Game Theory and Baseball, Introduction to Pitch Selection
Baseball is a game dictated by strategy. This was true in the baseball’s founding stages through the time of baseball greats such as Ty Cobb and Babe Ruth all the way until today. With the growing popularity of unique statistics such as the sabermetrics being used in baseball today the development and practice of the newest and best strategies for players and managers has become increasingly vital to success in the sport. The outcome of the duel between a pitcher and a batter is often determined just as much by mental preparation as it is by physical skill. This idea is encompassed by a quote from the notorious jokester and baseball legend Yogi Berra who said “Baseball is 90 percent mental and the other half is physical”. Because of the importance of mental preparation and the options that a batter and pitcher face in any given situation, Game Theory is an incredibly useful tool in determining what mindset batter and pitchers should have in different scenarios.
Hitters and pitchers are faced with four outcomes when at the plate, ball/swing, strike/swing, ball/take, strike/take. As the article discusses, naturally the hitter’s preferences on the outcome depend on the count (situation regarding the number of balls and strikes at any given time) and are the opposite of the pitcher’s preferences. Because of this direct opposition of interests there are very few dominant strategies for a hitter when deciding whether he is better of swinging or taking and the same is true for a pitcher when deciding whether to throw a strike or a ball. Most of the strategies for hitters and pitchers alike are mixed strategies, a strategy in which there is no clear choice and each player is indifferent between picking two choices depending on his/her’s opponents strategy. In a full count, when there are three balls and two strikes and therefore the situation is relatively equal, it turns out (the article explains in detail) that the only way the game reaches a Nash equilibrium is if a pitcher decides to throw a strike half of the time and the batter decides to swing half of the time. The percentage a pitcher should throw a strike and a batter should swing in order to reach the Nash equilibrium depends on the count, and as the article explains in a 2-2 count the pitcher should throw a strike 1/3 of the time and a batter should swing 1/3 of the time. This is due to the fact that if the batter takes a ball then there is no consequence for either player and the count simply moves on to a 3-2 count. These conclusions that the article reaches have very real and useful potential repercussions if adopted by major league baseball players and although there are faults in some of the articles assumptions, which the author is quick to point out, there definitely seems to be a connection between the applicable nature of Game Theory and the largely mental game pitchers and batters play in baseball.
The exercises the article discusses are an interesting application of Game Theory in the high stakes of professional athletics and are a useful tool for understanding the concepts of Game Theory particularly as it was discussed in class and the book. As the article also notes the situation presented and explained is a greatly simplified version of what actually happens in a real baseball game. This being said it is still a useful discussion and from a simple discussion such as this it can help players enter each situation in the game with the most beneficial frame of mind as far as their opponent’s best interests and theirs. This discussion of Game Theory in baseball applies directly to the discussion of dominant strategies in lecture that we have covered so far and the discussion of mixed strategies in chapter 6 of the book. The article also helps illuminate the usefulness of simple discussions of Game theory like we have discussed so far in class because of their potential to be extrapolated to more complex situations and the basic framework they provide for players to operate out of.
Game theory and baseball, part 2: introduction to pitch selection