ERA+ ... Is the formula correct?

[AaronGNP]

I hate for this to be my first post here, but I've been looking at ERA+ today, and it just doesn't seem right to me, at least not in context of OPS+.

I've always understood OPS+ to be OPS (technically the sum of its parts) in relation to league average, expressed as XXX% of league average.

In the simplest terms, a player with an .OBP of .300 and a SLG of .600 in a league with an OBP of .250 and a SLG of .400 would have a an OBP+ of 120, a SLG+ of 150 and an OPS+ of 170, assuming my math is correct.

But the accuracy of my math isn't my concern. My concern is that the SLG+ and OBP+ figures are quoted in relation to league average. If your OBP is .300 and the league is at .200, your OBP+ is 150, or 1.5 times that of league average.

However, I noticed ERA+ does not use this, and actually uses the inverse of this. The ERA+ formula (again, assuming I have the formula correct) is (LgERA/ERA)*100. So if the LgERA is 4.00 and your ERA is 3.00, you get an ERA+ of 133. However, it seems to me that one fourth of 4 is 1, and the ERA+ should actually be 125, or 1.25 times that of league average.

I understand that the formulas will be different, since ERA is an inverted statistic, but isn't there a better way to calculate ERA+?

I was grinding numbers, and I think I found a better formula:

((LgERA-ERA)/LgERA)+1)*100

This formula rightly puts LgERA in the denominator, and now factors ERA as a ratio of league average, rather than as a ratio of the player's ERA.

Thoughts? Feelings? Did I mess up somewhere or misunderstand something?

Thanks

AGNP

[SABR Matt]

If I understand your formula correctly, that's just (1 - (ERA/LgERA) + 1) * 100

or simply the ratio of ERA / LgERA

So what you actually want is the equivalent of OPS+ but for ERA.

We've dicussed this at length here and that's essentially the conclusion the sabermetricians here have reached...that it's silly to invert ERA+ just so that better pitchers get higher numbers.

[AaronGNP]

Obviously your formula is the same, however, the difference between my formula (or your revision) and the one currently in use is the current formula will actually yield higher ERA+ values, including infinity, and will also be in terms of a percentage of player's ERA, rather than as a percentage of the league average ERA.

Basically, in the current system, at the ERA gets lower, the ERA+ becomes exponentially out of proportion, since the player's ERA is in the denominator (unlike SLG+, OBP+ and by proxy, OPS+). The scale on which they operate is dependant on league average, rather than the player's average.

AGNP

[Patriot]

As Matt said, there was a discussion on this board a few months ago, and I don't think you'll get any argument from people here that ERA/LgERA is a more logical construct. The idea of doing it that way is nothing new, and dates back at least as far as Bill James' first Historical Baseball Abstract.

[Tango Tiger]

For some reason, no one in the world has a problem understanding that a pitcher wants a lower ERA... lower is better. "Gibson has a 1.12 ERA! Yay, that's great!"

Now, for some reason ERA+ has to have a bigger is better, ostensibly to put it in-line with OPS+ for hitters. This way, you have a 200 OPS+ and a 200 ERA+, and think, "yup, both great".

However, b-r.com, which is popularizing ERA+ also has OPS+ for pitchers (OBP and SLG allowed). And how is that handled? OPS divided by lgOPS, such that lower is better for the pitcher!

Not only is the ERA+ confusing as all getout, but you can't even use it mathematically, since the denominators is different. You can't do lgERA/ERA in season 1 and add that to lgERA/ERA in season 2 and divide by 2 and get anything resembling normal (even presuming equal number of IP in both seasons).

I think ERA+ is a foolish mistake, one that rather than perpetuating its mistake, should be cleaned up going forward. I've made my feelings known on this on Sean's blog.

[Bothrops Atrox]

I think ERA+ is a foolish mistake, one that rather than perpetuating its mistake, should be cleaned up going forward. I've made my feelings known on this on Sean's blog.

ERA+ is certainly flawed for the previously mentioned reasons, but it is still useful in obtaining a quick snapshot of how a pitcher compared to the league. It is a useful tool (even in its flawed BBR form) for those who don't have the time or want to put the hours or days worth of effort into more accurate stats. I would love to see it cleaned up and the mistakes unperpetuated, but I will still reference it when I need something quick and fairly accurate.

[Tango Tiger]

ERA+ is certainly flawed for the previously mentioned reasons, but it is still useful in obtaining a quick snapshot of how a pitcher compared to the league. It is a useful tool (even in its flawed BBR form) for those who don't have the time or want to put the hours or days worth of effort into more accurate stats. I would love to see it cleaned up and the mistakes unperpetuated, but I will still reference it when I need something quick and fairly accurate.

No one is saying it's not useful. I mean, if you take anything, and do:
1/anything
That's still useful! It's just the baseline is all messed up now. You have to remember that ERA+ and OPS+ for pitchers now do not share the same "lower is better".

It's like having Celsius and 1/Kelvin. One is the higher the number the hotter it is. The other is the opposite. But, the number in whatever form, is useful. You just have to understand that you have imposed an extra limitation.

From now until the day ERA+ is changed, someone, somewhere, will see an ERA+ of 200 one season and 67 the next season, and say, "see, overall, he's above average". And he'd be wrong. And this is people who are knee-deep in this sh!t. Imagine the typical baseball nut.