Distributing Plate Appearances between Position Players

In my last post, I distributed the number of innings between a men's fastpitch softball teams's pitching staff.

In this post, I will distribute the plate appearances for the position players on a men's fastpitch softball team.

In 2012, there were 492 regular season plate appearances distributed between 15 players.  I would like to distribute these 492 plate appearances for the 2013 regular season among the 14 players while maximizing the number of runs created by the team.

Recall the linear weights based runs created formula that I found for this men's fastpitch softball league.

Runs Created = 0.44*1b + 0.83*2b + 1.00*3b + 1.38*hr + 0.31*walks

I calculated the runs created per plate appearance for each of the 14 players.  Then I ranked the players by runs created per plate appearance.

I found the mean and standard deviation of the plate appearances for the team's players in the regular season for 2012.
 

Then I used the inverse normal probability distribution with the percentile found using the rank of the player’s runs created per plate appearance and the mean and standard deviation of the plate appearances for the team in 2012.  In this way, I could determine the ideal number of plate appearances for the 2013 season for each of the players.

rank	runs/pa	norm dist	new pa	new runs
1	0.30	0.93	56	17
2	0.25	0.87	50	13
3	0.24	0.80	47	11
4	0.22	0.73	44	10
5	0.22	0.67	41	9
6	0.21	0.60	39	8
7	0.20	0.53	36	7
8	0.19	0.47	34	7
9	0.17	0.40	32	6
10	0.17	0.33	29	5
11	0.16	0.27	27	4
12	0.14	0.20	24	3
13	0.14	0.13	20	3
14	0.13	0.07	15	2
			493	104

This team scored 90 runs in 2012.  So with this ideal distribution of plate appearances, they should be able to improve that to 104 runs in 2013.