Incidentally, MLB non-pitchers had an average GPA of .259, while "replacement level" is somewhere between .213 and .220.

But what are the average and replacement marks in component form: eg. by position?

While it's a nice & more accurate number to have, I feel a little uneasy by how haphazardly the OBP factor is changed just so it looks more like a BA. I realize 1.7 and 1.8 won't make a big difference, but if you're going to use this you might as well be as close as possible (and I realize the range is 1.7-2.0).

What I think would be interesting is to see how players ranked using OPS and GPA. I'm just too busy at the moment to pull up a spreadsheet and try it out.

I dunno, kinda useless metric, IMHO. The ideal is a metric that is both easy to calculate and accurate. This doesn't exist, so you gotta pick either easy to calculate or accurate. OPS is obviously easy to calculate but not very accurate, while EqA is difficult to calculate and accurate. A-Gleem has tried for a compromise, but I just don't think it works. It's too tough (for me at least) to figure out by just glancing at the numbers, so I gotta bust out the calculator or take a few seconds while my internal hourglass rotates. If I've gotta do that kind of work, I'm just gonna bring up Prospectus' EqA page.

That said, an improvement on GPA, I think, would be, instead of multiplying OBP by 1.8 and then adding SLG, simply halving SLG and then adding OBP. It's a lot easier and the accuracy of the ratio is about the same. Of course, it takes a more complicated calculation beyond that to get it took like BA. But I don't really care about that. It doesn't take much to learn a new scale, so I would bother trying to get it to look like BA.

Doesn't Paul DePodesta say in Moneyball that one point of OBP is more important than one point of SLG by a factor of 3?

Go to the U.S.S. Mariner blog for a good rant about junk stats. I'd regretfully have to say that GPA is just that.

Leigh: DePodesta actually says that the formula they use 'weights OBP three times.' People have interpreted this to mean that they use the formula 3OBP+SLG, but he doesn't give us the entire formula, so we have no idea if that's what he meant. I doubt it's that simple.

I agree with Nick G and Shrike. I enjoy Aaron's blog, but this stat is just noise (especially the supposedly brilliant twist of scaling to batting average).

DePodesta actually says that the formula they use 'weights OBP three times.' People have interpreted this to mean that they use the formula 3OBP+SLG, but he doesn't give us the entire formula, so we have no idea if that's what he meant. I doubt it's that simple.

I originally thought that they meant 3OBP+SLG, but from reading some more what I think it is, is that above a certain threshold an increase in one point of OBP is worth 3 times the value of a one point increase in SLG. And what the threshold is is of course the key.

http://somecalzoneforderek.blogspot.com/
I can't believe you guys are so cynical! I think it's pretty damn clever of Aaron. This more than anything he's done tells me that this kid is the real deal, a Neyer in the making.

After reading Tangotiger's report, I tried to implement OPS*1.7 + SLG in some of my postings here on BB. But because it was hard to make sense of what the numbers meant without a baseline, I kinda gave up on it.

Heck, the name alone (OPS*1.7 + SLG) made it unwieldy.

But with a nice, cheeky new name, and that brilliant /4 factor to boot (heck, James multiplied his results by 3 to arrive at Win Shares for the same easy to grasp reason), Aaron's made a meaningful statistic that much easier to use.

I've already used GPA on my other website to quickly compare Choi and Lee's minor league numbers (something I couldn't do with EqA).

Great work!

I'm disappointed to see no GPA's in Aaron's first post-GPA entry.

Did to the boy lose his nerve? He could have eased us into it, quoting GPA alongside BA/OBP/SLG.

For you Zumstegs out there, go back and read Tangotiger's article, "OPS: Begone!" He's not just pulling this stuff out of the air. (Man, DMZ's a good writer, full of insight, but he may have overtaken Mike of Mike's Baseball Rants as the internet's biggest baseball crank--although Mike's unsubstantiated comments about why Win Shares must be wrong, wrong! just because Bonds somehow, mysteriously ended up with fewer WS than Pujols is pretty hard to top.)

I'll try to address some of the points made here. First off, though, I want to say that GPA isn't ideally suited for heavy lifting.

What it *does* do, is provide one number, on an immediately-understandable scale, that scales almost exactly to EqA (except where weird park factors like Montreal or KC or San Diego or Colorado come into play, GPA is usually 0-3 points from EqA) with almost no calculation. I can do GPA in my head; not everyone multiplies by 9/5 that great, but it's certainly there. I'm not suer Jedediah Buxton could do EqA in his head.

