THE BOOK--Playing The Percentages In Baseball

Monday, October 23, 2006

Quick Custom Linear Weights

Following up on my post in this thread, I present a useful shortcut to coming up with custom Linear Weights using only OBP.  You are encouraged to tweak the various shortcuts to come up with something better.  Or to use this as a basis, to come up with your own shortcuts using SLG and BA as well. 

All run values are of the form:

X = a * (1 - b) * c + d

where
a = number of baserunners on base
b = chance of runner scoring
c = percent of available bases taken
d = chance of runner scoring from basehit

Here are my estimates:
a = 1.8*OBP.  The higher the OBP, the more runners will be on base.

b = 0.9 * OBP. The more runners, the more that will score, just by pushing them over.

c = 1.0 for HR, 3B.  0.80 for 2B.  0.50 for 1B.  0.15 for BB.

If we look at the single, the .10 runners on 3B will gain 1 base each, the .20 runners on 2B will gain 1.6 bases each of 2.0, and the .30 runners on 1B will gain 1.3 bases each of 3.0.  The weighted total is .81 bases gained out of 1.40, or 58%.  However, not all bases are created equal (the 3B to home plate is worth the most).

d = (s*OBP)/(1+(s-1)*OBP)
where d = 1.0 for HR
where s = 3.0 for 3B, 1.5 for 2B, 0.7 for 1B, BB

These are all very rough rules of thumb.  The end result are these custom LWTS values by OBP level (which assumes that the SLG is about 1.25-1.30 x OBP):

OBP… HR… 3B… 2B… 1B… BB
0.001 1.00 0.00 0.00 0.00 0.00
0.050 1.09 0.22 0.14 0.08 0.05
0.150 1.23 0.58 0.40 0.23 0.14
0.250 1.35 0.85 0.61 0.36 0.24
0.350 1.43 1.05 0.79 0.49 0.34
0.450 1.48 1.19 0.94 0.61 0.44
0.550 1.50 1.29 1.05 0.71 0.54
0.650 1.49 1.33 1.12 0.81 0.64
0.750 1.44 1.34 1.17 0.90 0.74
0.850 1.36 1.30 1.18 0.98 0.85
0.950 1.25 1.23 1.16 1.05 0.97
0.999 1.18 1.18 1.14 1.09 1.03

Explanation

The general form simply is broken down into two parts: moving runners over, and getting on.  The getting on is simply the chance of scoring from a single, double, triple, HR, the “d” part.  It provides a useful function that starts at 0 and ends at 1 for all non-HR events, with the triple having a much steeper curve and the walk as the slowest curve.

The moving runners over itself is split into two parts: the number of runners on base, and the “value-added” of moving them over to the next base(s).  For the triple and HR, the second part of the moving runners over is a statement of fact, being
1 minus chance of scoring from the average base

For the other three events, I estimate this.

I encourage everyone to read the first three articles in the BASERUNS box on my home page:
http://www.tangotiger.net/