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Abstract:
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We assess the competitive balance within two top soccer leagues: La Liga and Bundesliga. In order to facilitate comparisons between teams in different leagues and over time, we use Elo ratings, a score assigned to each team and adjusted after each match based on various match-related variables, to represent a team's strength at a particular point in time. We treat them as functional data over time, where each team has a curve (function) of Elo ratings over an interval of time, and the collection of curves is our sample. To gain insight into the history of success of teams within these leagues, we use a clustering algorithm that accommodates the sparse, irregularly-sampled data to cluster the team curves. After our clustering analysis, we not only trace the curve of each team within each cluster, but also consider team factors that characterize each cluster. Our results confirm our expectations that both La Liga and Bundesliga soccer leagues are dominated by a few teams, indicating that leagues need to review their structures and policies to facilitate greater competitive balance.
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