I feel a little uneasy by how haphazardly the OBP factor is changed just so it looks more like a BA

No, that's exactly what you want. Nothing is worse, in my opinion, than pompous over-precision in metrics; crediting guys with one-tenth of a run is so dumb I don't even have words to describe it - it's a trap I fall into constantly as well. GPA isn't as precise as it would be to run a best-fit curve to player/league/team numbers and come up with a weighting that way; I would argue that it doesn't need to be. The "precision" you gain in using 1.7 instead of 1.8 or what have you is an illusion... tiny fractions of a "run" on an individual player basis.

The key to GPA is exactly the scaling... if a league average is .259, replacement level a bit below .220 and a very good hitter is at .300, I know instinctively what to do with that, in a way that I just don't with 4.15 RC/27 or what have you. RC/27 is a great metric... I just don't have the same instinctive feel for it that I do after committing to memory thousands of batting averages. 25 years of looking at the backs of baseball cards and encyclopedias gives you a feel for BAs that you *cannot* pick up in two weeks.

junk stats. I'd regretfully have to say that GPA is just that.

I'm not sure why. Is EqA a junk stat to you? GPA, with the caveat that it isn't park-adjusted, pulls the same load as EqA does.

"Junk stat" means something in sabermetrics. It's not some term that Derek Zumsteg gets to pull out of his pompous ass and slap on anything that doesn't meet his imaginary standards. Zumsteg has the tongue of a supermarket pricing-gun, though I'm not sure the complexity of his internal workings measures up. A "junk stat" was addressed by James in the '88 Abstract... and it means something where disparate discrete stats are added together without explanation or reason. Don't be fooled by Zumsteg bending the meaning of the word.

EqA and GPA, for all their potential flaws, don't do that. EqA measures EqR per Out... on a logarithmic scale, yes, but there is a perfectly good explanation and reason for using EqR per Out... it's an excellent measure of a player's ability to produce runs. GPA uses (1.8*OBP + SLG)... again, an excellent measure of a player's ability to produce runs.

this stat is just noise

I see lots of signal. Don't know how much I will use it, but I am thinking of replacing OPS with it completely. I don't like OPS as a handy-dandy measure, this one is better and calculation for me is no more difficult.

It would be noise if it didn't communicate anything meaningful.

For you Zumstegs out there, go back and read Tangotiger's article, "OPS: Begone!" He's not just pulling this stuff out of the air.

I echo Jurgen's sentiments 100%.

For myself, I find BA/OBP/SLUG provides much more information with little cost in space. GPA does reduce it to a single number in an effective and relatively easy to understand why.

In a Baseball Primer study, primer readers, experts and a computer were asked to project the final 2003 hitting stats of a number of difficult to project major league hitters. The computer used historical OPS with age adjustments. In the result, the computer whomped primer readers and experts. I'm betting that GPA would do even better than OPS. For uses such as this, GPA is ideally suited.

I've been using almost this exact formula (I multiplied OBP by 2 instead...it doesn't make much difference at all) to help prep for roto for 2 years. It's a great way to instantly make the good/not good decision in your head. It's far from the perfect stat (how does it correlate with runs scored?) but that wasn't the point. The point was simply to improve on OPS. And it does.

As per Sean's excellent suggestion, I calculated positional averages and tentative "replacement levels".

Each player was assigned only one primary position, and a single category was created for all outfielders.

"Replacement level" is a bit of a misnomer... it consists in the average performance of all players at that primary position with 100 AB or less. Instead of a theoretical replacement, this measure how the actual "replacement players" (the guys at the ends of benches, AAA callups, etc.) performed - as well as a few guys who got hurt, etc. The "replacement" pools are not large, most are less than 1000 AB in total, so quite a bit of variation should be expected.

Averages (all MLB non-pitchers receive a position)

C .258/.321/.402 - GPA of .245
1B .270/.358/.457 - GPA of .275
2B .268/.333/.396 - GPA of .247
3B .261/.327/.430 - GPA of .255
SS .262/.318/.394 - GPA of .242
OF .274/.345/.448 - GPA of .267
DH .279/.355/.479 - GPA of .279

Replacement Performance

C .222/.293/.342 - GPA of .217
1B .258/.320/.392 - GPA of .242
2B .209/.289/.331 - GPA of .213
3B .190/.245/.259 - GPA of .175
SS .214/.274/.317 - GPA of .203
OF .215/.287/.341 - GPA of .214
DH (Not enough data)

Third basemen with less than 100AB were utterly brutal. Perry, Paquette, Selby, Lamb, Enrique Cruz, Augie Ojeda, Garrett Atkins, Palmer... most were off years, though some of those players had no business at all in the majors.

