Probability

Pythagorean W%

Runs scored and runs allowed become an expected winning percentage. Then we measure luck: the gap between the standings and the run differential.

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Inputs

Runs scored720

Runs allowed680

Games162

Actual wins (optional)88

Exponent

Result

.526

85.2 expected wins in 162 games

Record ahead of run differential

Expected wins: 85.2
Run diff: +40
Luck (W): +2.8
Exponent used: 1.83

720^1.83 / (720^1.83 + 680^1.83) = .526

Methodology

Bill James’ Pythagorean expectation treats runs like a scoring ratio. PythagenPat (1.83) is the usual modern default. Dynamic uses 1.50 × log10((RS+RA)/G) + 0.45.

W% = RS^x / (RS^x + RA^x)
Expected wins = W% × G
Luck = Actual wins − Expected wins

Limits Ignores clustering, bullpen leverage, and schedule. A +6 luck season often regresses; it is not proof the team “knows how to win.”