Nash Equilibrium in Baseball
Nash equilibrium has been employed to study the behavior of players in competitive sports and games. In this paper, the researchers model baseball as a game between the pitcher and batter. The pitcher wishes to minimize the number of bases the batter achieves, and the hitter aims to maximize it. However, this is still quite complicated as the pitcher can pitch a variety of pitches in various locations, and batters have various styles and techniques of hitting.
In this model, pitching and batting is simplified and the pitcher and batter’s strategies are generalized into a few options. The batter can either swing lightly, hard, or not swing at all. If the batter swings lightly, this will result in either a single or out. A hard swing results in all possible outcomes (home run, triple, double, single, out), but yields a base hit at a lower frequency. The batter may also not hit, resulting in a ball or strike.
In the model, the pitcher can either pitch a strike or ball, or mix of these. Given these strategies, the possible strategies in the model are as follows.
| Hitter’s Strategies | |||
| Pitcher’s Strategies | S,N | S,L | S,H |
| B,N | B,L | B,H |
Where S: Strike B: Ball N: No swing L: Light swing H: Hard swing
As such, the authors of the paper argue that is hypothetically possible to predict the optimal mixed strategy for batters and hitters in baseball, while acknowledging that the model is very simplified and does not account for factors such as variation in strategy and incentives.
Link: https://papers.ssrn.com/soL3/papers.cfm?abstract_id=2962445