Image Source: http://en.wikipedia.org/wiki/File:Shunsuke1_20080622.jpg

Given that the football world cup is over, I may have missed the window on this one, but it still is interesting!

The relevant current rules in football (that’s ‘soccer’ in Yankeeism  ) as as follows: teams play during 90 minutes. If, at the end of regular time, teams are tied (an event which, contrary to other sports, occurs with high probability), then they play an extra time. If the draw persists after the extra time, the winner is selected by penalty shoot-outs (a resolution judged “unfair” by many people).

Here, the incentive to perform efficiently is affected strongly by the ordering of the tasks (regular time, followed by extra time, followed by penalty shoot-out). This is illustrated in the following proposal: In the interest of making game more exciting, instead of shooting penalties after extra time (as it is currently the case), could it be preferable to shoot them before extra time and let them count only if the extra time is unsuccessful in breaking the tie?

The intuitive basis for such a proposal is the following: if penalties are shot before extra time, the team that wins (or loses, resp.) the penalty shoot-outs has the greatest incentives to preserve (or break, resp.) the tie and therefore plays more defensively (or offensively, resp.) than if penalties are shot after extra time. The analysis of this proposal comes down to determining whether the total level of offensive play is greater when both teams have average incentives to attack (penalties after extra time) or when one has high and one has low incentives to attack (penalties before extra time).

This proposal was investigated by Dr. Juan D. Carrillo from the Dept. of economics at University of Southern California. His theoretical analysis of the proposal was published in the paper “Penalty Shoot-outs: Before or After Extra Time?” in the Journal of Sports Economics in 2007.

His analysis suggests that moving penalty shoot-out to before extra-time could potentially make for a more exciting game. However, this doesn’t really mean it will work in practice. Theoretical analysis fails to take various psychological factors into account, including but not limited to: players have a tendency to overestimate their chances of winning at penalty shoot-outs, teams might feel less psychological pressure if they lose at penalty shoot-outs (it is just a matter of bad luck), public has a taste for close games.

So in order to put this hypothesis to test, Liam Lenten, Jan Libich (La Trode University, Australia), and Petr Stehlik (University of West Bohemia, Czech Republic) conducted an empirical assessment [link]. They found that bringing the shoot-out before extra-time substantially alter the players’ incentive in extra-time to produce more overall attacking play. In fact, the odds of extra-time scoring went up about three-fold.

So there might be a case for such a rule change after all!