# Pythagorean expectation

## Sports formula / From Wikipedia, the free encyclopedia

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**Pythagorean expectation** is a sports analytics formula devised by Bill James to estimate the percentage of games a baseball team "should" have won based on the number of runs they scored and allowed. Comparing a team's actual and Pythagorean winning percentage can be used to make predictions and evaluate which teams are over-performing and under-performing. The name comes from the formula's resemblance to the Pythagorean theorem.[1]

Sports formula

The basic formula is:

- $\mathrm {Win\ Ratio} ={\frac {{\text{runs scored}}^{2}}{{\text{runs scored}}^{2}+{\text{runs allowed}}^{2}}}={\frac {1}{1+({\text{runs allowed}}/{\text{runs scored}})^{2}}}$

where Win Ratio is the winning ratio generated by the formula. The expected number of wins would be the expected winning ratio multiplied by the number of games played.