It’s a World Cup penalty shoot‐out. What does the kicker do? Place the ball to the keeper’s left or blast it to down the middle and hope for the best? The decision the kicker takes could make him a national hero. Or, if he misses, haunt him for the rest of his days.
Some say penalties are a lottery but in fact they’re a classic example of Game Theory – the study of strategic decision‐making.
Game Theory is used in all walks of life, from politics to economics and biology to sports. It can help decide how much you charge for a product, how a country responds to a nuclear threat or even what movie to see on a first date. When the UK government auctioned off the 3G‐telecom network in 2000 they turned to game theorist Kenneth Binmore to help them. The result was a staggering sale price of £22bn, an amount far in excess of expectations.
So why exactly is trying to score a penalty from 12 yards an example of Game Theory? For a game to exist you first need players, in this case a penalty taker and a goalkeeper. Next you need a payoff i.e. you the benefit or happiness you get from taking a decision. The kicker’s payoff is a goal if he scores but no payoff if he misses. For the keeper, it’s the opposite.
In simple terms, statistics show that the best strategy for a penalty taker is to shoot towards the corners rather than down the middle. This makes it the kicker’s ‘Best Response’ REGARDLESS of the strategy adopted by the goalie. So whilst some professional footballers do indeed kick the ball down the middle and sometimes score, strategically speaking, this is not ideal.