More on Game Theory and Defensive Shifts

Last week, I took a look at defensive shifts and how players could possibly fight back by understanding game theory. We used bunt probability research conducted by Tom Tango to give us a better idea of what types of outcomes could go into our game theory matrix. We then solved for equilibrium to give us a rough estimate of the ratio that batters should bunt or swing away, and the ratio that defenses should shift or not shift. In this post, I will demonstrate a different game theory structure that might be more suited for looking at bunting into the shift.

In the previous post, we used a matrix also known as “normal form” to play the game. This time we will use the extended form also called a “game tree.” This form of game is more conducive to visualizing a sequential game. In a sequential game the first player makes a move and the second player counters. In our example, player one is the defense and player two is the batter.

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Beating Defensive Shifts with Game Theory

Barring a rule change outlawing them, it seems defensive shifts are here to stay. In fact, teams are using them increasingly and becoming more efficient at them in the process. This is not a good sign for predictable hitters such as David Ortiz, Brian McCann and the plethora of other pull-happy hitters. Smart baseball minds such as Tom Tango and Bill James have written about ways that hitters can essentially fight back by bunting or simply becoming a more well-rounded hitter. In this post I will attempt to build on some of these findings. More specifically I will be using game theory to help prove that hitters have a way out of their proverbial pickle.

 First, let’s discuss game theory.

 Simply put, game theory is the study of strategic ... Read full article at Banished to the Pen