Sabremetrics 301: Custom Linear Weights (December 18, 2003)
A handy chart.
--posted by TangoTiger at 04:19 PM EDT
Posted 6:04 p.m.,
December 18, 2003
(#1) -
Michael Humphreys
Tango,
Thanks for posting this great resource.
How would one evaluate Pedro using the data? His high SO, low BB and low HR reduce his run environment down to the two-runs-per-game level. So should we credit him with the normal weights (because his performance *created* that run environment) or with the weights at the two-or-three-run level (because that is the *marginal* impact of each of his events in the run environment he has created)?
Posted 7:07 p.m.,
December 18, 2003
(#2) -
tangotiger
That's a good question, and it brings up something worthwhile to talk about.
Those are the weights given that that is the normal run environment. Therefore, everythings adds up so that the marginal impact of all events equals ZERO. This is true for every one of those columns. Every pitcher should have a marginal impact of zero, because the pitcher himself is shaping that run environment.
That's step 1.
For step 2, the step where you try to compare Pedro to a league average pitcher, that's a simple enough step. If Pedro creates a 2 RPG environment while the batters he faces shapes a 5 RPG environment against all other pitchers, you give Pedro an extra 3 RPG (or 3 runs per 9 innings, or 3 runs per 27 outs, or -.111 runs per out).
In this particular example, his marginal outs are worth -.122 -.111 = -.233 runs.
(For a pitcher, the more negative the better.)
Posted 12:30 p.m.,
December 23, 2003
(#3) -
Matt
Neat stuff. But what's a "PickoffError"? How is it bad? I assumed it was an error on a Pickoff throw by the pitcher, which would often allow the runners to advance. So how could that have a negative run value? Maybe it's picking up something else, or I don't know what a PickoffError is.
Posted 1:10 p.m.,
December 23, 2003
(#4) -
tangotiger
I'll have to see exactly what happens in that case. I'll give you a breakdown later.
Posted 4:08 p.m.,
December 23, 2003
(#5) -
tangotiger
From 1974-1990, there were only 30 plays marked as "Pickoff Error".
Here's the breakdown:
a: 1 time, the runner got 2 extra bases
b: 11 times, the runner got an extra base
c: 17 times, the runner was out
d: 1 time, one runner was out, and the other runner advanced 1 base
So, if you work it out, that's 14 bases gained, and 18 outs (and 18 runners removed).
Applying a shorthand standard +.2 runs per base, and -.45 runs per out (with runner removed), and that's -5.3 runs over 30 opps, or -.18 runs per PickoffError. And that corresponds exactly to what the chart says.
For people who resist Linear Weights for whatever reason, realize that everything can be reduced to the Run Expectancy by the 24 base/out chart. And from that, you can generate the Win Expectancy by inning,score,base,out, you can generate Linear Weights run values for any run environment, you can generate Leveraged Index. The Run Expectancy chart itself can be constructed from a very basic Markov model. Basically, the "truth" lies completely in the Run Expectancy chart. Learn it, live it.
Posted 12:02 p.m.,
December 26, 2003
(#6) -
Matt
Got it, thanks for the breakdown.
Posted 4:55 p.m.,
February 11, 2004
(#7) -
tangotiger
Based on this chart, here are the SB breakeven rates, based on run environment:
RPG... breakeven
1 59.5%
2 63.7%
3 66.8%
4 69.3%
5 71.4%
6 73.2%
7 74.8%
8 76.2%
9 77.4%
10 78.5%
As you can see, and as you figured, when facing Pedro, steal alot. When in Coors, be very careful about stealing.
Posted 5:01 p.m.,
February 11, 2004
(#8) -
tangotiger
If you are looking to do this in your head:
(RPG+5)/4
That'll tell you how many steals you should make for every 1 CS.