QM logo


2010 Football World Cup Graphs

A team's strategy in one graph

By Javier López Peña and Hugo Touchette
School of Mathematical Sciences
Queen Mary, University of London

Paper on the football graphs

  • J. Lopez Pena, H. Touchette, A network theory analysis of football strategies. Proc. Euromech Physics of Sports Conference, 2012. arxiv:1206.6904

Some explanations

  • Centrality: The centrality measure displayed in the tables is the 'betweenness' of each node or player. The higher the betweenness of a player, the more important that player is in the network.

    Removing the player with highest betweenness will perturb the network or team most. 

    The player with highest betweenness is not necessarily the player receiving or making the largest number of passes. It is the player linking (over many passes) the largest number of other players.

    For the mathematical definition of betweenness, see Wikipedia
  • Centers of the network: We select the centers of a team as those players that have minimal distance to all other players. Thus a center of a team is a player that is easily reachable with only one pass.

    This may be confusing, but being a center does not necessarily mean having a high betweenness (centrality).

    For more information about graph distance, see Wikipedia
  • More about graph theory: see Wikipedia or MathWorld

Where to find the data

The pass data is freely available from the FIFA website
  1. From the 2010 World Cup site select 'Players'
  2. Select any player (e.g., Pique)
  3. Select 'Statistics'
  4. Select 'Passing distribution'
You'll find there the passes to and from all the other players in the same team.

Look also at the 'heatmap', the position density of the player. Interesting stuff.


  • Thanks to J. J. Merelo Güervós for the idea of using the FIFA data for network analysis
  • Thanks to Matt Parker and Simon Levey for writing the press release
  • Thanks also to Ana Belinda Peñalver Peña for spotting a few errors and imprecisions on the website
  • The data was aggregated from the FIFA website and processed using the mathematical software SAGE
  • The graphs were produced with the mathematical software Mathematica (version 7) available from Wolfram Research
  • A simplified version of the Mathematica notebook used to generate the graphs can be found here
  • The shirt pictures are from Wikipedia
  • The English formation shown is the one used on their last match against Germany
  • The Holland formation shown is the one used against Uruguay
  • The Spanish formation shown is the one that includes Torres
  • Copyright: Queen Mary, University of London 2010 for all images
  • For any inquiries, other than mathematical, please contact the Press Office of Queen Mary
© HT, JL 2010