Using equations from power indices to analyze figure skating teams

Power indices were originally developed to measure voting power. However, Saari and Sieberg (Games Econ Behav 36:241–263, 2001) and Saari (Chaotic elections, American Mathematical Society, Providence, 2001a) have suggested that the equations from power indices could potentially be used in some sports contexts as a way of evaluating athletes. This article explores this idea in the context of figure skating. The International Skating Union developed team events in figure skating for the 2014 Winter Olympic Games in Sochi, Russia and for other major competitions. In this article, we show how the Shapley–Shubik and Banzhaf indices can be used to analyze contributions of athletes to their countries’ teams in figure skating team events. We illustrate this approach by analyzing the results from the 2014 Winter Olympic Games figure skating team event. We also discuss some ways in which the numbers assigned by the equations from power indices can be used in the figure skating context.