The statistical tendency for extreme observations to be followed by less extreme ones closer to the population average.
Francis Galton named the effect in the 1880s after noticing that tall parents tended to have children shorter than themselves, and short parents children taller than themselves. The underlying math is universal. Any observed performance is the sum of a stable true-talent component and a noisy luck component. When you observe an extreme result — the noise was probably high. The next observation will, in expectation, contain less of that noise and come in closer to the true talent.
The implications for sports modeling are constant. A hitter posting a .380 batting average in April will, almost certainly, not maintain that pace. The .380 reflects true talent — but the gap between the .380 and his career line is mostly noise. The forward projection is closer to his career line than to the hot start.
Quantifying the regression is the harder problem. How much weight should you put on the new data versus the prior? The answer comes from Bayesian shrinkage: the size of the new sample, the variance of the underlying process, and the strength of the prior all enter the formula. In practice, sports models tune a regression weight per metric — pitcher strikeout rate stabilizes after fewer batters faced than pitcher hit rate, so the regression weight on strikeouts is lower.
The professional discipline around regression is to apply it before you act, not after. Anyone can look back at a hot streak and observe that it ended. The work is anticipating which currently-hot streaks are mostly luck and which reflect a real talent shift. The gap between observed performance and underlying advanced metrics — wOBA minus xwOBA, ERA minus xERA, shooting percentage minus expected — is the most direct signal that regression is overdue.
Every player rate stat in our system is regressed toward a prior. The shrinkage weight is tuned per metric — strikeout rate stabilizes fast, BABIP stabilizes slowly — and the prior is updated nightly. Without regression, our projections would be whipsawed by small-sample noise.