Key Players and Key Groups in Teams: A Network Approach Using Soccer Data

This paper provides a way of evaluating a player's contribution to her team and relates her effort to her salaries. We collect data from UEFA Euro 2008 Tournament and construct the passing network of each team. Then we determine the key player in the game while ranking all the other players too. Next, we identify key groups of players to determine which combination of players played more important role in the match. Using 2010 market values and observable characteristics of the players, we show that players having higher intercentrality measures regardless of their field position have significantly higher market values.Social networks, team game, centrality measures

Rank Centrality: Ranking from Pair-wise Comparisons

The question of aggregating pair-wise comparisons to obtain a global ranking over a collection of objects has been of interest for a very long time: be it ranking of online gamers (e.g. MSR's TrueSkill system) and chess players, aggregating social opinions, or deciding which product to sell based on transactions. In most settings, in addition to obtaining a ranking, finding `scores' for each object (e.g. player's rating) is of interest for understanding the intensity of the preferences. In this paper, we propose Rank Centrality, an iterative rank aggregation algorithm for discovering scores for objects (or items) from pair-wise comparisons. The algorithm has a natural random walk interpretation over the graph of objects with an edge present between a pair of objects if they are compared; the score, which we call Rank Centrality, of an object turns out to be its stationary probability under this random walk. To study the efficacy of the algorithm, we consider the popular Bradley-Terry-Luce (BTL) model (equivalent to the Multinomial Logit (MNL) for pair-wise comparisons) in which each object has an associated score which determines the probabilistic outcomes of pair-wise comparisons between objects. In terms of the pair-wise marginal probabilities, which is the main subject of this paper, the MNL model and the BTL model are identical. We bound the finite sample error rates between the scores assumed by the BTL model and those estimated by our algorithm. In particular, the number of samples required to learn the score well with high probability depends on the structure of the comparison graph. When the Laplacian of the comparison graph has a strictly positive spectral gap, e.g. each item is compared to a subset of randomly chosen items, this leads to dependence on the number of samples that is nearly order-optimal.Comment: 45 pages, 3 figure

Discovering Key Players and Key Groups in a Soccer Team Using Centrality Measures

In this thesis, I introduce that passing performance is crucial skill in the soccer game. I provide network centrality approaches to discover key players and key groups in a soccer team. The Utility Model of game theory evaluates each soccer player’s contribution to his team outcome. The approach of finding key players is to implement soccer passing network data with the combination of Nash Equilibrium with Bonacich Centrality Measure. We identify the key player by finding the top individual Inter-Centrality Measure, and also identify the key group of players that match better together in the game. The results verification will use 2013 market values, media attention, and team unbeaten probability by his appearance/absence