Usage of Markov chains as graph theory for mathematical analysis of football

Sammanfattning

In this thesis, we will be exploring how we can use Markov chains as a method to construct a graph during the 2024/2025 season for Hammarby’s women’s football team. This graph will be explored using tools for graphs from the book (Newman, 2010). We study twelve graph-theoretic metrics, and these metrics will measure different aspects of the team and players’ passing structures. These metrics are grouped into Centrality, Bridge, and Similarity measures. Centrality measures how central a player is to the passing structure. Bridges measures how well the team manages to bridge the gap between the different blocks, such as defenders, midfielders and strikers and if there are players who play as bridge players, which makes these gaps smaller. Similarity quantifies how similar different players are in their decisions and if there exist pairs of players who pass more to each other rather than to the rest of the team. We will see that these groups of metrics are precisely the groups in which we can create a model to evaluate these aspects of football better with a machine learning model. We will also see that when it comes to passing structure, the most important players for Hammarby are the defenders, who are most involved in the passing structure and the build-up play. This is due to Alice Carlsson, who is a defender and is the most valuable player when it comes to build-up play for Hammarby based on these metrics. We will also see that the midfielders as a group will be important, as the midfielders have similar scores to the defenders. If we exclude Carlsson, the midfielders are equally important in some metrics.