I'll try to address some of the points made here.

Well done, Craig.

c.c. a copy to DMZ. (Although he's so thin-skinned, he'd probably go off on a big tirade wondering why people are always against him.)

Nick said: "while EqA is difficult to calculate and accurate"

The r-squared between Aaron's number and EqA is probably at least 0.90 (it's 0.99 with one of my own accurate and hard to calculate metrics). Aaron's number really means nothing, but it correlates extremely highly with a number that does, and also has the same scale. And that in the end, means something.

Nick said: "simply halving SLG and then adding OBP."

This was kind of my suggestion. Take OBP, divide by 2. Take SLG, divide by 4. And you get again a similar batting average scale, and a number that correlates at 0.9x with advanced metrics.

Or take what Nick said, and then divide by 2 again.

Pistol said: "above a certain threshold an increase in one point of OBP is worth 3 times the value of a one point increase in SLG. And what the threshold is is of course the key. "

(OBA - x) * 3 + (SLG - y)
becomes
3OBA + SLG - (3x+y)
becomes
3OBA + SLG - z

It doesn't matter what "z" is. You are still left with 3OBA+SLG.

***

As mentioned elsewhere, Aaron's number is especially for those who ONLY want one number, and one which they can do by themselves using ONLY OBA and SLG. And, doing that, doing 1% of the work that I do, or Clay does, or others do, gets you 99% of the way there.

I've already used GPA on my other website to quickly compare Choi and Lee's minor league numbers (something I couldn't do with EqA).

Wait a minute, Jurgen. If you ever told me that Some Calzone For Derek was your blog, I apologize for my memory, which is like Chris Woodward's glove -- adequate most of the time, with some embarrassing glitches.

I will be a more frequent visitor -- you can never have too much calzone -- and you'll be added to our Blog links ASAP.

The formula, and the comments on this thread, raised a question in my head. I hope no one thinks I'm trolling or being obtuse here, I'm honestly curious (perhaps uninformed): why is OBP considered so much more valuable than SLG%? Put another way, while I'm full aware that OBP is a vitally important stat, what is the rationale behind giving it so much more quantified importance than slugging?

For a quick calculate in your head method, take OBP divide in half and add that to one quarter of SLUGGING.

1/2OBP + 1/4SLUG

This still falls into the 1.7 - 2.0 range as suggested, but is much easier to do on the fly.

A .300/.400/.500 hitter calculates out to .150 + >125 = .325

http://www.baseballprimer.com/articles/authors/tangotigre.shtml
Steve, go to the above link, and read the first 2 articles.

Ooops... that should be .150+ .125 = .325

and

Ooops again, tangotiger made the same suggestion earlier.

Mental note: always preview posts and read the previous posts first.

I give up!

Seriously, why hasn't someone in baseball discovered Tangotiger and hired him?

http://economics.about.com
The absolute last thing I want to do is get into a math argument, but:

"above a certain threshold an increase in one point of OBP is worth 3 times the value of a one point increase in SLG. And what the threshold is is of course the key. "

Does not at all imply this:

(OBA - x) * 3 + (SLG - y)

The relationship between OBA and SLG could be highly non-linear, but have this relative weighting between the two for some level of the two stats. Take the function:

z = x^4 + ln(y)

Suppose we start with x = 2,y = 3. If we increase x by 1 and hold y constant, z increases by 65. If we increase y by 1 and hold x constant, z increases by 0.2876. If our objective is to maximize z, then a one point increase in x is 226 times more valuable than a one point increase in y for initial values (2,3). This does not imply that our original function was:

z = (226x + y) / some constant

Though for levels of x and y sufficiently close to (2,3) we can use this function to approximate the effects of a one point increase (but not say a 0.1 point increase or a 2 point increase).

I think this is what DePodesta was talking about, that at some level of OBP and SLG an increase in one point of OBP is equivalent to an increase of 3 points of SLG. I have no idea if he's correct, but I have a feeling the metrics he's using are highly non-linear.

Cheers,

Mike

Thanks for the kind words!

If MGL has offered to work for free, and no one's taken him up on it, and as long as Tom Ruane and Tom Tippett are still free agents, my guess is that MLB teams just can't see any value in it. (Not to say that they are wrong.)

Mike,

I don't want to argue the math, but say you've got 3 players that are equals (as a given... use whatever numbers you want):

.380/.590
.400/.550
.420/.510

Please show how it would be possible that a 1 point difference in OBA can be balanced against a 3 point difference in SLG.

