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G-Elo: generalization of the Elo algorithm by modeling the discretized margin of victory

  • Leszek Szczecinski EMAIL logo
Published/Copyright: February 10, 2022
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Journal of Quantitative Analysis in Sports
From the journal Journal of Quantitative Analysis in Sports Volume 18 Issue 1

Abstract

In this work we develop a new algorithm for rating of teams (or players) in one-on-one games by exploiting the observed difference of the game-points (such as goals), also known as a margin of victory (MOV). Our objective is to obtain the Elo-style algorithm whose operation is simple to implement and to understand intuitively. This is done in three steps: first, we define the probabilistic model between the teams’ skills and the discretized MOV variable: this generalizes the model underpinning the Elo algorithm, where the MOV variable is discretized into three categories (win/loss/draw). Second, with the formal probabilistic model at hand, the optimization required by the maximum likelihood rule is implemented via stochastic gradient; this yields simple online equations for the rating updates which are identical in their general form to those characteristic of the Elo algorithm: the main difference lies in the way the scores and the expected scores are defined. Third, we propose a simple method to estimate the coefficients of the model, and thus define the operation of the algorithm; it is done in a closed form using the historical data so the algorithm is tailored to the sport of interest and the coefficients defining its operation are determined in entirely transparent manner. The alternative, optimization-based strategy to find the coefficients is also presented. We show numerical examples based on the results of the association football of the English Premier League and the American football of the National Football League.

Keywords: adjacent categories model; Elo algorithm; margin of victory; rating
Corresponding author: Leszek Szczecinski, Institut National de la Recherche Scientifique, Montreal, Canada, E-mail:

  1. Author contribution: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The author declares no conflicts of interest regarding this article.

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Received: 2020-10-19
Revised: 2021-10-12
Accepted: 2022-01-07
Published Online: 2022-02-10
Published in Print: 2022-03-26

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. G-Elo: generalization of the Elo algorithm by modeling the discretized margin of victory
  4. Evaluating the performance of elite level volleyball players
  5. Review
  6. Optical tracking in team sports
  7. Research Article
  8. MSE-optimal K-factor of the Elo rating system for round-robin tournament
  9. Influence of advanced footwear technology on sub-2 hour marathon and other top running performances
https://doi.org/10.1515/jqas-2020-0115
Keywords for this article
adjacent categories model; Elo algorithm; margin of victory; rating

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. G-Elo: generalization of the Elo algorithm by modeling the discretized margin of victory
  4. Evaluating the performance of elite level volleyball players
  5. Review
  6. Optical tracking in team sports
  7. Research Article
  8. MSE-optimal K-factor of the Elo rating system for round-robin tournament
  9. Influence of advanced footwear technology on sub-2 hour marathon and other top running performances
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