I have decided to try something new for this blog. Throughout November, which has five Fridays this year, I will post a five-part series on Complexity and Complex Systems as they appear and/or pertain to college life.

And nothing says college like college sports—personally, I don’t care for sports, but even I cannot deny the marriage of higher education and physical competition.

A great place to start learning about Complex Systems, I took a look through the New England Complex Systems Institute website, almost immediately coming across Luís Vilar et al’s paper on soccer.

The authors are concerned with the emergent behavior of teams as a whole. That is, instead of analyzing the actions of individual players, they examine how these actions interlock to form complex patterns at a team-wide level.

Physical Competition. A few years ago, in October 2010, eight cameras and tracking software captured the exact movements of all players on both teams, excluding goalies. This footage lead to a grid representing the playing field and points moving about the grid, just as the players moved in real life.

A series of calculations were performed based on these points to cut the grid into “areas of play.” A team’s “advantage” in each of these areas was based on the number of players each team had there. For example, if Team A had 3 players and Team B had 2 players in the center play area, Team A would have an advantage of 1 and B an advantage of -1.

Actions of Individual Players. As a player moves from one point on the field to another, he decreases his team’s advantage at one location and increases it at another.

Vilar et al exploit this increase/decrease effect to represent a team’s overall strategy, by counting how many times each team had each advantage in each play area. A soccer strategy, then, taking into account the interactions between teams, could be represented with seven histograms: one for each play area.

Complex Patterns. Many factors go into the decisions made by each player, including the decisions made by each other player. Even in an ideal, non-random world, this level of complex interaction is too great to work out by hand or machine.

Vilar et al avoid these difficulties by following a statistical route. The movements of players and evolution of strategies are all contained within the histograms the authors produced.

They showed that the winning team more consistently maintained higher advantages at key play areas throughout the game: the front when attacking and the rear when defending.

The losing team, although following a similar strategy, had higher variation in their strengths, ultimately leading to their defeat. ∎

Read more in this series and follow me on Twitter. Let’s chat sometime.