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Records in Athletics through Extreme-Value Theory

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  • Einmahl, J.H.J.

    (Tilburg University, School of Economics and Management)

  • Magnus, J.R.

    (Tilburg University, School of Economics and Management)

Abstract

In this paper we shall be interested in two questions on extremes relating to world records in athletics.The first question is: what is the ultimate world record in a specific athletics event (such as the 100m for men or the high jump for women), given today's state of the art?Our second question is: how `good' is a current athletics world record?An answer to the second question will also enable us to compare the quality of world records in different athletics events. We shall consider these questions for each of twenty-eight events (fourteen for both men and women).We approach the two questions with the probability theory of extreme values and the corresponding statistical techniques.The statistical model is of nonparametric nature, but some `weak regularity' of the tail of the distribution function will be assumed.We will derive the limiting distribution of the estimated quality of a world record.While almost all attempts to predict an ultimate world record are based on the development of top performances over time, this will not be our method.Instead, we shall only use the top performances themselves.Our estimated ultimate world record tells us what, in principle, is possible now, given today's knowledge, material (shoes, suits, equipment), and drugs laws.
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Suggested Citation

  • Einmahl, J.H.J. & Magnus, J.R., 2006. "Records in Athletics through Extreme-Value Theory," Other publications TiSEM 5cedc3d8-e623-46d5-a550-5, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:5cedc3d8-e623-46d5-a550-51c2eae15b1c
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    References listed on IDEAS

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    1. Michael E. Robinson & Jonathan A. Tawn, 1995. "Statistics for Exceptional Athletics Records," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 499-511, December.
    2. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    3. M. I. Barão & J. A. Tawn, 1999. "Extremal analysis of short series with outliers: sea‐levels and athletics records," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 469-487.
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    Cited by:

    1. Cai, J., 2012. "Estimation concerning risk under extreme value conditions," Other publications TiSEM a92b089f-bc4c-41c2-b297-c, Tilburg University, School of Economics and Management.
    2. Russell Brook T. & Hogan Paul, 2018. "Analyzing dependence matrices to investigate relationships between national football league combine event performances," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 14(4), pages 201-212, December.
    3. 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.
    4. M. Ivette Gomes & Armelle Guillou, 2015. "Extreme Value Theory and Statistics of Univariate Extremes: A Review," International Statistical Review, International Statistical Institute, vol. 83(2), pages 263-292, August.
    5. Daoud, Adel, 2018. "Unifying Studies of Scarcity, Abundance, and Sufficiency," Ecological Economics, Elsevier, vol. 147(C), pages 208-217.
    6. Gbari, Kock Yed Ake Samuel & Poulain, Michel & Dal, Luc & Denuit, Michel, 2016. "Extreme value analysis of mortality at the oldest ages: a case study based on individual ages at death," LIDAM Discussion Papers ISBA 2016012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Ray C. Fair & Edward H. Kaplan, 2017. "Estimating Aging Effects in Running Events," Cowles Foundation Discussion Papers 2100, Cowles Foundation for Research in Economics, Yale University.
    8. Ahmed, Hanan, 2022. "Extreme value statistics using related variables," Other publications TiSEM 246f0f13-701c-4c0d-8e09-e, Tilburg University, School of Economics and Management.
    9. de Valk, Cees, 2016. "A large deviations approach to the statistics of extreme events," Other publications TiSEM 117b3ba0-0e40-4277-b25e-d, Tilburg University, School of Economics and Management.
    10. Hong En Tan & De Wen Soh & Yong Sheng Soh & Muhamad Azfar Ramli, 2021. "Derivation of train arrival timings through correlations from individual passenger farecard data," Transportation, Springer, vol. 48(6), pages 3181-3205, December.
    11. 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.
    12. Kiriliouk, Anna, 2020. "Hypothesis testing for tail dependence parameters on the boundary of the parameter space," Econometrics and Statistics, Elsevier, vol. 16(C), pages 121-135.
    13. Ray C. Fair & Edward H. Kaplan, 2017. "Estimating Aging Effects in Running Events," Cowles Foundation Discussion Papers 3000, Cowles Foundation for Research in Economics, Yale University.
    14. Krajina, A., 2010. "An M-estimator of multivariate tail dependence," Other publications TiSEM 66518e07-db9a-4446-81be-c, Tilburg University, School of Economics and Management.
    15. 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.
    16. Shaul Bar-Lev, 2008. "Point and confidence interval estimates for a global maximum via extreme value theory," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(12), pages 1371-1381.

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    More about this item

    JEL classification:

    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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