Baseball Pythagorean Win Expectation Calculator
Estimate a baseball team’s expected winning percentage and season wins from runs scored and runs allowed, using Bill James’s Pythagorean formula.
How it works
Expected win % = RS² ÷ (RS² + RA²) · Expected wins = win % × games
Bill James found that a baseball team’s winning percentage tracks the square of its runs scored divided by the sum of the squares of runs scored and runs allowed — hence “Pythagorean.” It captures the idea that outscoring opponents by a wide margin should translate into wins, and teams that beat their Pythagorean record often do so on luck in close games rather than skill.
Worked example
A team scoring 750 runs and allowing 700 has an expected win % of 750² ÷ (750² + 700²) = 562,500 ÷ 1,052,500 = 0.534, or roughly 87 wins in a 162-game season.
Sources: Pythagorean expectation — Wikipedia
Frequently asked questions
Why is it called Pythagorean?
Because the formula squares runs scored and runs allowed, echoing the a² + b² form of the Pythagorean theorem — even though it has nothing to do with right triangles.
What if a team beats its Pythagorean record?
Winning more games than the run totals predict usually reflects good luck or a strong bullpen in one-run games, and it tends not to persist. The Pythagorean record is often a better guide to true talent.
Should I use exponent 2 or 1.83?
The classic exponent is 2; sabermetricians later refined it to about 1.83 for a slightly better fit. This baseball calculator uses 2 — use the general exponent calculator to try other sports and exponents.
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This calculator is for educational purposes. Double-check important results before acting on them.