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A Comparison of Olympic and Paralympic Performances Percy, DF A comparison of Olympic and Paralympic performances Percy, DF http://dx.doi.org/10.1080/01605682.2018.1447246 Title A comparison of Olympic and Paralympic performances Authors Percy, DF Type Article URL This version is available at: http://usir.salford.ac.uk/id/eprint/46106/ Published Date 2019 USIR is a digital collection of the research output of the University of Salford. Where copyright permits, full text material held in the repository is made freely available online and can be read, downloaded and copied for non-commercial private study or research purposes. Please check the manuscript for any further copyright restrictions. For more information, including our policy and submission procedure, please contact the Repository Team at: [email protected]. Journal of the Operational Research Society ISSN: 0160-5682 (Print) 1476-9360 (Online) Journal homepage: http://www.tandfonline.com/loi/tjor20 A comparison of Olympic and Paralympic performances David F. Percy To cite this article: David F. Percy (2018): A comparison of Olympic and Paralympic performances, Journal of the Operational Research Society, DOI: 10.1080/01605682.2018.1447246 To link to this article: https://doi.org/10.1080/01605682.2018.1447246 © 2018 The Author(s). Published by Taylor & Francis Published online: 21 Mar 2018. Submit your article to this journal View related articles View Crossmark data Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=tjor20 JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY, 2018 https://doi.org/10.1080/01605682.2018.1447246 OPEN ACCESS A comparison of Olympic and Paralympic performances David F. Percy Salford Business School, University of Salford, Salford, UK ABSTRACT ARTICLE HISTORY In 2012, Oscar Pistorius created history as the first amputee sprinter to compete in the Olympics. Received 10 February 2016 Other athletes achieved amazing feats long before the Paralympics were introduced, including Accepted 20 February gymnast George Eyser who won six medals at the 1904 Olympics with a wooden leg, and 2018 others who competed in both Games. An exciting challenge of considerable interest is to KEYWORDS compare performances of Olympic and Paralympic athletes, so contributing to improving Sports; practice of OR; integration of the two competitions. We generalise the recent dynamic shrinkage method for decision support systems; class handicapping and apply it to competition results from equestrian individual dressage at recreation; decision the London 2012 Summer Games and cross country skiing at the Sochi 2014 Winter Games. Our analysis analysis generates promising results and surprising revelations. It also offers a fair method for comparing performances by athletes from other diverse groups, with potential benefits of extra incentive and reward systems for motivating unified sporting participation in general settings. 1. Introduction Ildikó Újlaky-Rejt˝o (Hungary) who won two golds in 1964, deaf swimmer Jeffrey Float (USA) who won a gold The history of multi-sport competitions is rich and in 1984 and blind archer Im Dong-Hyun (South Korea) can be traced back thousands of years. Major interna- who won golds in 2004 and 2008. tional multi-sport competitions began with the modern Speaking before the London 2012 Olympic and Para- Olympic Games, with summer events starting in 1896 lympic Games, the Chair of the Organising Committee, and winter events starting in 1924. Olympic Games are Lord Coe, said: “We want to change public attitudes open to all competitors, though there are now many towards disability, celebrate the excellence of Paralympic other international multi-sport competitions aimed at sport and to enshrine from the very outset that the two specific communities. Perhaps surprisingly, the Deaf- Games are an integrated whole”. This objective was lympic Games for deaf athletes began in the summer achieved with overwhelming success in London and of 1924 and the winter of 1949, whereas the hugely subsequently at the Rio de Janeiro Games in 2016. popular Paralympic Games for athletes with physical Meanwhile, the operational research community has disabilities began in the summer of 1960 and the winter shown considerable interest in performance measure- of 1976. Another important competition is the Special ment for multi-sport competitions. Olympics World Games for athletes with intellectual The predominant technique that has been used for disabilities, which began in the summer of 1968 and the analysing the success of nations at the Olympic Games winter of 1977. Other major international