Linear Weights to Predict Expected Runs Produced by a Team

In my last post, I talked about Bill James Pythagorean Formula to convert runs for and against into an estimate of winning percentage.

Here are the results for the regular season of an Ontario league.

Team	RF	RA	Actual	Estimated	Diff
A	109	59	0.694	0.773	-0.079
B	94	81	0.605	0.574	0.031
C	92	86	0.556	0.534	0.022
D	74	84	0.447	0.437	0.010
E	106	113	0.421	0.468	-0.047
F	79	102	0.395	0.375	0.020
G	90	119	0.389	0.364	0.025

Notice that the error is less than 10% for all of the estimates.

Pete Palmer provided a method called “Linear Weights” to estimate the number of runs contributed by an individual player.

A simplified version of his formula is

Runs = 0.46*1b + 0.85*2b + 1.02*3b + 1.4*hr + 0.33*walks

The coefficients would need to be modified to apply to this league.   I took all of the individual batting statistics for the league and found that the following formula would be able to estimate the runs produced by each player.

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

Here are the values for Team G.

1B	2B	3B	HR	Walks	Runs
112	11	7	10	29	89

This team actually scored 90 runs.  So this estimate is quite accurate.

Using Linear Weights, I can also estimate the offensive contribution of each player to the team.

In my next post, I show how I can estimate the runs against for a team using pitching statistics.  Then I can use the Pythagorean formula to estimate the winning percentage.