Pythagorean expectation

Pythagorean expectation estimates the win percentage a team "should" have based on the points, runs or goals it has scored and allowed, rather than its actual tally of wins and losses. It was developed by baseball analyst Bill James, who named it for its resemblance to the Pythagorean theorem, and has since been adapted, with different exponents, to basketball, football and other sports.

The basic form is Win% ≈ RS^exp / (RS^exp + RA^exp), where RS and RA are runs, or points, scored and allowed, and the exponent is fit to each sport, commonly cited near 1.83 for baseball and much higher, in the low double digits, for higher-scoring sports like basketball. A team whose actual win percentage diverges sharply from its Pythagorean expectation, often because of an unusual record in close, low-scoring games, tends to move toward its Pythagorean number over the following stretch of games, an example of regression to the mean.

Analysts use Pythagorean expectation to identify teams that are over- or under-performing their underlying run or point differential and to project future record more reliably than recent win-loss record alone. The main pitfall is reading a gap between actual and Pythagorean record as proof of a hidden skill, such as "clutch" performance, rather than largely a matter of variance in close games; some of the gap can persist, but most research finds it mostly does not.