multi-sport is data envelopment analysis (Churilov & Flitman, 2006; competitions include the Commonwealth, Asian, Pan- Gomes & Lins, 2008; Li,Lei,Dai,&Liang, 2015; Li, American, All-Africa, Pacific, European, Youth Olympic, Liang, Chen, & Morita, 2008; Lozano, Villa, Guerrero, and Invictus Games. &Cortés, 2002; Yang, Li, & Liang, 2015; Zhang, Li, There are some remarkable stories of disabled ath- Meng, & Liu, 2009). This procedure is inherently non- letes who participated in open competition at Olympic parametric, which makes it robust against model mis- Games. Among the most notable of these are gymnast specification at the cost of reduced power and clarity. George Eyser (USA) who won three gold medals in 1904 Another recent and relevant method, which is more despite a wooden leg, deaf-mute boxer Carlo Orlandi parametric in nature, is multiple attribute decision mak- (Italy) who won a gold in 1928, lower-leg amputee ing (Ballι & Korukoˇglu, 2014; Li,Kou,Lin,Xu,&Liao, Oliver Halassy (Hungary) who won golds for water 2015; Rezaei, 2015). Both approaches offer ways for polo in 1932 and 1936, Károly Takács (Hungary) who combining observations of several different attributes won golds for shooting in 1948 and 1952 with a badly to compare individual units. The main differences be- injured hand, hammer thrower Harold Connolly (USA) tween those formulations and the developments in this who had Erbs Palsy yet won a gold in 1956, deaf fencer CONTACT David F. Percy [email protected] © The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/ by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. 2 D. F. PERCY paper are that we focus on comparing a single measure In order to combat these problems, Percy (2011) across units that belong to natural or contrived clusters. proposed a shrinkage method for class handicapping, In this respect, we add to the literature by tackling which uses data from only the current competition that the specific problem of comparing disparate groups of is in progress. This method is based on ideas developed competitors. The resulting methodology offers poten- by Efron and Morris (1975), Efron and Morris (1977) tial benefits for applications in many diverse situations. that relate to James-Stein estimators. Copas (1983)pro- In this paper, we consider how, and to what ex- vides a comprehensive description of these estimation tent, we might compare the performances of Olympic procedures and Wang, Huwang, and Yu (2015)present and Paralympic athletes in order to offer enhanced a recent application of them in the context of quality integration of the two competitions. The next section control charts. A subsequent paper by Percy (2013) reviews a suitable methodology for making such com- presents a mathematical justification for this shrinkage parisons and then we generalise this theory to enable method based on an objective Bayesian analysis of a its application to a much wider variety of sports. After suitable probability model. this abstract development, we present some empirical The shrinkage method for class handicapping can be analyses based on data collected from sports compe- applied interactively, either immediately after events titions at the London 2012 Summer Games and the where athletes compete together and results are ob- Sochi 2014 Winter Games. Then we extend these ideas served simultaneously, or dynamically during events to consider applications of the generalised shrinkage where athletes compete sequentially and results are not method to compare diverse categories. Finally, we con- observed simultaneously. There are two purposes of clude the paper by discussing these results, suggesting the present paper: firstly to generalise this approach for how Olympic and Paralympic Games might develop application to a considerably broader range of sports; in future, and considering whether other population secondly to investigate how we might use it to compare subgroups could or should be integrated in a similar the performances of Olympic and Paralympic athletes. manner. To facilitate this analysis, we start with a brief review of the shrinkage method. 2. Shrinkage method for class handicapping Suppose that we observe racing times rij for i = 1, ..., m and j = 1, ..., ni corresponding to athlete The International Paralympic Committee invests con- j in class i.Definer˜i· to be the sample median racing siderable effort in allocating athletes to disability classes, time of class i and r˜·· to be the overall sample median in order to ensure that all athletes in any particular racing time. The purpose of using medians rather than class have
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