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Pythagoras at the Bat

In: Social Networks and the Economics of Sports

Author

Listed:
  • Steven J. Miller

    (Williams College)

  • Taylor Corcoran

    (The University of Arizona)

  • Jennifer Gossels

    (Princeton University)

  • Victor Luo

    (Williams College)

  • Jaclyn Porfilio

    (Williams College)

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 without needing expensive simulations, though at the cost of requiring play-by-play data.

Suggested Citation

  • Steven J. Miller & Taylor Corcoran & Jennifer Gossels & Victor Luo & Jaclyn Porfilio, 2014. "Pythagoras at the Bat," Springer Books, in: Panos M. Pardalos & Victor Zamaraev (ed.), Social Networks and the Economics of Sports, edition 127, pages 89-113, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-08440-4_6
    DOI: 10.1007/978-3-319-08440-4_6
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