This is a research paper that aims to determine whether a centralized or decentralized passing structure is more beneficial for x school under 16 football team using Markov chains and eigenvector centrality.
Aim -
To determine whether centralized or decentralized passing structure is more beneficial for ___
school under 16 football team using Markov chains and eigenvector centrality.
Introduction -
Analyzing team’s tactics play a crucial role in the football universe to remain competitive. My
school football team has not been performing to their full potential in the recent times and has
faced marginal losses. Our football team presents a very attacking style of football after having
been inspired by the huge football clubs in Europe like Liverpool FC, Borussia Dortmund FC etc.
Our understanding of the reason behind the losses is that the football team cannot capitalize on
the chances created with possession due to a weak link between midfield and attack, which forces
gaps between attack and defense. The lack of a stable midfield allows opponents to counter attack
quickly and score goals. After all, football is a game which is won by goals and a weak midfield po-
sitioning will worsen the condition.
Unfortunately, conventional methods of post-game analysis often fail to analyze and visualize the
complex mathematical implications and patterns sufficiently. Therefore, I have decided to utilize
discrete mathematics in order to provide a concrete and reliable framework that will help my
school football team improve their overall performance. The methods I have used are Markov
chains and eigenvector centrality in order to identify a distinct relation between our positioning
and passing structure and hence, the goals scored and conceded.
Math Concepts -
Graph Theory - to look at the passing structure for a team as a weighted graph with nodes repre-
senting the players and edges representing the passes
Markov Chain model - used in order to find the eigenvector centrality for said graph. 1
1 “Markov Chains.” Brilliant Math & Science Wiki, brilliant.org/wiki/markov-chains/.
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