William Melville, Samuel Wise, Grant Nielson, Tristan Mott, Christopher Archibald, David Grimsman
This paper presents a novel approach to positioning baseball fielders to maximize expected outs or minimize expected runs allowed against an opposing hitter. We find evidence that our positioning approach is an improvement over MLB average positioning in terms of both hits and runs allowed. We then extend our approach to adaptable hitters who adjust their batted ball strategy in response to the defense’s positioning strategy by modeling the interaction as a zero-sum game and solving for an equilibrium pair of strategies. We demonstrate two examples where the game theory model is appropriate: against shift-beating hitters who pull the ball less frequently when the defense shifts against them and against pull-heavy left-handed hitters who threaten to bunt against an extreme shift.