In 2006 two nations took to the field in Berlin, Germany in front of a worldwide audience of 715 million people. Italy were to play France in the final of the FIFA World Cup. The match itself would later become famous for that “head butt” by France’s Zinédine Zidane. But despite being eclipsed by a moment of madness, the 90 minutes of the match played out with each team only scoring 1 goal, ending with Italy winning it on penalties.
Football at its most basic is one played between two teams of eleven players each using a spherical ball. With each team striving to score by driving the ball into the opposing goal — sometimes as the result of skillful interactions among players, other times by hook or by crook. This is the view of researchers from Japan in a recent paper. Publishing in PLoS One the team analysed the 2006 FIFA World Cup final from a purely mathematical view, reducing players to nodes and vertices connected by links representing passes. Apt, as the match itself had nothing exceptional about it.
“Football can be regarded from the network perspective as a competitive relationship between two cooperative networks with a dynamic network topology and dynamic network node.”
Their aim was to examine the network. The network of passes and interactions between players, nodes, and hubs. And to see if they could apply the power law to the perceived network. The power law, a way to describe two differing quantities, can be applied to anything and has been applied to distributions of a wide variety of physical, biological, and man-made phenomena.
Football can be a metaphor for everything. Life, death, birth and redemption. Nations that are the punchlines to each others jokes and nations that drop bombs on each other are reconciled through football.
Football, in their eyes, is simply a competition between two complex networks — a competitive relationship between two cooperative networks with a dynamic network topology and dynamic network node. Two networks trying to get the better of one another by their inherent network actions and interactions — passes and strikes.
The self-organization of networks frequently coincides with the appearance of power-law distributions. They analyzed the probability distribution that emerged in the passing behavior. Investigating the human dynamic movement pattern in a real setting. Indeed, they did show that the power law degree distribution presented itself in the passing behaviour between those two teams in Berlin.
Your playmaker, the player Italians call “fantasista” is a node that has more connections than an average node — a hub through which all things go through. Researchers highlighted this as a unique feature in football games — or more accurately the “stochastically switched dynamics” of the playmaker throughout the game. In many other networks the hub is taken as a static feature. In football, the function of the hub switches, shifting the topology of the network depending on the attacking opposing team.
What goes on during a football game can be described another way — two competing networks that will never synchronise because their “goals” are mutually exclusive. Two networks connected by a feedback loop — external inputs represented by the actions of the opposing team — changing and modifying the system inherently.
Analysing a football match in such a way hasn’t really been done before. All in all, it allows a different view of a game, and also has its implications that can be applied to biological and communication networks. But, as of yet, cannot be used to predict anything about how the game will possibly unfold.
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Yamamoto, Y., & Yokoyama, K. (2011). Common and Unique Network Dynamics in Football Games PLoS ONE, 6 (12) DOI: 10.1371/journal.pone.0029638