw improvement — both were pure regression, and it taught them the false lesson that punishment works.
- The sophomore slump, “hot” fund managers who cool off, and the Sports Illustrated cover jinx are the same artefact: extreme performances are unrepresentative, and the follow-up is measured anyway.
- Runs 100% in your browser — simulations are computed locally on your device.
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