Performance benchmarking of achievements in the Olympics: An application of Data Envelopment Analysis with restricted multipliers

Data envelopment analysis (DEA) is a useful tool for measuring the relative efficiencies of participating nations in the Olympic Games. DEA models with restricted multipliers have been used to refine efficiency evaluations by imposing additional information. Existing DEA models for evaluating Olympic medals do not focus on multiplier restrictions regarding input. To fill this research gap, this study incorporates a data fitting technique of medal prediction using ordinary least squares regression in input multiplier restrictions of the conventional DEA model. We show that the efficiency of the proposed model can be decomposed into the achievement ratio of substantial medal total and the unit value index of medals. Such decompositions can be used to analyze the effectiveness of host nations and athlete development initiatives. For an illustrative empirical application, we examine the target that the Brazilian Olympic Committee (BOC) set for the 2016 Summer Olympic Games (Rio 2016). Our results explain the extremely high feasibility of Brazil's target of being in the top 10 medals table in Rio 2016.