Pythagoras at the Bat

TL;DR

The paper explores the Pythagorean formula for estimating team strength in sports, providing theoretical justification, analyzing recent data, and discussing potential generalizations to improve predictive accuracy without complex simulations.

Contribution

It offers a theoretical foundation for the Pythagorean formula, analyzes recent season data, and proposes generalizations to enhance predictive power efficiently.

Findings

Data supports the model's accuracy for recent seasons.

Theoretical proofs justify the formula and estimators.

Potential for improved models using play-by-play data.

Abstract

The Pythagorean formula is one of the most popular ways to measure the true ability of a team. It is very easy to use, estimating a team's winning percentage from the runs they score and allow. This data is readily available on standings pages; no computationally intensive simulations are needed. Normally accurate to within a few games per season, it allows teams to determine how much a run is worth in different situations. This determination helps solve some of the most important economic decisions a team faces: How much is a player worth, which players should be pursued, and how much should they be offered. We discuss the formula and these applications in detail, and provide a theoretical justification, both for the formula as well as simpler linear estimators of a team's winning percentage. The calculations and modeling are discussed in detail, and when possible multiple proofs are given. We analyze the 2012 season in detail, and see that the data for that and other recent years support our modeling conjectures. We conclude with a discussion of work in progress to generalize the formula and increase its predictive power \emph{without} needing expensive simulations, though at the cost of requiring play-by-play data.