Game Theory in Professional Sports
http://www.nber.org/digest/oct09/w15347.html
The funny thing about game theory is that it can be applied to explain everything from basic economics to terrorist attacks; it is very rarely used to explain actual games like sports. Yet, when you think about it, part of what makes sports so interesting is game theory, which has exactly to do with questions of how much we know, how much our opponents know, and how much they know of what we know.
In an article by the National Bureau of Economic Research, Laurent Belsie analyzes a new study examining two of the biggest zero-sum contests: pitch selection in Major League Baseball and play calling in the National Football League. Researchers Kenneth Kovash and Steven Levitt state that in professional sports, players and coaches do not play the minimax. Essentially, when two players are locked in a zero-sum contest, they always make rational choices, or the “minimax” solution – the set of plays that minimizes their maximum possible loses. What Kovash and Levitt discover with their study is that Major League Baseball pitcher’s throw too many fastballs and National Football League teams pass less than they should. While the study is certainly interesting, the deviations are very slight. According to Belsie, knowing this information would increase a NFL teams wins per season by .5 while their MLB counterparts can increase their wins per season by 2. Professional football and major league baseball is a very good example of a close-information sport. In football, there is a series of strategic plans that are devised in secret and that is sprung on your opponents on game day. Baseball is more like Texas Hold ‘em poker: everything’s evident except the pitch that is about to be thrown.
The concept of open-information is something not found in a discussion of professional football and major league baseball, but it is a very interesting topic of think about. Chess is probably the most famous open-information game. When you are playing Chess, you have all the information the other players has; nothing is concealed from you. There is never anything concealed from you in the strategic sense.
Applying game theory to sports is very interesting and introduces the idea that you can understand many phenomena in sports if you see them as logical games rooted in guessing your opponent’s plans. While the results from Kovash and Levitt’s study are certainly interesting, I question the significance of their results. Are their numbers really significant enough to suggest that following their suggestion will result in a better record?