Regression to the Mean

Every observed performance is some mix of skill and circumstance. When you select the most extreme results — the hottest starts, the worst slumps — you are selecting cases where circumstance happened to run in one direction. Circumstance does not persist. Skill does.

So the next stretch comes in closer to the middle. Not because the player "cooled off," and not because of pressure or complacency. Because the unusual part was never repeatable to begin with.

Two common misreadings:

• "He's due." Regression does not push results back to compensate. A hitter in an 0-for-20 stretch is not owed hits. His *next* at-bats are simply drawn from his real ability, which was always better than 0-for-20 suggested.
• "He regressed, so he got worse." Regression toward the mean is not decline. A player who hit .380 in April and .295 the rest of the way did not deteriorate. His April was an overestimate.

The mean being regressed toward is his true level — which for a good player is still good.

The rule: the smaller the sample and the more extreme the result, the more you should shade it back toward the population.

• A 40-at-bat .400 start regresses a lot. It is mostly noise.
• A 600-at-bat .310 season regresses a little. It is mostly signal.
• A stat that stabilizes slowly (batting average) regresses more than one that stabilizes quickly (strikeout rate) at the same sample size.

This is exactly what our own NFL Draft Kit numbers do: last season's per-game production is pulled toward the positional mean based on how many games a player actually appeared in. A player with four games gets pulled hard; a player with seventeen barely moves.