Pitcher vs. Batter – The Game Theory of Baseball
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Baseball is a sport often recognized as being slow paced and sometimes regarded as boring. In reality, baseball is a sport of meticulous detail and intense strategy often overlooked by the common viewer. In her article, Hattie James outlines the distinct connection between game theory and choice in baseball. How a pitcher selects their pitch type and location has vast implications on the corresponding in-game payouts. Similarly, the batter must decide whether or not to swing at the pitch thrown by the pitcher. In the example below, I modeled the common scenario of a pitcher choosing pitch type and the batter’s decision to swing.
In this payoff grid, we can assume the batter is a great overall hitter with a fastball preference over the curve. Should the pitcher throw a fastball, the batter will either take it for a strike netting a -2 payoff for the batter and a payoff of 2 for the pitcher. Due to the batter’s aptitude for hitting fastballs, swinging would net him a payoff of 5 (likely a hit) with -5 going to the pitcher in this scenario. As the batter struggles against the curve, we can assume the payoff for taking a curve for a strike would be greater than that of a fastball, -1, and the pitcher’s payoff would be less at 1. Finally, we assume the payoff of a swing on a curveball would be 2 (lower than fastball) with the pitcher’s payoff being -2. There exists a dominant strategy for the batter (swing) as regardless of the pitch thrown, the batter’s payoffs are higher when swinging. In this situation, there exists a single pure strategy Nash equilibrium that arises from the batter’s skill gap in hitting fastballs vs. curveballs. The equilibrium is a combination of “swing” and “curveball” as they are each other’s best payoff outcomes.
If we take a technical step back you’ll notice there exists simple logical explanation for this phenomenon. The pitcher wants to throw curveballs to his advantage, and the batter wants to swing because he’s a skilled hitter and doesn’t want to take the strike. While baseball might not be everyone’s sport, it’s important to recognize the strategy in any sport and be able to provide a means of logical explanation for in game decisions.
