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Extension of the Elo rating system to margin of victory

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  • Kovalchik, Stephanie

Abstract

The Elo rating system is one of the most popular methods for estimating the ability of competitors over time in sport. The standard Elo system focuses on predicting wins and losses, but there is often also interest in the margin of victory (MOV) because it reflects the magnitude of a result. There have been few theoretical investigations and comparisons of Elo-based models. In the present study, we propose four model options for an MOV Elo system: linear, joint additive, multiplicative, and logistic. Notations and guidance for tuning each model are provided. The models were applied to men’s tennis for several MOV choices. The results showed that all MOV approaches using within-set statistics improved the predictive performance compared with the standard Elo system, but only the joint additive model yielded unbiased ratings with stable variance in the simulation study. This general framework for MOV Elo ratings provide sports modelers with a new set of tools for building systems to rate competitors and forecast outcomes in sport.

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  • Kovalchik, Stephanie, 2020. "Extension of the Elo rating system to margin of victory," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1329-1341.
    • Handle: RePEc:eee:intfor:v:36:y:2020:i:4:p:1329-1341
    DOI: 10.1016/j.ijforecast.2020.01.006
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    Cited by:

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    2. 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.
    3. Angelini, Giovanni & Candila, Vincenzo & De Angelis, Luca, 2022. "Weighted Elo rating for tennis match predictions," European Journal of Operational Research, Elsevier, vol. 297(1), pages 120-132.
    4. He, Xue-Zhong & Treich, Nicolas, 2017. "Prediction market prices under risk aversion and heterogeneous beliefs," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 105-114.
    5. Lim, Alejandro & Chiang, Chin-Tsang & Teng, Jen-Chieh, 2021. "Estimating robot strengths with application to selection of alliance members in FIRST robotics competitions," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    6. Marc Garnica-Caparrós & Daniel Memmert & Fabian Wunderlich, 2022. "Artificial data in sports forecasting: a simulation framework for analysing predictive models in sports," Information Systems and e-Business Management, Springer, vol. 20(3), pages 551-580, September.
    7. Lasek, Jan & Gagolewski, Marek, 2021. "Interpretable sports team rating models based on the gradient descent algorithm," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1061-1071.
    8. Ramirez, Philip & Reade, J. James & Singleton, Carl, 2023. "Betting on a buzz: Mispricing and inefficiency in online sportsbooks," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1413-1423.

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