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

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  • Szczecinski Leszek

    (Institut National de la Recherche Scientifique, Montreal, Canada)

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.

Suggested Citation

  • Szczecinski Leszek, 2022. "G-Elo: generalization of the Elo algorithm by modeling the discretized margin of victory," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 18(1), pages 1-14, March.
  • Handle: RePEc:bpj:jqsprt:v:18:y:2022:i:1:p:1-14:n:5
    DOI: 10.1515/jqas-2020-0115
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    References listed on IDEAS

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    1. Mark E. Glickman, 1999. "Parameter Estimation in Large Dynamic Paired Comparison Experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 377-394.
    2. Kovalchik, Stephanie, 2020. "Extension of the Elo rating system to margin of victory," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1329-1341.
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    Cited by:

    1. László Csató, 2024. "Club coefficients in the UEFA Champions League: Time for shift to an Elo-based formula," International Journal of Performance Analysis in Sport, Taylor & Francis Journals, vol. 24(2), pages 119-134, March.
    2. L'aszl'o Csat'o, 2023. "Club coefficients in the UEFA Champions League: Time for shift to an Elo-based formula," Papers 2304.09078, arXiv.org, revised Oct 2023.

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