Too Close and Too Far
https://en.wikipedia.org/wiki/Penalty_shoot-out_(association_football)
As the world most popular sport, football is a team-oriented sport that requires support from not only a group of fans but sometimes a whole country. So, winning a game can be national goal, especially during FIFA World Cups. However, records have shown that even the best teams are unlucky when it comes to penalty shoot-out. Based on facts, teams have had a number of penalty shoot-outs–this occurs whenever the score is tied and extra time has expired. As a football fan, this to me is the most thrilling part of football; however, even as a young fan of Real Madrid, I have always wondered why is penalty shoot-out the last resort, even for World Cup games? Plus, is it a fair way of handling tie games?
In Football, many fans dislike the idea of penalty shoot-out because, as proved in Game Theory, it demonstrates more luck than skill. Penalty kicks are characterized as having a mixed Nash equilibrium. In a rational game, both players want to win. In this case, the goalie plans to block the shot and the kicker does everything to score. They are both aware of their own payoffs and the one of the opponent. However, they cannot predict precisely what the other person will do; therefore, they should randomize because they do not have a dominant strategy. The mixed Nash equilibrium of this game confirms the importance of probability in payoffs. This randomness can drive skilled players back home because of one scored/saved penalty kick. I am not going to deny, but I enjoy watching penalty kicks, even though this system does not seem fair, for both players. So, is it fair?
“As a goalie, you think the kicker is too close. As a kicker, you think the goalie is too far.”
The fact that this system is not fair to both players makes the system equal–meaning both teams are more likely to win or lose. For example, a goalie who is extremely good at saving balls on the left side will use the right side more in order to randomize his strategy to confuse the kicker. The kicker can also apply this smart strategy, even under pressure. More importantly, for a kicker, there is an urge not to miss, and, for a goalie, there is an urge to save. This adrenaline contributes enormously to the matches of Football, and there is not a better place or way to test the professionalism of the players. “A shoot-out is usually used only after one or more of the other methods fail to produce a winner.” (Wikipedia).