Innovative Applications of O.R.Performance benchmarking of achievements in the Olympics: An application of Data Envelopment Analysis with restricted multipliers
Introduction
Data envelopment analysis (DEA) is a mathematical programming method for measuring the relative efficiencies of peer decision-making units (DMUs). Since the first DEA model was introduced by Charnes, Cooper, and Rhodes (1978), many models have been developed for performance benchmarking. Thompson, Singleton Jr, Thrall, and Smith (1986) employed a DEA methodology and developed an assurance region method to refine efficiency evaluations with survey data and expert opinions. A further generalization of the assurance region method is provided by Charnes, Cooper, Wei, and Huang (1989) and Charnes, Cooper, Huang, and Sun (1990), in which the feasible region of weights is restricted to a polyhedral convex cone. Such DEA models impose multiplier constraints on the inputs or outputs and provide acceptable evaluations due to the use of additional information such as prior knowledge, experience, and expert opinions.
Japan has become an Olympic setting since the Summer Olympic Games were first staged in Asia in 1964. After Tokyo was selected as the host city of the 2020 Summer Olympics, the Japanese government established a sports agency in 2015 and launched several athlete development initiatives to increase its medal tallies. As the upcoming Olympic Games gets closer, interest in predicting and measuring the performance of Olympic achievements is rising. According to the Japanese Olympic Committee (JOC), Japan plans to win 30 gold medals in the upcoming Summer Olympics. However, due to the developing global situation in light of the COVID-19 pandemic, the International Olympic Committee (IOC) and JOC announced that the Tokyo 2020 Summer Olympic games are rescheduled to a date beyond 2020 but not later than summer 2021. As the IOC President Thomas Bach said in the message titled Olympism and Corona II, sport is widely recognized as an essential factor in fighting the pandemic and accepted as an integral part of the solution for the crisis recovery. We believe that the performance of the Olympic Games Tokyo 2020 will be an important factor that contributes to building a better world after COVID-19. One of the research topics in our study is to investigate and predict the performance of the Olympic Games Tokyo 2020. However, to illustrate the validity of our method, we evaluate the performance of the past five Olympic games and examine the feasibility of Brazil’s target to be in the top 10 medals table in Rio 2016.
Moving on, PricewaterhouseCoopers also predicts the total number of medals for the major participating nations every Olympic year. Past predictions were reasonably accurate by adopting a multiple regression method using explanatory variables such as the total number of medals won at the previous Olympic games, the GDP, and the population. However, due to the lack of official Olympic rankings of nations relative to the achieved number of gold, silver, and bronze medals, several studies employ DEA to benchmark the performance of participating nations (e.g., de Carlos, Alén, and Pérez-González (2017); Churilov and Flitman (2006); Lei, Li, Xie, and Liang (2015); Li, Lei, Dai, and Liang (2015); Li, Liang, Chen, and Morita (2008); Lins, Gomes, de Mello, and de Mello (2003); Lozano, Villa, Guerrero, and Cortés (2002); Yang, Wu, Liang, and O’Neill (2011); Yang, Li, and Liang (2015), Jablonsky (2018)). It is worth noting that the valuations of gold, silver, and bronze medals are identical in the regression analysis, while the DEA models with restricted multipliers account for the difference among the valuation of three medal colors. However, previous studies on evaluating Olympic medals do not focus on multiplier restrictions for input. To fill this research gap, this study incorporates a data fitting technique of medal prediction using ordinary least squares regression (OLS) in input multiplier restrictions of the conventional DEA model. Such a model can be used to benchmark the performance of Olympic achievements, given the prediction of a medal total, which is an upper bound of the total number of medals. Other models attempting to combine both the OLS and DEA include stochastic nonparametric envelopment of data (StoNED) proposed by Kuosmanen (2006) (see also Kuosmanen & Johnson, 2010). The production frontier of the StoNED approach is based on a convex nonparametric least square, which is a nonparametric representation of a monotonic and concave regression function. By contrast, the production possibility set in our approach is derived from the multiplier-formulation DEA technology, and the multiplier restrictions incorporated are based on the OLS technique. We also propose a decomposition of the efficiency for analyzing the effectiveness of host nations and athlete development initiatives.
The remainder of the paper is structured as follows. Section 2 provides methodological details of the multiplier formulation and decomposition of the proposed DEA model. Section 3 analyzes the performance of Olympic achievements for participating nations and examines the effectiveness of host nations and athlete development initiatives. Section 4 presents the study on examining the target of being in the top 10 for Brazil in Rio 2016. Section 5 provides a further study on Japan’s target of 30 gold medals for the upcoming Summer Olympic Games. Section 6 concludes.
Section snippets
A DEA model with restricted multipliers for Olympic evaluation
In this study, DMUs are the participating nations to have won at least one medal to start the process of benchmarking the performance of Olympic achievements. Suppose that there are DMUs (nations) to be evaluated. Three output variables are considered: the number of gold (), silver (), and bronze medals (). Regarding the inputs, we adopt the GDP () and the population (). The previous DEA literature commonly uses GDP per capita instead of GDP, as argued by Lozano et al. (2002),
Application
This section analyzes the performance of Olympic achievements for 412 DMUs by using the proposed DEA model in Section 2. The DMUs are nations that participated in the Olympic games of Sydney 2000 (80), Athens 2004 (74), Beijing 2008 (86), London 2012 (85), and Rio 2016 (87). The numbers in parentheses count the participating nations that have won at least one medal. In addition, the nations in different Olympic years are treated as different DMUs.
A study on Brazil’s target to be in the top 10 medals table in Rio 2016
In Section 3.4, we concluded that the effectiveness of the host nation for Brazil in Rio 2016 is observable and the effectiveness of the athlete development initiatives are also observable relative to the indices and . In 2012, the Brazilian Olympic Committee (COB) set the target of being in the top 10 medals table for the Rio 2016 Summer Olympic Games. However, according to the medal tally published by the International Olympic Committee (IOC), Brazilian athletes won 19 medals
A further study on Japan’s target of 30 gold medals in Tokyo 2021
In 2018, the Japanese Olympic Committee (JOC) set the target of 30 gold medals for the upcoming Summer Games in Tokyo. In this section, we examine whether such a target will be achieved or not. The input vector of Japan () in Rio 2016 is used for predicting the total number of gold medals in Tokyo 2021, which is . For the input vector we consider the following output possibility set that satisfies :
Conclusion
This study proposed a multiplier-formulation DEA model by considering the substantial medal total, which is considered as an upper bound of the number of medals and can be derived by a data fitting technique subject to the downside deviations of DMUs. We show that the efficiency of the proposed DEA model can be decomposed into the achievement ratio of substantial medal total and the unit value index of medals. The efficiency and decomposed components are further used to benchmark the
Acknowledgments
The authors are grateful to the anonymous referees for useful comments which improved the presentation of the original version of this paper. This work was supported by JSPS KAKENHI Grant Number 17K01251.
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