Sunday, December 10, 2006

Network study of Brazilian soccer players

Two brazilian physicists got a CD-ROM from a famous sports magazine (Revista Placar - 2003) packed with historical data (yearly stats covering 13,411 soccer players and 127 clubs) and modeled a network representing the connection between brazilian soccer players (players are connected when they played together on a club).

As a summary of the scientific article, here are some interesting findings:

  • Average degree of separation: 3.29: That means a player can reach any other player with an average of 3.29 hops. In other words, the network can be classified as a small-world (similar findings were made for movie actors who starred on the same movie, mathematicians who co-authored papers, etc).
  • The network was broken in many clusters in 1971 and 1972, after that there is only one component. Which means that in the early seventies there wasn't much mobility among clubs: some players and the players they've played with used to work on the same clubs.
  • The network is becoming more assortative with time: This seems to indicate the existence of a growing segregationist pattern, where the players transfer occurs, preferentially, between teams of the same size. This also means that players are increasingly more likely to play with players equally well-connected. This same behaviour is found on the network of mathematicians who co-authored papers.
  • The mean connectivity is increasing. The authors can think of two reasons for that: the player’s professional life is turning longer and/or the players transfer rate between teams is growing up.
  • The clustering coefficient is decreasing with time: Also in this case, there may be two possible explanations: the players transfer rate between national teams is increasing - - so players get a chance to play in several clubs, thus generating less clusters of clubs - and the exodus of the best Brazilian players to foreigner teams (which has increased, particularly, in the last decades).
  • Choosing randomly, a Brazilian soccer player has ten times less chance to have scored 36 goals than 13 goals. The player with the highest score is Roberto Dinamite with 186.
If you're interested on the type of analysis done on the referenced article, a great introduction to the new science field dedicated to studying networks can be found on Linked: How Everything Is Connected to Everything Else and What It Meansby Albert-Laszlo Barabasi (who is cited on the article itself).