Effort of rugby teams according to the bonus point system: a theoretical and empirical analysis

Abstract

Using a simple game-theoretical model of contests, we compare the effort exerted by rugby teams under three different point systems used in tournaments around the world. We consider a point system that awards four points to the winning team, no points to the losing team, and two points to each team in a case of a draw. The other two point systems award bonus points depending on the final score. They both award a bonus point for losing by only one try. One of these two systems gives an extra point to the team that scores four or more tries while the other gives it for scoring three more tries than the other team. We develop two models. One is a static one, intended to compare the joint efforts equilibria as to find which point system maximizes the effort exerted by the teams. The other is a dynamical model, providing a framework for the analysis of equilibrium payoffs and find the one in which teams exert more joint effort. In both models, the point system that maximizes the amount of effort in rugby is the one that awards a bonus point for scoring three more tries than the opponent. To evaluate the real-world validity of this claim we run empirical analyses using data from matches under the three point systems being evaluated. The empirical results confirm our theoretical conclusions.