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.