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THE BOOK--Playing The Percentages In Baseball

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Wednesday, February 07, 2007

Why does 1.7*OBP+SLG make sense?

By Tangotiger

This is a step-by-step explanation as to why you should use some form of modified OPS, and not just OPS.  If someone ever talks to you about OPS and how it should be weighted, send them here.


Start with a standard hitting line based on 600 PA:
AB: 540
H: 145
2B: 30
3B: 3
HR: 17
BB: 50
K: 100
HBP: 5
SF: 5

This produces a BA/OBP/SLG line of: .269/.333/.430, which is pretty typical these days.

Now, what happens if we add 1 hit and 1 AB to this batting line (i.e., a single)?  The OBP and SLG numbers go up by .0011 each.

And if we instead add 1 hit, 1 double, and 1 AB to this batting line (i.e., a double)?  The OBP and SLG numbers go up by .0011 and .0029 each.

A triple causes this: .0011, .0048
A HR causes this: .0011, .0066
A walk or hit batter causes this: .0011, .0000
An out causes: -.0006, -.0008

Now, we know what the run values of each event is, courtesy of this:
http://www.tangotiger.net/RE9902event.html

And those numbers are:
Event LWTS
1B: 0.474
2B: 0.764
3B: 1.063
HR: 1.409
BB: 0.336
out: -0.302

Now, all we have to do is run a regression of the change in OBP and SLG numbers against the LWTS numbers.  And what do we get?  An r=.9993 (almost perfect), with this equation:
283 * OBP + 162 * SLG
which is the same thing as:
(1.75*OBP + SLG) * 162

And, if we apply this equation to this table:
Event OBP, SLG
1B: 0.0011, 0.0011
2B: 0.0011, 0.0029
3B: 0.0011, 0.0048
HR: 0.0011, 0.0066
BB: 0.0011, 0.0000
out: -0.0006, -0.0008

What do we get?
Event RegressedRunValue
1B: 0.485
2B: 0.785
3B: 1.084
HR: 1.384
BB: 0.314
out: -0.286

If we remove the triple from the analysis (because there are so few of them), we get this, with an r=.9995:
(1.73*OBP + SLG) * 163

And if we apply this to the OBP and SLG differentials, we get this:
Event Actual Regressed
1B: 0.474 0.485
2B: 0.764 0.786
3B: 1.063 1.087
HR: 1.409 1.389
BB: 0.336 0.313
out: -0.302 -0.286

As you can see, our equation of 1.73*OBP+SLG is fairly close to the actual LWTS run values. 

***

Now, if we take this equation:
(1.73*OBP + SLG) * 163

You may be wondering about that “163”.  Remember that the OBP and SLG differentials I presented was based on 600 PA.  If I would have used 6000 PA, that multiplier would have been 1630.  In short, the multiplier is 0.27 * PA.  So, the real equation is this:
Runs: (1.73*OBP + SLG) * 0.27 * PA

In order to convert from runs to wins, you need to divide by something around 10 to 11 (that’s your runs to wins converter).

Wins: (1.73*OBP + SLG) * 0.025 * PA

In order to compare to league average, you would do:
lgOPS: 1.73*lgOBP + lgSLG, which, as luck would have it, is very close to 1.0 (it’s actually 1.014).  For simplicity’s sake, if we make the equation:
1.69*OBP+SLG, this will give us a result of exactly 1 for the 2006 season.

So, to compare to league average, you can have this version of OPS:

Wins above average = (1.69*OBP+SLG - 1) * .025 * PA

A guy with a .430/.670 and 600 PA would give us:
Wins above average
= (1.69*.430+.670 - 1) * .025 * 600
= +6.0

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