Game Theory in Baseball: A 3-0 Count
Game theory is ever present in our daily lives and especially in games that we observe on a daily basis. This article discusses the applications of game theory in the game of baseball, and specifically in the case of a 3-0 count in an at bat. A 3-0 count occurs in an at bat between a pitcher and a batter during a game of baseball when the first three pitches are balls outside of the strike-zone. In this situation there are two options for each player in the game to choose before the pitch is thrown, the pitcher can either throw a pitch down the middle to ensure a strike and avoid a walk or he can try to throw one on the edge of the strike-zone, making a walk more likely but also making the pitch harder to hit. The batter has a similar two fundamental options in that he can either swing at the pitch, or take the pitch no matter what. These four options produce the game pictured below as discussed in the article.
This is an interesting situation in the game of baseball because of its possible implications on the game as a whole. If the pitcher is to throw a pitch down the middle and the batter is to swing, it is very possible that the hitter will end up with a base hit and possibly runs scored depending on how powerful the hit and how many runners on base. However, if the pitcher does not throw a strike, he risks putting the hitter on base and furthering his situation of danger in the inning overall. The grid of this situation creates a mixed strategy Nash Equilibrium where the hitter and pitcher should both randomize their choices. The article states that this ratio should be approximately 87% on the corner and 13% down the middle for the pitcher and similar ratios for the hitter that he should only swing 14% of the time and not swing the other 86%. I find that this ratio is the ideal strategy for this situation because I feel this is not usually what you see in this situation in Major League Baseball. I feel that most times in this situation the pitcher is mainly just trying to throw a strike because three straight balls before that often signifies that he does not have good control over the location of his pitches and therefore, also as a result of that, the batter will often not swing on a 3-0 pitch. The context of the game can also come into effect in this situation. You will often see situations where a pitcher is not throwing many pitches for strikes that the manager will tell the batter to “take a strike,” meaning that the batter shouldn’t swing until the pitcher is able to throw a strike. Therefore meaning that if the count reaches 3-0, the batter will jot swing because he believes he has a high chance of drawing a walk. This has become especially prevalent in the era of data analytics in baseball and an increased emphasis on walks & On Base Percentage (OBP).