Game Theory in Pitcher/Batter Matchups in Baseball
In the sport of baseball, it is widely understood that the orientation (left/right) of the hitter against the orientation of the pitcher is a crucial aspect of the predicted outcome. It is advantageous for the pitcher to have the same orientation as the hitter, whereas it is advantageous for the hitter to have the opposite orientation of the pitcher. The root cause of such advantages can be derived from the ability to see the ball as it is leaving the pitchers hand, along with the manner of which the ball will approach the plate, dependent upon the pitchers throwing arm. In the article I have referenced above, two researchers from BYU analyze the current baseball strategy behind using pitchers advantageously to maximize the amount of same arm/same side of the plate matchup. This paper is created through the lens of best maximizing pitcher matchups, yet it can be expanded to going both ways in order to maximize both pitcher and hitter matchups. Therefore, managers from both teams must determine when they will put in a relief pitcher to matchup against a hitter of a certain orientation and when to put in a pinch hitter to counter the pitcher’s arrangement. Such matchups are further complicated by the presence of switch hitters (hit lefty and righty) who can trump any pitching orientation.
In class we spoke a lot of game theory, and payoff matrices. In this specific model, game theory can be easily applied to better understand and maximize the efficiency of this game. The payoff matrix would look as such:
Matrix Pitcher
Hitter Right Left
Right L,W W,L
Left W,L L,W
Switch W,L W,L
It is very clear that dominant strategy for the manager of the hitting team is always to use a switch hitter. Although it is very clear that this is the best strategy, it is often the case that the manager does not have a switch hitter on the bench, or already used all of their switch hitters. Therefore, the payoff matrix can be edited for the times when there is no switch hitter available:
Matrix Pitcher
Hitter Right Left
Right L,W W,L
Left W,L L,W
The interesting part about baseball is that the manager who makes his decision second will always win. This theory is not a decision where they must choose at the same time, yet they will go tit-for-tat. Therefore, in this theory the optimal strategy is always to choose second, and when you are left to chose first both managers will see a mixed strategy Nash Equilibrium of (Left,Right) = (1/2,1/2).