Game Theory In Soccer
When a striker tries to beat a goalkeeper and score a goal, he has a choice of shooting at the near post or the far post. The paper looks at the 2002-2003 Italian Serie A games in an attempt to model the choices of where the goalkeeper should defend and where the striker should attack.
The model devised has the following notations for the goalkeeper vs striker scenario. The posts are F (far) and N (near), and the goalkeeper stands at a distance (p) from the far post. Thus, p = 0 means the goalkeeper is at the far post and p= 1 puts the goalkeeper at the near post. The striker shoots at one post or the other (F or N) such that the probability he will choose the near post is q. The probability to shoot at the far post will then be q. In assigning the probabilities, the goalkeeper’s ability and position relative to the posts are taken into account. Likewise, distance, skill and field position are considered for the shot accuracy rating by the striker.
The end result is a zero-sum game where there is a winner and a loser – the keeper guards a post while the striker takes his shot. When analyzing the games, there is no equilibrium from a pure strategy – shooting at the near post or far post. But when the striker tries to aim somewhere in between, there is a mixed Nash equilibrium. The findings are that the optimum strategy depend solely on the striker’s location on the field which affects the accuracy of the shot. Other factors such as the striker skill drop out. The optimum strategy is such that:
i) If you are the goalkeeper, guard the near post
ii) If you are the striker, shoot for the far post.
This is intuitive as in real life, and we see how game theory can be used to model these subconscious decisions.