![]() 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. 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. 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. 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. 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. 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. Hitters and pitchers are faced with four outcomes when at the plate, ball/swing, strike/swing, ball/take, strike/take. 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. 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”. 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. 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. 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. Game Theory and Baseball, Introduction to Pitch Selectionīaseball is a game dictated by strategy.
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