There has been much discussion about the NFL overtime rules after Kansas City beat Buffalo with a touchdown in the first drive of overtime. Buffalo’s offense did not even get on the field to try and respond. It seems unfair to me.
Soccer tried the equivalent overtime rule in the 1994 World Cup. If teams were tied at full time, there was a period of extra time and the first team to score won. At least each team was on the field and could score. This golden goal rule has since been abandoned because it promoted too defensive a game. Teams were afraid to let a goal in, knowing they would lose the game.
Nowadays (and before the ill-fated golden goal experiment), soccer teams play two 15-minute periods of extra time and if the match is still tied, the game goes to penalty kicks. I watched two games this weekend that went to the lottery of penalties. Manchester United lost to Middlesbrough in the English FA Cup and Senegal beat Egypt in the final of the African Cup of Nations (AFCON) for their first title.
Economists have actually studied penalty kicks as an application of game theory. In game theory, my actions depend on what I think you will do. If I think the goalkeeper will dive to his left, I should kick to his right. But, the goalkeeper, knowing this, may decide to dive right. If I anticipate this, then I should kick to his left, etc. The result is that the kicker and goalie should randomize over which way to kick and dive. Economists call this a mixed strategy. This is equivalent of randomizing in Rock Paper Scissors. If I always play rock, my opponent will learn that and always win by playing paper.
In a paper published in 2002, Chiappori, Levitt and Groseclose used data from 459 penalty kicks in the French and Italian leagues. They found that no kickers with at least four penalty kicks always kicked in the same direction. Only three out of 26 kickers with three penalties always shot in the same direction. A kickers direction of shot was not related to the previous kick, or the average of previous kicks, suggesting that players do randomize across different kicking strategies.
On Sunday, Sadio Mane won the AFCON for Senegal by beating the Egyptian goalkeeper, Mohamed Abou Gabal, with Senegal’s fifth penalty. Earlier, Gabal had saved a penalty in the 7th minute of the game when Mane shot straight down the center of the goal. Mane, perhaps understanding game theory, changed his strategy for the shootout and went hard and low to the keeper’s right. Senegal had won 4-2 on penalties.