And, in any case, a hitter in a team, does have a quasi-linear effect in creating runs to his team. That is, putting Delgado on a team that scores 4.0 RPG or on a team that scores 5.0 RPG will have a similar effect. To be sure, he will have more effect on the 5 RPG team, but it won't be much. (The greater the difference in the teams, and the more extreme the hitter, the less the effect will be close to linear.)

http://economics.about.com
I don't want to argue the math, but say you've got 3 players that are equals (as a given... use whatever numbers you want):

.380/.590
.400/.550
.420/.510

Please show how it would be possible that a 1 point difference in OBA can be balanced against a 3 point difference in SLG.

I just showed you how the two can make a difference of 226 points. I should be able to do 3. :)

I can make a formula that shows the two have a 100 point difference or a -5 point difference or if Carlos Delgado loses 30 points of slugging that interest rates will fall by 75 basis points. Particularly if I can "use whatever numbers I want". That doesn't imply that the formula is anything more than gibberish.

If you can say it with words, you can say it with math. Obviously we can express the concept with words. Why wouldn't we be able to with math?

If you think the DePodesta is wrong, that's a different issue entirely. I just think the quote in Moneyball implies that he's using a non-linear formulation. From what I've read about the A's, I wouldn't be surprised if he's using some sort of bastardized asset pricing formula. Heck, I wouldn't be surprised if he was using something based Black-Scholes.

Cheers,

Mike

What I'm saying Mike is that I can't envision how you can get those 3 players to come out the same.

This must also mean that I just didn't understand your example.

So, what I'm asking is for you to take 3 similar players (like my list, or anything you want), and show how you can have an equation that says that "1 point of OBA equivalent to 3 points of SLG" be any different than 3OBP+SLG.

Then, we can evaluate if that equation makes any sense.

http://economics.about.com
So, what I'm asking is for you to take 3 similar players (like my list, or anything you want), and show how you can have an equation that says that "1 point of OBA equivalent to 3 points of SLG" be any different than 3OBP+SLG.

How about z = (OBP/150)^4 + ln(SLG/150)*226/3

I think you're missing my point. I have no idea if DePodesta is right. If it will make you happy, I'll say publicly that your formulas are completely correct and his are all complete nonsense.

My point is that the quote in Moneyball doesn't not at all imply that DePodesta is using OBP*3 + SLG (or something like it). My guess would be that he's using a highly non-linear formulation which probably doesn't have OBP and SLG at all as arguments. But for some level of performance that he's looking at, a increase of 3 points of SLG is equivalent to a 1 point increase in OBP.

It's a very simple mathematical point.

Mike

For the sake of completeness, I should say that one of my earlier remarks where I seemingly signed off on Zumsteg's inflamatory rant was misleading. I was overly dismissive of GPA as merely a scaling stat for EqA; for that I apologize. I expressed that opinion simply because I have little trouble in eyeballing BA/OBP/SLG when I want to roughly rate player performance, so I don't particularly see the need for GPA.

Thanks to Craig for running out the table with positional data.

http://economics.about.com
Oops.. I goofed the last co-efficient in:

How about z = (OBP/150)^4 + ln(SLG/150)*226/3

It shouldn't be 226/3. But you get the idea.

Cheers,

Mike

I have little trouble in eyeballing BA/OBP/SLG when I want to roughly rate player performance, so I don't particularly see the need for GPA.

That's exactly where I'm at. I even tested myself to see if it was really true: I ranked the 2003 Blue Jay batters "by eye", looking at their OBP and SLG numbers. I then calculated their GPAs, and my list corresponded exactly. To me that means that GPA doesn't tell me anything I don't already know from two very common and physically meaningful stats.

Using the first equation (with the 226/3), we get the following as equals:

.380/.521
.381/.518

So, in this case, we constructed an equation where we fitted 1 pt of OBA = 3 pts of SLG. Now does this hold at other levels of OBA and SLG?

The Moffat equation yield the following as equals:

.340/.726
.341/.723
(3:1 ratio)

However, the Moffat equation also says:

.340/.480
.341/.478
to be equals (2:1 ratio) as well as

.300/.400
.301/.399
(1:1 ratio)

So, what Mike is saying, I think, is that at some level, you may have a 3:1 ratio, but that that ratio may end up being 2:1 or 1:1.

I can concede that this is possible (probable), I find it very unlikely that this is the case for:
1 - a hitter within a team
2 - a team at the current MLB run environment

The impact of a player, within a team, is so small that it can't have that effect. Take 8/9ths of a .340/.410 team, and 1/9th of a .450/.650 team, and you get a .352/.437 team, which would be equivalent to a .353/.435 team, which would make that 1/9th player as
.459/.632. (+9 OBA, -18 SLG).

