Pythagorean Win Percentage Calculator (Basketball)

Pythagorean Win Percentage Calculator

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 For^Exponent ÷ (Points For^Exponent + Points Against^Exponent)

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 = 4672^13.91 ÷ (4672^13.91 + 4517^13.91)

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%.

More resources

• Wikipedia – Pythagorean Expectation – An entry on the concept of Pythagorean Expectation.
• Steven J. Miller – A Derivation of the Pythagorean Win-Loss Formula in Baseball – An analysis of Pythagorean Win/Loss approaches in Basketball.
• Glossary entries on Pythagorean Win Percentage from NBA Stuffer.
• Kaggle – Applying Expectation to Major Sports – An analysis of Pythagorean Expectation when it comes to sports such as Basketball, Baseball, and more.