When to rush a ‘behind’ in Australian rules football: a dynamic programming approach

In Australian rules football, points are scored when the ball passes over the goal line. Six points are awarded for a goal when the ball passes between the two centre posts, and one point for a ‘behind’, when the ball passes between a centre post and an adjacent outer post. After a behind, the defending team has a free kick from the goal line. It may be worthwhile, particularly in the closing stages of a game, for a defending team voluntarily to concede a behind, by themselves passing the ball between the two outer posts, either to avert the possibility of an imminent goal or to increase the probability of scoring a goal themselves. A dynamic programming model is used to analyse this situation.