# A new statistic

August 8, 2005 3 Comments

Okay, it’s actually simply an attempt to correct an old one. Last week, I wrote that GPA is a better statistic than EQA and easier to use for comparison purposes. But there is a problem with GPA; something that makes it not so accurate.

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Imagine the weights given to each type of hit by OBP and SLG. In OBP, 1B = 1; 2B = 1; 3B = 1, HR = 1; and BB = 1. They all have equal weights. On the other hand in SLG, the weights are: 1B = 1; 2B = 2; 3B = 3, and HR = 4. Thus, OPS gives the following weights:

BB = 1

1B = 2

2B = 3

3B = 4

HR = 5

GPA, which weights OBP as 1.8 times SLG, gives the following weights:

BB = 1.8

1B = 2.8

2B = 3.8

3B = 4.8

HR = 5.8

But what ratio would be correct? Using linear weights, this is an easy question to answer. The answer is roughly:

BB = 2

1B = 3

2B = 5

3B = 7

HR = 9

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See how big the difference is between GPA and the true weights? GPA undervalues extra base hits while overvaluing walks and singles. So, you might say, why not simply decrease the value of OBP? Because then walks will be undervalued, as they are in OPS. It’s not a big problem, but we’re looking for a measurement that pretty much pinpoints the actual value of each component.

What screws the whole thing up is walks. So why not forget about walks for a moment, and simply find the right weight for OBP to make the other ratios work? That’s simple enough: .5*OBP + SLG gives us the following weights:

1B = 1.5

2B = 2.5

3B = 3.5

HR = 4.5

Does that look a little familiar? It should; multiply those values by two and you get the true weights which I quoted a little earlier. But here’s the problem: walks are given a weight of .5 in such an equation, half of what they should be. So here’s an idea: why not add some extra value for walks by adding .5*BB% to the equation. That would double the value of a walk and give us the perfect ratios we’re looking for. What is BB% though?; it’s simply OBP – BA. So, we end up with the following formula:

SLG + .5*OBP + .5*(OBP – BA)

which is equal to

SLG + OBP – .5*BA

or in other words

2*OPS – BA

Can it really be that simple? Yes! As you can see, both OPS and BA are very valid statistics, especially if combined the right way. And if you want to approximate the GPA scale, simply divide by 7. Thus, GPA2 = (2*OPS – BA)/5. It’s more accurate than the original GPA and just as simple.

So how does GPA2 compare to GPA? Let’s take a look at the top-ten hitters this season based on GPA. GPA2 is in parentheses:

1. Derrek Lee – .367 (.374)

2. Jason Giambi – .358 (.350)

3. Albert Pujols – .356 (.358)

4. Miguel Cabrera – .352 (.356)

5. Alex Rodriguez – .347 (.340)

6. Travis Hafner – .343 (.336)

7. Nick Johnson – .340 (.315)

8. Adam Dunn – .331 (.344)

9. Carlos Delgado – .330 (.319)

10. Brian Giles – .325 (.303)

As you can see, GPA overrates high-OBP guys like Giambi, Johnson, Delgado, and Giles while underrating the high-SLG guys like Dunn. GPA2 corrects for that, while maintaining GPA’s simplicity.

Your analysis is interesting but ultimately invalid because you are mixing different demominators. SLG has a denominator of AB and OBA has a denominator of PA. Becuase of the different denominators, you can’t add the weights together. If the weights for OPS were truly W+2S+3D+4T+5HR as you state, you could figure that for players and divide it by PA to get OPS.

Good site, BTW.

To finish up the last post, I forgot that you are right of course that 1 walk produces an OPS of 1, and 1 single produces an OPS of 2, etc. But what is more interesting is the marginal value of one additional walk or single or what have you when we add it to a real player’s OPS. And in that case the weights are not 1, 2, 3, 4, 5.

If you want to put OBA and SLG over the same denominator to get OPS, you have to do this:

OPS = ((H+W)*AB + TB*(AB+W))/((AB*(AB+W))

This as much as anything illustrates the silliness of OPS as a serious analytical stat(it is fine for quick stuff of course). Why multiply on base events by ABs? Why multiply TBs by PAs? Why use a denominator of AB*PA? The only possible justificiation is that its convienient and it “works”.

Thanks, Patriot. You are correct. But I do like the idea behind a stat like GPA or even EQA: to allow a quick-and-dirty measure of a player’s value. (2*OPS-BA)/5 should make for an accurate comparison of two players. I would not recommend using this for anything more than that.