THE BOOK--Playing The Percentages In Baseball

Monday, January 18, 2010

Revising MORP

MORP is BPro’s (Nate Silver originally) version of converting “wins above replacement” into dollar terms.  I have argued many many many times that MORP is not the best way: 1200000*(WARP^1.5) + 380000 . If you put it in millions of dollars, it’s: 1.2 * WARP^1.5 + minimumSalary.  That was for 2007.

If you guys know me, I prefer simplicity to complications, and that exponent to me is a complication.  If we can avoid the exponent with little to no loss in accuracy, get rid of the exponent.  I’m looking through my archives, and limiting myself just to the first 10 hits, I have said the following:

Mar, 2007:

Here then is the new chart:

war warp Me$ MORP$
1.00 2.40 4.2 4.9
2.00 3.40 8.0 7.9
3.00 4.40 11.8 11.5
4.00 5.40 15.6 15.5
5.00 6.40 19.4 19.8
6.00 7.40 23.2 24.6
7.00 8.40 27.0 29.6
8.00 9.40 30.8 35.0
9.00 10.40 34.6 40.6

The divergence happens at around the 6 WAR level.  Other than Pujols, no one exceeds that.  (THT has Santana and ARod at around 5.5, which is less than 1 MM difference between me and MORP$).

And, since most of you that I was crazy to consider Pujols worth as much as I said he was in $ terms (that if a player is tooooo good, that there’s some sort of “diminishing returns"), you guys are going to hate the ever-rising value of his MORP$.

So, let’s all agree that linear is the easiest, safest cleanest way to work and think about this, and anything else will make you go through so many mathematical gymnastics that it makes you see something (like MORP/WARP do) that simply isn’t there.
...
Nate pointed out that it’s at the lower-end that you’ll see the biggest difference, and he’s right:

war warp Me$ MORP$
(1.00) 0.40 (3.4) 0.7
(0.50) 0.90 (1.5) 1.4
0.00 1.40 0.4 2.4
0.50 1.90 2.3 3.5
1.00 2.40 4.2 4.9
1.50 2.90 6.1 6.3
2.00 3.40 8.0 7.9

Those are huge gaps.  And all that MORP does is show us how you have to decide whether to trust the superlow replacement level of WARP or mine in WAR.

I don’t see the benefit of the exponent in MORP, and just see the downside of the superlow repl level in WARP.

May, 2007:

Furthermore, it’s compounded by Nate’s MORP, which is based on WARP.  MORP (salary value) has to have an exponential function to make WARP and salary match.  However, if WARP were more properly calculated, MORP would be linear.  It’s the classic two-wrongs-make-a-right, but leaves all with the impression that salary and value are exponentially related.  If WARP had a .300 repl level, WARP and salary would be linearly related.

Dec, 2007:

BP: please, will you disavow WARP and MORP?  As discussed in the past, the only reason MORP isn’t linear is to counteract the poor construction of WARP.  Fix WARP, and then MORP becomes rather linear.  C’mon guys.  Time to fix what’s broken.

Feb, 2008:

And two, the use of WARP’s superlow replacement level forces a MORP equation that is exponential to counteract that!  In this case two wrongs (low replacement level plus exponent) DO make a right!

May, 2009:

I have no doubt that when the new WARP makes its official debut that the new MORP will look unsurprisingly like my WAR to $ model (as best seen at Fangraphs).

This is hardly exhaustive.  Matt, new blood at BPro, looks like he’s going to revamp MORP.  Let’s see where he goes with it and how it compares to my simple model.