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Friday, September 10, 2010

Tango’s Lab: Game Score

By Tangotiger, 04:19 PM

Let me present you with 4 different versions of Game Score, where the starting point is not 50, but 40 (in honor of replacement level).  And, the Game Score should be akin to a win%.

Note that since a .400 win record is 40 Game Score points, that means that we have to multiply wins by 100 to get to Game Score points. So, .400 x 100 = 40.  Also remember that runs / 10 = wins.  So, runs x 10 = Game Score points.

Version 1
Let’s start off with the easy one, and look only at IP and runs allowed (and don’t you dare say ER… this thread has no place for you in that case… don’t even talk about it).  Each run allowed is 10 Game Score points.  The average pitcher will have 6 IP and 3 runs allowed (for an average of 50 Game Score points).  So, just solve:
50 = 6 * IPvalue - 3 * 10 + 40
Solve for IPvalue of 7.

That’s our equation:
GameScore = 7 * IP - 10 * R + 40

You’d have to tailor a specific equation for each season, but, this should suffice for illustrative purposes.

Version 2
Let’s look only at K and BB and IP.  We know that each K is worth as much as each BB, and each BB is about 0.3 runs, or 3 Game Score points.
50 = 6 * IPvalue + 3 * (SO-BB) + 40
Solve for IPvalue of 0.

That’s a nice one right?  If you have as many K as BB, your Game Score is 40 (replacement level).

Version 3
The FIP version.  We do the -13 * HR, -3 * BB, +2 * SO as our FIP part of Game Score.  The average pitcher will have a FIP portion of -13x1 -3x3 +2x6 = -10 in a 9 inning game, or about -6.7 in a 6 inning game.
50 = 6 * IPvalue - 6.7 + 40
Solve for IPvalue of 3.

Version 4
The LWTS version.  It’s -5 points for hit, -8 extra points for a HR, -3 points for a BB.  The average pitcher will have about -42 points in a 6 inning game.
50 = 6 * IPvalue - 42 + 40
Solve for IPvalue of 9.

Now, you just have to figure out which of the versions you like.  Let’s say you equally weight them at 25% each, you get this:

GameScore
= 40
+ 4.75 * IP
+ 1.25 * SO
- 1.25 * H
- 2.25 * BB
- 2.50 * R
- 5.25 * HR

You can try to get round numbers, and adjust the IP, and you get something like this:
GameScore
= 40
+ 4.5 * IP
+ 1 * SO
- 1 * H
- 2 * BB
- 2 * R
- 5 * HR

The question you have to ask yourself is: how much do I really want to weight each of the 4 versions?  Maybe to you, it’s all about runs (version 1).  Or it’s all about FIP, or all about Component runs.  Or some combination that you prefer.

Come up with your preferred weighting scheme, and tell me what you come in at.

Note: I didn’t double-check my math.  I just winged it, so don’t take anything here as official.

(7) Comments • 2010/10/19 • SabermetricsLinear_WeightsPitchers
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September 10, 2010
Tango’s Lab: Game Score