PageRank and Load, Closeness, Eigenvector Centralities in Football
How Network Metrics Reveal a Player’s True Role
Football analysis has evolved.
We no longer rely only on counting passes, shots, or possession to explain what happens on the pitch. Today, network analysis helps us understand how teams behave as systems: where the game truly flows, which players connect phases, who belongs to the structural core, and who becomes the team’s trusted destination under pressure.
That’s exactly the mindset behind the analysis available in my Football Hacking web app. Instead of treating passing numbers as isolated stats, the app helps you read matches as networks—where centrality metrics become tactical tools.
👉 Explore the app here (and follow along with the examples in this post):
https://footballhacking.streamlit.app/
In this article, I’ll break down four centrality metrics that, when combined, reveal a player’s real role far better than raw pass counts: load centrality, closeness centrality, eigenvector centrality, and PageRank.
Individually, each metric captures a different layer of the team’s structure.
Together, they give you a framework to answer four questions that matter in real football analysis:
Where does the system depend?
Who is well-positioned to reach everyone quickly?
Who belongs to the influential core?
Who does the team trust as a destination?
Football as a Network System
Let’s align on the mental model.
In a passing network:
Players are nodes.
Passes are edges.
Direction, frequency, and weight matter.
A team is not just 11 isolated individuals—it is a connected system. And every team expresses its model through the shape of that system.
When you open a match inside the Football Hacking web app and inspect the passing network and centrality metrics, you’re looking at a structural fingerprint of the team’s behavior.
👉 Open any match network and start exploring:
https://footballhacking.streamlit.app/
Load Centrality: Where the System Depends
Load centrality measures how much of the network’s total flow passes through a given player.
In simple terms, it answers:
“If the ball is circulating, how much does the system depend on this player to connect different parts?”
A player with high load centrality often acts as:
A bridge between phases or zones
A bottleneck that keeps the network coherent
A structural dependency
These players may not lead the team in passes. What matters is that without them, the network fragments.
Typical football examples include:
A pivot connecting defenders and midfielders
A fullback responsible for most progression on one side
A goalkeeper acting as a distributor under pressure
Key idea: load centrality identifies systemic risk and dependency.
👉 In the app, sort players by load centrality and ask: who does the system rely on?
https://footballhacking.streamlit.app/
Closeness Centrality: Who Can Reach Everyone Fast?
While load centrality is about dependency, closeness centrality is about access.
Closeness centrality measures how close a player is to everyone else in the network, on average. It answers a different question:
“How quickly can this player reach all other players through short paths?”
