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

FIORAVANTI, FEDERICO; TOHMÉ, FERNANDO; DELBIANCO, FERNANDO; NEME, ALEJANDRO

INTERNATIONAL JOURNAL OF GAME THEORY

SPRINGER HEIDELBERG

Año: 2021

0020-7276

Using a simple game-theoretical model of contests, we compare the effort exertedby rugby teams under three different point systems used in tournaments around theworld. We consider a point system that awards four points to the winning team, nopoints to the losing team, and two points to each team in a case of a draw. The othertwo point systems award bonus points depending on the final score. They both awarda bonus point for losing by only one try. One of these two systems gives an extra pointto the team that scores four or more tries while the other gives it for scoring threemore tries than the other team. We develop two models. One is a static one, intendedto compare the joint efforts equilibria as to find which point system maximizes theeffort exerted by the teams. The other is a dynamical model, providing a frameworkfor the analysis of equilibriumpayoffs and find the one in which teams exertmore jointeffort. In both models, the point system that maximizes the amount of effort in rugbyis 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 datafrom matches under the three point systems being evaluated. The empirical results confirm our theoretical conclusions