Towards fair ranking of Olympics achievements: the case of Sydney 2000
Introduction
“Ever since the dissolution of the Soviet Union, the United States leading the medal tally has become the stock story of the Summer Olympics”—this is the way Mainichi Daily News—The International Newspaper of Japan started the article dedicated to this topic on Saturday, September 30, 2000. In this sense, Sydney 2000 XXVII Summer Olympic Games was not an exception. Or was it? It all depends on the way you count the athletes’ achievements. Too often, according to some critics (Levelplayingfield.org (2000)) the Olympics generate attention about who has won the most medals rather than for whom winning those medals represents the greatest accomplishment—which, it is claimed, contradicts the very core of the Olympic spirit.
Surprisingly enough, despite their obvious importance for the area of sport and Olympics, Operations Research oriented discussions of various ranking systems so far were very limited [1]. The best-known reference containing a summary for Operations Research applications in sport [2], as well as the more recent Special Issue of the European Journal of Operational Research [3], discuss the issues such as strategies in team sports, planning and scheduling of sporting events and competitions, decision making in individual sports, but provide virtually no discussion on ranking systems and “fair” sports awards design. Since these reviews are very well written and quite complete, this leads the reader to the conclusion that the analysis of ranking systems within the context of sport competitions has been somewhat neglected by the operations research professionals. Even very recently published papers by Lozano et al. [4] and Lins et al. [5] concentrate more on the technical issues of the data envelopment analysis-based approach to measure the performance of nations at the Summer Olympics such as zero-sum modifications and cross-efficiency analysis.
The difference between the work of Lozano et al. [4] and Lins [5] and this paper is as follows:
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this paper combines the power of data-mining tools and DEA-based approach to present a study of the factors influencing countries’ preferences towards different ranking systems
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this paper uses different sets of input parameters for the DEA study
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this paper uses the “utilities” of medal counts, not the numbers of medals per se, as outputs for the study
Leaving the issues of the Olympic spirit beyond the scope of this paper, the objective of this discussion is to address the Operations Research related questions posed by the arguments presented above, such as whether it is possible to design an objective impartial system of analysis of the Olympic results which the majority of participating countries would agree upon as a measuring tool without significant bias towards, lets say, countries with large population, or “rich” countries—those whose GDPs are significantly higher than the average. One of the specific issues this paper addresses is the relationship between the fact that the country naturally belongs to a given group of countries based on their demographic and/or developmental characteristics and its tendency to have specific preferences as far as the concept of fair ranking is concerned. This is achieved by combining data mining techniques of unsupervised learning type (self-organizing maps) and DEA-based follow-up study.
It is reasonably obvious that none of the ranking systems commonly used to summarize and compare the Olympics achievements of different countries take into account the multiple criteria and multiple attribute nature of the situation under consideration. This study also demonstrates that the introduction of the multiple criteria framework, where each criterion is assigned its own weight that is proportional to the contribution of this criterion to the overall picture, would allow much more flexible modelling framework for the situation under consideration.
The rest of this study is organized as follows: the next section provides the discussion of various ranking systems used in sport; Section 3 describes the input parameters used in this study; unsupervised data mining technique of Self-Organizing Maps and its applications to the problem under consideration is discussed in Section 4; Section 5 is dedicated to the analysis of single-factor vs. total-factor productivity approach and the ranking problem under consideration is reformulated as a data envelopment analysis model using total-factor productivity paradigm; Section 6 is concentrating on the outputs of the model; Section 7 presents the discussion of the results of the DEA model being applied; while Section 8 concludes the paper.
Section snippets
Alternative ranking systems
Consider the following example: a new winner emerged in the medal stakes—tiny Bahamas. With a population of just 307,000 Bahamas’ two medals (one gold and one silver) have pushed it to the top of a table that was maintained by the Australian Bureau of Statistics which measured the number of medals won on a per capita basis (Australian Bureau of Statistics website: http://www.abs.gov.au). For Bahamas, this number is 154,000 per medal, while for the United States it is 2,870,000. This means that
Data description
The issues of data availability and relevance for a given case study usually lead to a selection of a minimum data set—the one that reflects the trade-off between the authors’ understanding of the underlying process and considerable difficulty of obtaining solid quality data related to the points under consideration. In this particular case study, the problem is further complicated by the necessity of getting the information on all participants of Sydney 2000 Olympics, including the countries
Identifying homogenous groups of participants by clustering
Based on the data attributes described above, the problem of clustering participating countries into groups each of which contains members of similar profile was addressed. Self-organising maps (SOMs) [6], [7] is the best-known unsupervised neural network approach to clustering. Its advantage over traditional clustering techniques such as the k-means algorithm [8] lies in the improved visualization capabilities resulting from the two-dimensional map of the clusters. Often patterns in a
Productivity analysis framework
Having familiarized ourselves with the factors influencing countries’ performance and corresponding grouping of participants, in this section we consider the ranking problem posed in the beginning of this paper from a productivity measurement perspective. This framework regards every participating team as a unit capable of producing certain useful outputs by consuming a variety of inputs. Obviously, the smaller the amount of inputs consumed and the larger the amount of outputs produced, the
Defining appropriate outputs
It is mentioned by a number of authors (including Coelli et al. [17]), when selecting input parameters for a DEA-based model, special care should be exercised in order not to include inputs which are not directly relevant to the problem. One of the limitations of DEA is that the method itself is not capable of understanding whether the inputs and outputs suggested are really linked by the production process under consideration, and therefore it is up to the decision maker to carefully select
DEA results and discussion
Software package DEAP [4] was used to obtain the solution for this DEA model. Table 4 provides most detailed information regarding different teams’ efficiencies under the assumption of constant return to scale (column 5), variable return to scale (column 6), scale efficiency (column 7), and whether the country is operating on increasing (irs)/decreasing (drs) returns to scale. Also, for every country, the list of peers (i.e. other teams a given country found itself to be comparing to) as well
Summary and conclusions
In this paper, a study of the methodology combining data mining techniques and DEA to analyze the real achievements of various Olympics participants is presented. The discussion is stimulated by the following question: whether it is possible to design an objective impartial system of analysis of the Olympics results which the majority of participating countries would agree upon as a measuring tool without significant bias towards some of the participants.
As well as analyzing some existing
References (18)
- et al.
Olympic ranking based on a zero sum gains DEA model
European Journal of Operational Research
(2003) - et al.
Classifying and characterizing efficiencies and inefficiencies in data envelopment analysis
Operations Research Letters
(1986) A new measure of baseball batters using DEA
Annals of Operations Research
(1997)Operations research in sports
- Sport and computers. European Journal of Operational Research 2003,...
- et al.
Measuring the performance of nations at the summer olympics using data envelopment analysis
Journal of the Operational Research Society
(2003) Self-organized formation of topologically correct feature maps
Biological Cybernetics
(1982)Self-organisation and associative memory
(1988)- et al.
Data clusteringa review
ACM Computing Surveys
(1999)