Optimal Ball Placement in Rugby Conversions

Abstract

Abstract. In the game of rugby, attempting to score a conversion following a try gives rise to a situation which may be modeled mathematically as an optimization problem, namely, that of choosing the best spot from which to kick the ball. Due to its appeal and simplicity, this problem has been widely used as an example of an application of mathematics to sports. Starting from the model suggested by Hughes over 30 years ago, on which all other models used until now have been based, we analyze the situations in which these models are not applicable. From this we will see how the quantity to be optimized should be changed in order to overcome these problems and also to obtain results which are compatible with the data quoted in the literature for professional players, for the whole range of possible scenarios.To obtain more realistic results, we then incorporate the initial speed and elevation angle of the ball into the model.