Penalty kick shootouts are one of the most exciting parts of sports, and with the World Cup coming up soon there very well may be some high profile shootout matchups that draw worldwide attention. However, a shootout is brutal for goalies; the shot comes from so close that a goalie has almost no time to react and cover the entirety of the net, which is why you often see goalies dive the opposite way of the shot. A casual soccer fan may find that funny, but someone who knows soccer understands that such an occurrence is often inescapable; in order for a goalie to have any chance to stop the shot, he often has to decide on a direction to dive before the shot takes place.
If you are the shot taker your goal is obviously to kick the ball to the opposite side that the goalie dives, all but ensuring a goal. However, the best strategy to actually accomplish that for the shot taker isn’t exactly clear. If the goalie is perfectly centered and shows no indication of which way he intends to dive, what is the best decision for you, the theoretical shot taker, to make? Perhaps you run through some mind games in your head; ‘the past 3 shots have gone right, maybe I should go left to be unpredictable’ you think.
However, even this so-called unpredictability is in a way predictable, as a rational goalie may also think that those are your exact thoughts. Maybe more tangible is that a particular shot taker tends to shoot more to the left throughout his entire career; it may only be a small 55/45 split, but if a goalie knows this, it gives him an edge over the worst case 50/50 odds for him. In a way, any kind of strategy by the shooter could be predicted by a goalie, giving a slight boost to the goalie’s odds of guessing correctly.
Thus, in a closed game theory environment, the best strategy for the shot taker would be to flip a coin before taking the shot: heads he goes left, tails he goes right. If the goalie is aware that the shooter utilizes this decision making strategy, then the goalie has no way to gain an advantage on the shot taker. The side the shot goes to is completely random as opposed to the feigned randomness discussed before. The goalie has no information at his disposal to make a decision on the direction of his dive, and therefore his odds of diving the correct way are the worst they can be at 50/50.
Of course this strategy is pretty much exclusively theoretical because not every shot taker and goalie is completely rational, nor are they all aware of all pieces of information that could help them better predict where they should dive or shoot. However, should the day come where analytics becomes so ingrained in the world of soccer that such a scenario does become real, where all goalkeepers would be aware that a particular shooter goes right 53% of the time, then it would be in the best interest of the shot takers to make their decisions completely by random chance in order to negate any possible advantage the goalkeeper might have.
Georgetown University Class of 2016