The Impact of Substitutions on Average Runs Per Game

In a previous post, I found the 9 players out of 14 that should be in the lineup. I would now like to answer the question: what is the impact of substituting a player not included in best 9 into the lineup?

Using my Monte Carlo simulation, the best 9 players are expected to score 6.5 runs per game.

The table below shows the average runs per game scored when one of the player not in the lineup (player 4, 5, 8, 9, or 13) is substituted for one of the best 9 players. 

When player 4 is inserted in the lineup for player 1, the average runs per game falls to 5.4.

In the columns of the table, I show the average runs per game when each player is substituted into the lineup for the 9 possible substitutions. One can see that when player 4 is inserted in the lineup, the expected runs per game varies between 6.1 and 5.3 with an average of 5.8.

Substitute Player              4        5       8        9       13       Ave  Lossed Runs

                                                                                                   Per Game

Player Substituted For

         1                            5.4     5.7    5.4     5.0     5.4      5.4        1.1

         2                            5.4     5.6    5.3     5.0     5.4      5.3        1.2

         3                            5.3     5.5    5.2     4.9     5.3      5.2        1.3

         6                            5.9     6.1    5.9     5.5     5.9      5.9        0.6

         7                            6.1     6.4    6.1     5.7     6.1      6.1        0.4

       10                            5.9     6.1    5.9     5.5     5.9      5.9        0.6

       11                            6.1     6.3    6.0     5.7     6.0      6.0        0.5

       12                            6.1     6.3    6.1     5.8     6.1      6.1        0.4

       14                            5.9     6.2    6.0     5.6     6.0      5.9        0.6

Average                          5.8     6.0    5.8     5.4     5.8

Lossed Runs Per Game   0.7    0.5    0.7     1.1     0.7

At the bottom of the table, I estimate the loss in average runs per game when each player is inserted into the lineup.

Player 5 has the least negative impact (a loss of 0.5 runs per game) when inserted into the lineup.

Player 9 has the greatest negative impact (a loss of 1.1 runs per game) when inserted into the lineup.   If he is a defensive specialist, he should be replaced in the batting order by the designated hitter.

The other players 4, 8 and 13 have the same negative impact on runs per game (a loss of 0.7) which is not much different from the substitute with the least negative impact, player 5. 

 Thus, these players (4, 5, 8 and 13) could be substituted into the lineup without much negative impact.

The rows in this table show the impact of taking one of the 9 best players out of the lineup. If player 1 is taken out of the lineup, the average number of runs per game drops to 5.4 from 6.5 (a loss of 1.1 runs per game).

The results in the rows would suggest that players 1, 2 and 3 should not be removed from the lineup unless absolutely necessary. The other players (players 6, 7, 10, 11 and 12) could be replaced with a substitute with relatively less impact on the average runs per game.