Networks and College Sports
Syracuse University and Pittsburg University have recently left the Big East Conference to join the Atlantic Coast Conference. Their departure from Big East left the Big East with only 7 teams, while the ACC grew to 14 teams.
Syracuse and Pitt both had payoffs for their decision. These payoffs were affected by monetary considerations, reputation, and most importantly, the quality of the teams in their own and other conferences. Since generally any team can apply and switch conferences, teams’ payoffs are highly dependent on what on what other teams are doing. From this, some form of messy and complex payoff matrix could be made to exactly model payoffs for all teams and which conference they would prefer to join. In reality, teams probably incorporate many of the network’s properties in their decision-making, without qualitatively writing out a full payoff matrix.
Since Syracuse and Pitt did decide to leave the Big East and join the ACC, their payoffs for joining the ACC were greater than other options given what other teams were doing. And ever since Syracuse and Pitt switched to the ACC, this has affected other teams inside and outside of the ACC. Lesser-known teams are now scrambling to fill in the now-vacated spots in the Big East, while the other powerhouses in the Big East are now considering leaving for bigger conferences. This illustrates the connectedness of this network of athletic teams.
Another interesting aspect of graph theory, though not taught in this class, can be applied to sports. If each team is a node, and a directed edge to another node indicates a win over that team, we can create a matrix. Each column will represent a separate team and each row will also represent a different team. So if there are N teams or nodes, then the matrix will be of size N * N. In this matrix, if two nodes are connected, then a 1 is put into the matrix to indicate that the first team has beaten the second team. The nodes that aren’t connected will have a 0 in the corresponding entry of the matrix. Essentially this matrix illustrates the 1-step connections in the graph. And squaring this matrix actually shows the number of 2 step connections between the nodes of the graph. In a sense, this indicates the strength of schedule of the teams, a crucial aspect of ranking teams in sports. This basic representation only works if each team only plays the other teams at most once. However, more complicated analysis of matrices can be used to model more complex game schedules.