Graph theory-based mathematical modeling and analysis to predict a football dream team

Abstract

The popularity of football among fans to analyze the game has been immense with the advent of internet. The concept of making a dream team in football has become a new fashion for the football lovers. The paper focuses in helping achieving this prediction of a football dream team. The aim of this research is to assess the dynamics of a complex topological structure when prompted with random entities whose attributes are known to us. Using graph theory and vectorial distances, the dream team is evaluated on the basis of individual abilities and interplayer synergy. Instead of focusing on discrete events in a match, this framework proposes an idea in which a dream team is quantified on the basis of their positional attributes. Each player is rated in accordance to the position he is playing, which eventually helps in finding the overall team rating. The second part of this research uses graph theory to evaluate structural and topological properties of interpersonal interactions of teammates. Teammates are treated as nodes of a graph, where each edge exemplifies the strength of their interpersonal interaction. The strength of the bond depends on on-field interactions via ball passing, ball receiving and communication which depend on experience of playing together, Nationality and Club. The methodology adopted in this paper can be a formidable basis for similarly situated larger setups involving much larger intricacies. Using this framework, we can see the behavior of a hypothetical topological structure whose node attributes are known to us, thus projecting its performance as a team and individual entities.