Balancing the Innings for a Pitching Staff

In my last post, I discussed Pete Palmer’s Linear Weights formula.  I showed how it could be used to estimate the number of runs produced by a men’s fastpitch softball team.

In this post, I will look at a similar idea of linear weights to evaluate a pitching staff.  Then I will use the linear weights to balance the innings assigned to each pitcher to minimize the runs given up by a men’s fastpitch softball team.

I took the pitching statistics for the primary pitchers in a local men’s fastpitch softball league.   I calculated various pitching statistics in terms of their values per inning.  Then I used multiple linear regression to estimate the runs allowed per inning pitched as a function of hits allowed (non-homeruns), walks (base on balls and hit by pitch), strikeouts, and homeruns allowed per inning pitched.

Here is the data that I used.

Pitcher	Hits	Walks	Strikeouts	Homeruns	Runs Allowed
1	1.05	0.42	1.32	0.08	0.58
2	1.23	0.57	0.91	0.16	1.25
3	1.49	0.47	1.24	0.17	1.18
4	0.79	0.26	1.44	0.12	0.32
5	0.83	0.68	1.43	0.00	0.48
6	1.03	0.34	1.52	0.08	0.76
7	1.09	0.34	1.07	0.10	0.73
8	1.13	0.54	1.02	0.17	1.22
9	1.42	0.46	0.46	0.07	1.05
10	1.31	0.20	0.76	0.06	0.71
11	1.09	0.76	1.27	0.15	0.97
12	1.19	0.65	1.19	0.11	0.98
13	0.46	0.33	1.77	0.06	0.40
14	1.15	0.66	0.66	0.16	1.23

The formula that I obtained from the linear regression is

Runs Allowed = 0.42*Hits + 0.55*Walks – 0.14*Strikeouts + 2.36*Homeruns

Pitchers 1, 2 and 3 are on the same team.  

I wanted to balance the number of innings between the three pitchers.  I found that one good way to do that was to equalize the runs allowed by each pitcher.

Here are the results.

	Weight	0.42	0.55	-0.14	2.36
Games	Innings	Hits	Walks	Strikeouts	Homeruns	Runs Allowed
9	60	1.05	0.42	1.32	0.08	40
5	37	1.23	0.57	0.91	0.16	40
5	36	1.49	0.47	1.24	0.17	40
19	133					120

So the manager should plan to throw pitcher 1 for 60 innings or the equivalent of 9 games during the season.  Pitchers 2 and 3 would be expected to throw 37 and 36 innings respectively which represents approximately 5 games each.

The entire ptiching staff would be expected to allow 120 runs during the season.

I can now use the expected offensive production of the batters on the team from the previous post and the expected runs allowed by the pitchers shown here in the Pythagorean formula to estimate the winning percentage of the team during the regular season.