A network-based dynamical ranking system

Physics – Physics and Society

Scientific paper

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Scientific paper

Ranking players or teams in sports is of practical interests. From the viewpoint of networks, a ranking system is equivalent a centrality measure for sports networks, whereby a directed link represents the result of a single game. Previously proposed network-based ranking systems are derived from static networks, i.e., aggregation of the results of games over time. However, the score (i.e., strength) of a player, for example, depends on time. Defeating a renowned player in the peak performance is intuitively more rewarding than defeating the same player in other periods. To account for this factor, we propose a dynamic variant of such a network-based ranking system and apply it to professional men's tennis data. Our ranking system, also interpreted as a centrality measure for directed temporal networks, has two parameters. One parameter represents the exponential decay rate of the past score, and the other parameter controls the effect of indirect wins on the score. We derive a set of linear online update equations for the score of each player. The proposed ranking system predicts the outcome of the future games with a higher accuracy than the static counterparts. It is also capable of tracking temporal fluctuations of individual players' scores.

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