# Pythagorean Win Percentage Calculator (Basketball)

LAST UPDATE: September 24th, 2020

## Definition – What is Pythagorean Win Percentage?

Pythagorean win percentage is an estimation of where a win percentage “should” be. It uses only points for and against.

Fans of Pythagorean Win Percentage believe that it helps show if a team is ahead or behind an “expected” win percentage. Teams should regress towards their Pythagorean Win Percentage in the long term.

Bill James invented it for baseball. Daryl Morley is credited with being the first to adopt it to basketball, using the exponent 13.91. Basketball statistician John Hollinger applied it basketball using the exponent 16.5.

## Formula – How to calculate Pythagorean Win Percentage

Points ForExponent ÷ (Points ForExponent + Points AgainstExponent)

Where:

• Points For” is the number of points the team has scored.
• Points Against” is the number of points scored against the team.
• Exponent” is changed depending on the method used. Daryl Morley used 13.91 as an exponent, John Holinger used 16.5.

### Example

A team’s statistics show that over 56 games 4672 points for and 4517 points against. The exponent used for this example will be 13.91.

Pythagorean Win Percentage = 467213.91 ÷ (467213.91 + 451713.91)

Pythagorean Win Percentage = 11.04 ÷ (11.04 + 6.90)

Pythagorean Win Percentage = 11.04 ÷ 17.94

Pythagorean Win Percentage = 0.6154, or 61.54%

Therefore, the pythagorean win percentage predicts that this teams’s win percentage should be 61.54%.