You'll be hard pressed to find a situation where the 3:1 ratio holds.

The value of GPA (or EqA for that matter) is strictly for those people who:
1 - want one number
2 - that uses OBA and SLG only
3 - that can give them some meaning instantly
4 - and accurately represents the overall performance

If you don't want one number (i.e., you prefer OBA/SLG), then GPA is not for you.

If you don't want to be limited to only the information captured by the weighting scheme of OBA and SLG (i.e., you prefer the proper weighting of each H,HR,BB, etc), then GPA is not for you.

If you prefer a metric that tries to measure something in runs or wins, then this metric is not for you.

http://economics.about.com
So, what Mike is saying, I think, is that at some level, you may have a 3:1 ratio

That's precisely what I said in my initial message (#25):

"I think this is what DePodesta was talking about, that at some level of OBP and SLG an increase in one point of OBP is equivalent to an increase of 3 points of SLG"

Again, I have no idea what DePodesta's formula is. I'm not really at all interested in discussing what formula is better than what other formula. I just wanted to point out that the sentence in Moneyball does not at all imply DePodesta is using OBP*3+SLG.

Cheers,

Mike

What I'm saying Mike is that I can't envision how you can get those 3 players to come out the same.

You can if they deliver, on average, the same value for money. Mike's idea that DePodesta is talking about a value formula instead of a gross production formula, is in my view likely correct.

If you are saying that you can have 2 players that are paid the same amount, but that one gives you more bang for the buck, then I agree.

That is, the market is underpaying for the walk, such that 1 OBA point is paid as much as 3 SLG points, when it should be paid 2 SLG points.

I just want to say how nice it is to see a well-respected sabrmetrician like tangotiger visiting our blog and participating in our discussions.

Also, no matter who's right or wrong, can't we all agree that it's nice to see someone finally challenge Moffat's annoyingly superior math skills? =)

http://economics.about.com
I just want to say how nice it is to see a well-respected sabrmetrician like tangotiger visiting our blog and participating in our discussions.

I agree 100%. Whether you agree with his work or not, he's done a lot of interesting work and is well known in the stathead community.

Also, no matter who's right or wrong, can't we all agree that it's nice to see someone finally challenge Moffat's annoyingly superior math skills?

Thanks. I'm really quick to brag, so I think it's only right to point out that as far as mathematicians go, I'm incredibly lousy. If math skill was batting skill, I'd be Mario Mendoza. Like Mendoza and Ozzie Guillen, I've been able to scratch out a career despite my obvious flaws, which is good because I like eating and my girlfriend has expensive tastes.

I suppose when you compare Mendoza and I to the general public, our skills don't look quite so bad. :)

Cheers,

Mike

This is a bit of a tangent (but then, this whole thread is a tangent)...
Does anyone else have the feeling that the sabrmetric work people like DePodesta, Law, and now James and Voros might suffer from the fact that they can no longer put it out there to the general public? I'm utterly clueless when it comes to math, but at least when I see a new formula or theory from Clay Davenport or tangotiger, I know that it has had to run the gauntlet of popular opinion. Guys working top-secret for major league clubs have no such opportunity to have their theories critiqued, and therefore might not know if they are working with a flawed idea.

Although I suppose Voros and Bill James might be able to hammer at each other's ideas... but still, no one's good enough in this field that they never make mistakes or wrong assumptions.
Just something I've been musing on.

Thanks again for the kind words!

I think we all would be better off sharing, though I had my first email exchange with Bill James a few months ago, and I would never want to work with him.

So, I think the only people who would suffer would be those who already thrive in working with others.

tango: heh I know that James is notoriously difficult to handle, I meant more from the aspect of having other knowledgeable people check your work and critique your theories. I can't count the dozens of times I've gone over something repeatedly only to have someone else waltz in and point out an obvious error I simply couldn't see because I was too close to the work.

http://www.thepixiepit.co.uk/scrabble/rules.html
One stat I kind of enjoy is what I'll abbreviate as the STS. One of its benefits is that you can measure hitters and pitchers on the same scale. I don't have a complete listing, but I believe Javier Vazquez is the major league leader in STS. A sampling:

Name SS
Vazquez 37
Halladay 15
Delgado 10
Rodriguez 20
Bonds 8
Pujols 15
Stewart 10
Martinez 19

For an explanation of how these scores are calculated, click on my name.