Defensive Positioning of the Team

In an earlier post, I discussed how to find the best bating order.  However, this method neglected the defensive positioning of the players.

In this post, I will describe how to find the best lineup considering both offensive and defensive aspects of the team's performance.

First, I found the positions of each of the players on the team can play.  I wanted to find the best lineup and batting order for each of the three pitchers on the team.

For each of the three pitchers, I developed 100 random lineups that filled the 9 defensive positions along with the DH.  I did not consider the batting order at this point.  However, I ran the Monte Carlo simulation for each of the random lineups with a random batting order.  Then I screened out the lineups that did not provide sufficient average runs per game.   In this way, I had all of the defensive positions filled and still had a reasonably good average runs per game.

On examination of the lineups that were not screend out, I found that seven players were in each of the lineups.  They were the strongest offensive players.  I reordered the lineups so that these seven players would be in a specific place in the first seven positions in the batting order to maximize the average number of runs per game.  One of these players could possibly play DH.

The last three players in the lineup filled out the defensive positions.  So at this point, I had a number of lineups with batting orders that provided good offensive statistics.

I ran the Monte Carlo simulation to do a runoff of the batting orders to find the best offensive lineup for each pitcher while also having all of the defensive positions filled out.