Pythagorean Win Expectation Calculator
Enter points or runs scored and allowed to see how many games the team should have won.
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Pythagorean Win Expectation Calculator by TheCalcTools
How the Pythagorean Win Expectation Calculator works
Teams that outscore opponents by more usually win more games. Bill James found that wins follow runs scored squared divided by runs scored squared plus runs allowed squared.
Later analysts fitted different exponents for other sports. A team winning many more games than expected has often been lucky in close games, and tends to regress.
The formula
Worked example
Using the default values shown in the calculator:
| Runs or points scored | 780 |
|---|---|
| Runs or points allowed | 690 |
| Games played | 162 |
| Actual wins (optional) | 88 |
| Exponent | 1.83 (refined baseball) |
- 780^1.83 ÷ (780^1.83 + 690^1.83) = 55.6%.
- Over 162 games that is 90.0 wins; the team actually won 88 (-2.0).
Result:
| Expected winning percentage | 55.6% |
|---|---|
| Expected wins | 90.0 |
| Actual wins minus expected | -2.0 |
| Expected losses | 72.0 |
Frequently asked questions
Is this a prediction?
It estimates how good a team has been, not how it will do. It is often a better guide to future results than the actual win-loss record.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.