Sports and Imperfect Game Theory
Game theory is an inherent part of any competitive endeavor, and therefore is very prevalent to the field of sports and athletic performance. Moreover, the application of game theory is most apparent in the most competitive levels of play, professional sports. Given this, many professional sports teams have teams of statisticians, mathematicians, economists, and professionals working behind the scenes to support players, managers, and coaches to make the best strategic decisions to maximize the chances of success.
Yet, many times these strategies can be imperfect. Studies such as “Professionals Do Not Play Minimax: Evidence from Major League Baseball and the National Football League” have shown that many professional teams do not have perfect game theory, and in the fields of baseball and football, this decreases the potential for wins by 2 and .5 per season, respectively. When analyzing pitch count in baseball, this inefficiency becomes very apparent, as it is predicted through analysis of over 3 million pitches, that by decreasing the number of fastballs thrown by 10 percentage points, that runs per season would convert to about 15 less runs per season, a statistic that can have a large impact on professional franchises.
Of course, there are variables to this, including pitcher fatigue, the order in which pitches should be thrown, and the skillsets of the batter and pitcher. Yet, through analysis of these pitches, there are many fixes that can be made to the way pitchers generally play to improve performance.
Similarly, football bears similar results in the NFL. By studying over 100,000 plays, it can be determined that passing is more effective in gaining first downs and yardage, and that if teams were to increase their passing by 14% from 56% to 70%, that teams would score 10 points more each season.
However, one must take into account that defenses or offenses may adapt to this behavior, and come up with ways to better counter the new strategy. Evidently, we have not reached an equilibrium point in these sports, and the game and players are always changing. However, studies such as the aforementioned highlight the many inefficiencies that exist in sports, which in many cases make it unpredictable, and exciting.
Source: https://www.nber.org/digest/oct09/game-theory-and-major-league-sports