Analysis of sports statistics via graph-signal smoothness prior

Since teams in a sporting league compete head-to-head according to a structured schedule, it is natural to interpret statistics emanating from competitions as signals on a graph modeling similarities among competing entities. In this paper, we analyse available sports statistics to predict game outcomes from a graph signal processing (GSP) perspective: GSP tools are used to remove (denoise) unwanted variability to reveal underlying predictable trends, and to interpolate missing data-predicted game outcomes in terms of point differential. First, we construct a graph for the desired graph-signal (point differential for every team pair): for an N-team league, we construct N subgraphs Gj, each containing N - 1 nodes representing teams competing against opponent j. We next assign weight to each intra-subgraph edge based on similarity in observed statistics (e.g., total points scored, assists, etc) of the two connecting nodes (teams). We then connect nodes in different subgraphs representing the same teams, where the weight of an inter-subgraph edge connecting nodes in subgraphs Gk and Gi now reflects the similarity between opponents k and l. Finally, assuming a graph-signal smoothness prior, we compute the desired graph-signal on the constructed graph via an alternating convex programming procedure. Experimental results show that our graph-based scheme achieves better prediction than a competing k-nearest neighbor (kNN) scheme.