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.

使用简单的比赛理论博弈模型，我们比较了橄榄球队在世界锦标赛中使用的三种不同积分系统下所付出的努力。我们考虑一种分数系统，在平局的情况下，奖励获胜的团队4分，败方不得分，每队2分。其他两点制则根据最终分数来奖励加分。他们俩都因一次尝试失败而获得了加分。这两个系统中的一个给得分大于或等于四次尝试的团队加分，而另一个系统则得分比另一个团队多三分。我们开发了两个模型。一个是静态的，旨在比较共同努力的平衡，以找出哪个得分系统可以最大程度地发挥团队的作用。另一个是动力学模型，提供一种分析均衡收益的框架，并找到团队共同付出更多努力的框架。在这两种模型中，使橄榄球工作量最大化的得分系统是一种比对手多得分3次而获得加分的系统。为了评估此要求在现实中的有效性，我们使用来自正在评估的三点系统下的比赛数据来进行实证分析。实证结果证实了我们的理论结论。为了评估此要求在现实中的有效性，我们使用来自正在评估的三点系统下的比赛数据来进行实证分析。实证结果证实了我们的理论结论。为了评估此要求在现实中的有效性，我们使用来自正在评估的三点系统下的比赛数据来进行实证分析。实证结果证实了我们的理论结论。