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Statistical Prediction of Future Sports Records Based on Record Values

Author

Listed:
  • Christina Empacher

    (Institute of Statistics, RWTH Aachen University, D-52056 Aachen, Germany)

  • Udo Kamps

    (Institute of Statistics, RWTH Aachen University, D-52056 Aachen, Germany)

  • Grigoriy Volovskiy

    (Institute of Statistics, RWTH Aachen University, D-52056 Aachen, Germany)

Abstract

Point prediction of future record values based on sequences of previous lower or upper records is considered by means of the method of maximum product of spacings, where the underlying distribution is assumed to be a power function distribution and a Pareto distribution, respectively. Moreover, exact and approximate prediction intervals are discussed and compared with regard to their expected lengths and their percentages of coverage. The focus is on deriving explicit expressions in the point and interval prediction procedures. Predictions and forecasts are of interest, e.g., in sports analytics, which is gaining more and more attention in several sports disciplines. Previous works on forecasting athletic records have mainly been based on extreme value theory. The presented statistical prediction methods are exemplarily applied to data from various disciplines of athletics as well as to data from American football based on fantasy football points according to the points per reception scoring scheme. The results are discussed along with basic assumptions and the choice of underlying distributions.

Suggested Citation

  • Christina Empacher & Udo Kamps & Grigoriy Volovskiy, 2023. "Statistical Prediction of Future Sports Records Based on Record Values," Stats, MDPI, vol. 6(1), pages 1-17, January.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:1:p:8-147:d:1031871
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    References listed on IDEAS

    as
    1. John H. J. Einmahl & Sander G. W. R. Smeets, 2011. "Ultimate 100‐m world records through extreme‐value theory," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(1), pages 32-42, February.
    2. Grigoriy Volovskiy & Udo Kamps, 2020. "Maximum product of spacings prediction of future record values," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 853-868, October.
    3. Noubary Reza D, 2010. "Tail Modeling, Track and Field Records, and Bolt's Effect," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(3), pages 1-21, July.
    4. Jafar Ahmadi & M. Doostparast, 2006. "Bayesian estimation and prediction for some life distributions based on record values," Statistical Papers, Springer, vol. 47(3), pages 373-392, June.
    5. Einmahl, John H. J. & Magnus, Jan R., 2008. "Records in Athletics Through Extreme-Value Theory," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1382-1391.
    6. Grigoriy Volovskiy & Udo Kamps, 2020. "Maximum observed likelihood prediction of future record values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1072-1097, December.
    7. Noubary Reza D, 2005. "A Procedure for Prediction of Sports Records," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 1(1), pages 1-14, October.
    8. Wang, Bing Xing & Yu, Keming & Coolen, Frank P.A., 2015. "Interval estimation for proportional reversed hazard family based on lower record values," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 115-122.
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