Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > History and Overview

arXiv:1406.0758 (math)
[Submitted on 29 May 2014]

Title:Pythagoras at the Bat

Authors:Steven J. Miller, Taylor Corcoran, Jennifer Gossels, Victor Luo, Jaclyn Porfilio
View PDF
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.
Comments: Version 1.0, 25 pages, 6 images. This is an older version; a slightly updated version will appear in "Social Networks and the Economics of Sports", to be published by Springer-Verlag
Subjects: History and Overview (math.HO); Other Statistics (stat.OT)
Cite as: arXiv:1406.0758 [math.HO]
  (or arXiv:1406.0758v1 [math.HO] for this version)
  https://doi.org/10.48550/arXiv.1406.0758

Submission history

From: Steven Miller [view email]
[v1] Thu, 29 May 2014 04:33:52 UTC (701 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.HO
< prev   |   next >
new | recent | 2014-06
Change to browse by:
math
stat
stat.OT

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)