Using “Small World” Theory to better understand team dynamics in soccer
As professional sports continue to grow increasingly competitive, with every team searching for every advantage they can incur, increasingly advanced methods of analysis are being used to optimize performance. The 2011 movie Moneyball depicts just this, telling the true story of the resurrection of the baseball team the Oakland A’s. Due to budget limitations, the team is unable to acquire conventionally high-valued players. Instead, the team employs revolutionary statistical analysis to create a winning team from less desired players. Since the Oakland A’s did so, statistical analysis has become commonplace amongst professional sports programs. However, another form of objective analysis may prove to be of use to professional sports programs as well: the “small world” theory.
The “Small World” theory began with a short story but was born into theory in the famous six degrees of separation study by Stanley Milgram. By asking a group of people to attempt to get a letter from them to a specific target in Boston. The people were able to mail it to whomever they deemed most likely to be able to get the letter to the target themselves. Eventually, many of the letters made it to the target, and Milgram studied the chain of people these letters took. This led Milgram to conclude that, on average, any given person is six degrees of separation away from any other given person. More broadly, Milgram’s discovery proved that social networks with many short-distance links and just a few long-distance links can lead to very short avg paths between nodes.
In recent years, it has become evident that the “Small World” theory could be used to very precisely represent the complicated inter-player dynamics of soccer. In a 2015 study, researchers gathered data from 30 premier league soccer matches in which the championship-winning team played. In total, they recorded 7583 collective offensive actions and 22518 intra-team interactions. They used this information to construct a network representation of the team, in which each player was a node. Due to the nature of the sport, the researchers found that the network exhibited a very short average path length considering the number of nodes. Through the use of this network, researchers were able to derive many useful metrics about each player. By defining the scaled connectivity as the sum of the connection weights of a player i to those connected to him, where connection weight between players is a measure of how much the pair interacted in play, the researchers were able to objectively measure how cooperative each player was. Furthermore, clustering coefficients for each player were used to describe the extent to which the teammates a player interacted with the most cooperated. Combining these two metrics, the researchers assigned each player with a global rank, representative of each players total team productivity. By using a network to encode the actions of the team, the researchers were able to quanitifiably measure many aspects of performance that are usually left to subjective observation.
On top of assigning objective metrics to every player for different aspects of performance, the researchers also concluded that defenders and midfielders are the players who exhibit the highest levels of connectivity, whereas strikers tended to interact less with their teammates. They further suggested that similar analysis could be used within the sport to “detect under-performing players, fix weak spots, detect potential problems amongst teammates, as well as to detect weaknesses in the opposing team.” As professional sports teams continue to search for advantages wherever they can be found, network analysis could become a crucial component of objective evaluations of player performance and team dynamics.
