Pythagorean Win Percentage Calculator (Basketball)

Pythagorean Win Percentage Calculator

What is Pythagorean Win Percentage?

Pythagorean win percentage is an estimation of where a team’s win percentage “should” be based only on their points for and against.

Bill James invented it for baseball and later adapted to other sports such as basketball.

Daryl Morley is credited with being the first to adopt the concept to basketball, using the exponent 13.91. Basketball statistician John Hollinger applied the formula to basketball using the exponent 16.5.
Pythagorean win percentage is often close to the actual result of a team’s performance in the regular season.

How to calculate Pythagorean Win Percentage

Pythagorean Win Percentage is calculated as:
$\text{Pythagorean Win Percentage} = \text{Games Played}\frac{\text{Points For}^\text{Exponent}}{\text{Points For}^\text{Exponent} + \text{Points Against}^\text{Exponent}}$

Example

A team’s statistics show that over 56 games 4872 points for and 4517 points against. The exponent used for this example will be 13.91.
$\text{Pythagorean Win Percentage} = \frac{4672^13.91}{4672^13.91 + 4517^13.91}$
$\text{Pythagorean Win Percentage} = \frac{11.04}{11.04 + 6.90}$
$\text{Pythagorean Win Percentage} = \frac{11.04}{17.94}$
$\text{Pythagorean Win Percentage} = 0.6154$
$\text{Pythagorean Win Percentage} = 61.54$
Therefore, the pythagorean win percentage predicts that this teams’s win percentage should be 61.54%.

More resources

Wikipedia – Pythagorean Expectation
Steven J. Miller – A Derivation of the Pythagorean Win-Loss Formula in Baseball

Pythagorean Win Percentage Calculator (Basketball)