Measure of the Ability Dominance of Tournament Systems and Subjective Judgment

Tomoyuki Maekawa, Hidehito Honda, Kazuhiro Ueda

Abstract: Tournament systems in sports contests need to reflect players' performance appropriately as well as draw people's interest. In this study, we formulate the relationship between players' strengths and winning probabilities based on the Elo rating system. We propose a scale for evaluating the extent to which a tournament system reflects the strength of players. To calculate the scale concretely, we explain three approaches. We then conduct a web survey to investigate people's judgments of ability dominance and the interestingness of tournament systems. We simulate a number of types of tournament systems to predict the result by using stochastic modeling. The results show that the people's judgments of ability dominance are consistent with the stochastic scale and that the expected interestingness reflects the uncertainty of winning. Our findings will be helpful for designing and evaluating systems of real sports contests.