Game Theory – Soccer Penalty Kicks
I am a not the biggest football fan, but I do occasionally tune into the World cup, Copa America, or any big soccer tournament when they’re going on. Most recently, over the summer, I was watching the Euro 2020 final, in which Italy defeated England 3-2 in penalties. This penalty kick shootout reminded me of our discussion of game theory in class.
In penalty kicks, for both the goalie and the kicker, the strategies for the most part are pretty simple. The kicker must decide to kick either to the right or left side (kicking down the middle is very uncommon). Now, because the ball is moving very fast, the goalie must guess in advance which side to defend and jump either left or right. Basically, both the goalie and kicker choose their strategies simultaneously.
Below is a penalty kick payoff matrix:
| Goalie | |||
| Left | Right | ||
|
Kicker |
Left | Kicker Loses, Goalie Wins | Kicker Wins, Goalie Loses |
| Right | Kicker Wins, Goalie Loses | Kicker Loses, Goalie wins | |
This matrix is a zero-sum game, meaning an advantage that is won by one of two sides is lost by the other. So, if the kicker and goalie choose the same strategy (both left or both right), the goalie will win. But, if the kicker and goalie choose opposite strategies (kick left/ defend right or kick right/ defend left), the kicker will win.
However, despite the payoff matrix above being as simple as the flip of a coin, in real life the game theory of penalty kicks can be a lot more complicated. For instance, every player has a stronger and a weaker side – both goalies and kickers. Most goalies know which foot the player is going to use, and kickers know which side the goalie is more dominant on. For instance, if a kicker always kicks to his stronger side every time, the goalie will know. However, if the kicker kicks to his weak side, it might throw the goalie off, but the kicker is also more likely to miss the net (compared to his strong side). Overall, the game theory of penalty kicks in real life is a lot more complicated than simple 50/50 odds.
Reference: https://econlife.com/2018/07/world-cup-penalty-shootouts/