from Amazon
Wednesday, June 24, 2009
Blogosphere Question of the Day, 06/24; OR Why should OPS die?
Inside The Book blog reader asks his blog readers this question:
I was catching up on the issues of By the Numbers and read the following quote in the the November 2008 issue:
“An OPS of .800 will always generate more runs than an OPS of .700, given the same amount of playing time.”
I know the above statement is not always true, but do you? I want to give out a prize and decided that I the first person to prove that it is false, using math, will get to choose the first team I will study in depth with my new disabled list database. I know it is not much, but that is all I can really offer. Hopefully there will be more of these to come in the future.
One of his readers already gave out the answer, and not the theoretical mumbo-jumbo I am about to give below. He actually found real-life examples (though I suspect that maybe SB was in there, or park factors, or something). It’s for this reason that I want OPS to die a quick death among serious analysts (as well as its offshoot, the less obscene OPS+). It can survive for quick things. Anway here’s my answer:
Here’s the general form:
1.8*OBP1+SLG1 = 1.8*OBP2+SLG2
OBP1+SLG1+.100 = OBP2+SLG2
That’s two equations, with 4 unknowns.
***
Now suppose we make it easier to follow and create a Mr. Underrated with an OBP and SLG of .400.
1.8*.4+.4 = 1.8*OBP2+SLG2 = 1.12
.4+.4+.1 = OBP2+SLG2 = .9
So, we are down to two equations and two unknowns. This is where your high school math comes into play, and why the high school kids out there should listen to your math teacher.
Take the first equation and subtract the second equation. So:
1.8*OBP2+SLG2 = 1.12
-(OBP2+SLG2 = .9)
Which becomes:
1.8*OBP2+SLG2 = 1.12
-OBP2-SLG2 = -.9
Add the two and you have:
.8*OBP2 = .22
which is:
OBP2=.275
Which we can plug into either of our two equations and get SLG=.625
So, a .400/.400 OBP/SLG is equivalent to a .275/.625 OBP/SLG. They both have a wOBA of around .365, and similar Linear Weights.
What we see here is how OPS breaks at the extremes. If it breaks at the extremes, it’s going to bend alot as you start marching toward the extremes. How much bend are you willing to accept? Well, about as much as your seriousness on the matter.
If you are put in a position that you MUST defend OPS, then stand down and admit you have no defense. If you MUST defend OPS+, you do have one leg to stand on. But not two. You can put up a bit of defense, but not much more.