A measure of competitiveness in leagues: a network approach

Abstract

Many sports are played competitively in a league format. Final positions are based on the aggregations of the points won at each game. Issues of promotion, relegation and much else will depend on the position in the league. However, the results may also be seen to constitute a network of inter-team relations in which the links represent the degree to which a pair of teams have similar performance. This idea is taken as the basis for the construction of a systemic measure of competitiveness in the league. The basis for the model is the construction of a blockmodel on a network of binary relations. The method is illustrated by application to nine seasons of the English soccer Premier League.

Keywords:

• sports
• cluster analysis
• mathematical programming
• networks and graphs

Acknowledgements

I thank Dr Les Proll of the University of Leeds for helpful discussion on the LP formulation of the blockmodel.