Pythagorean Expectation Calculator
A team’s expected win percentage from the points, runs or goals it has scored and conceded — Bill James’s Pythagorean expectation — and how many wins luck has added or taken away.
Teams win in proportion to scored^k ÷ (scored^k + conceded^k), where the exponent k is fitted to the sport: about 1.
How the pythagorean expectation calculator works
Teams win in proportion to scored^k ÷ (scored^k + conceded^k), where the exponent k is fitted to the sport: about 1.83 for baseball, 2.37 for American football, 2 for ice hockey, 13.9 for basketball (scores are high and close) and 1.3 for football. A team whose actual record is well above its expectation has been lucky in close games and tends to regress.
Formula: win% = S^k ÷ (S^k + A^k)
Worked examples
| Inputs | Expected win percentage | Note |
|---|---|---|
| Baseball: 800 for, 700 against, 162 games | 56.1 % | 56.1% — about 91 wins |
| Basketball: 9,000 for, 8,700 against | 61.6 % | 61.6% |
| Hockey: 250 for, 250 against | 50 % | 50% |
FAQFrequently asked questions
Why does basketball have such a big exponent?
Because scores are high and every game is decided by a small share of the points, a small edge in scoring margin turns into a big edge in wins. Baseball’s 1.83 reflects low, variable scores where a run means a lot.
Is the exponent fixed?
It is fitted from history and varies a little by era and league; some versions make it depend on the total scoring (Pythagenpat). The values here are the widely used ones; use the custom option for your own league.
What does “luck” mean here?
The gap between actual and expected wins is mostly the record in one-run or close games, which is largely random. Teams several wins above expectation tend to fall back the next season.
Does it work for football (soccer)?
Less well, because draws exist and scores are low; the 1.3 exponent gives a rough win share. It is better used for points-per-game style comparisons than for exact predictions.
Where these figures come from
- World Handicap System — Rules of Handicapping — the score differential and handicap index formula
- International Cricket Council — Playing Conditions — over structure and run-rate definitions
- Major League Baseball — Official Rules — the published definitions for baseball statistics
Last checked: September 2026. Formulas follow the governing bodies where one publishes them — the World Handicap System for golf, the ICC playing conditions for cricket run rates.