First Order Approximations of the Pythagorean Won-Loss Formula for Predicting MLB Teams' Winning Percentages

TL;DR

This paper mathematically demonstrates that a linear predictor of MLB winning percentages is a first-order approximation of the Pythagorean Won-Loss formula, explaining its effectiveness.

Contribution

It proves the linear predictor is a first-order approximation of the Pythagorean formula and validates the empirically accepted exponent value using MLB data.

Findings

Linear predictor is a first-order approximation of the Pythagorean formula.

Estimated coefficient closely matches the accepted value of 1.82.

Model explains the strong predictive power of the linear predictor.

Abstract

We mathematically prove that an existing linear predictor of baseball teams' winning percentages (Jones and Tappin 2005) is simply just a first-order approximation to Bill James' Pythagorean Won-Loss formula and can thus be written in terms of the formula's well-known exponent. We estimate the linear model on twenty seasons of Major League Baseball data and are able to verify that the resulting coefficient estimate, with 95% confidence, is virtually identical to the empirically accepted value of 1.82. Our work thus helps explain why this simple and elegant model is such a strong linear predictor.