The complete defensive strategy: Defining complementary pitching and fielder positioning strategies in baseball

In baseball, the characteristics of a pitch have an effect on a batted ball's trajectory. For example, batters are more likely to hit a fastball to the opposite side of the field and to pull a changeup. In this paper, we present novel matchup and pitch-specific approaches to positioning fielders to maximize outs and minimize runs allowed against opposing hitters. Unfortunately, the pitch-specific approach may reveal information about the upcoming pitch to the opposing batter. Thus, we combine our pitch-specific positioning strategy with an existing pitch selection game theory model that assumes the batter can observe the pitch up to a decision point, at which point they must decide whether to swing at or take the pitch. The combined pitching and positioning strategies, which we call the complete defensive strategy, complement each other by mixing in an occasional bluff where the pitcher throws the wrong pitch for the positioning strategy. Thus, the batter cannot use the positioning strategy to perfectly predict the upcoming pitch, and the defense is able to utilize the pitch-specific positioning strategy. We show that the matchup and pitch-specific approaches to positioning are not significantly more effective at preventing hits or runs than a previously defined batter-specific approach. Thus, although a baseball team could use our methodology to define pitch-specific positioning strategies that do not tip the pitch to the batter, they could define similarly effective positioning strategies using much simpler models that only consider the batter's tendencies.