**ABB#** (November 24, 2003)

Aaron has tried to give OPS a little more palatable flavor. As we know, OPS is not a good construction. 1.7*OBP + SLG combines those two metrics in a much better fashion. But, as Aaron points out *But really, if you asked how good someone hit in 2003 and you were told they had a 1.180 total for OBP*1.7 + SLG, would you know right away if that were good or bad? I know I wouldn't.* And that's a good point. So what does Aaron do? He simply divides the number by 4. Does that give you a better scale?

I just did a quick study, and it's a damn near perfect scale. What I did was selected the 287 batters with at least 250 AB in 2002. I have a metric that converts Linear Weights into a rate stat (I won't bore you with the details). Anyway, then I simply ran a regression of Aaron's number against my number. The r was 0.999, which is about as close to perfect as you can get. The standard deviation of Aaron's number and my number were both .035, meaning that they have the exact same scale. The standard deviation of batting average was .029, meaning that the spread of Aaron's number and batting average are also pretty darn close.

Since:

1 - 1.7 * OBP + SLG has such a strong correlation to Linear Weights Ratio

2 - The scale of Aaron's number is pretty much a match for batting average

3 - The overall league average of Aaron's number (0.253 in my group of players) is similar to batting average (.271)

I think that Aaron's number is a pretty good number to show.

Expanding my database of players to look at 1993-2002, and the best-fit for OPS to my Linear Weights metric is: 1.85 * OBP + SLG. Dividing by 4 to get Aaron's number, and the overall average is now .271, which compares very favorably to the group batting average of .278. The standard deviation is .035, which compares to the standard deviation of the batting average of .030. (I would also bet that Aaron's number and EqA would also match with a very high r as well.)

I think some variant of Aaron's number is something good to popularize.

*--posted by TangoTiger at 02:57 PM EDT
*

Finally, I ran a regression using all players from 1919 to 2002, with at least 300 PA, and the best-fit between OPS and Linear Weights was:

0.45 * OBA + 0.25 SLG + .016

Or: (1.8 * OBA + SLG) / 4 + .016

So, whether you decide to use that ".016" to get the overall average to match the batting average is up to you (it may be more annoying than it's worth).

"1.8" is the best constant to use, but if you use 1.7 it's almost as good. (The advantage of 1.8, is not only in its accuract, but it also bumps up the overall average a little closer to the real batting average.)

If you insist on NOT having the intercept, then the best-fit would be

(2 * OBA + SLG) / 4

which is OBA/2 + SLG/4.

My recommendation is to use this last one.

**Posted 4:00 p.m.,
November 24, 2003
(#2) -
****studes
(homepage) **

Wow, Tango. I really like the formula at the end. It's simple and elegant, really. It's even something that some could do in their heads, roughly. Maybe.

My first thought when I read Aaron's column was "well, why not just use BRA (OBP times SLG) instead?" The downside is that you don't have a number that's roughly comparable to BA. But I wonder how OBA/2 + SLG/4 compares, in terms of fit, to BRA?

I know you don't have this in your database, but the other comparison I can think of is EqA, which the Prospectus folks derived to approximate the same scale as BA, I believe.

**Posted 4:14 p.m.,
November 24, 2003
(#3) -
****tangotiger
**

Comparing the recommended new Aaron number to OBAxSLG, and you get an r-squared of .975. So, no sense in using a harder metric, when all you want is a quick estimate, right? As well, the scale of OBAxSLG is higher (.032 for batting average, .036 for the recommended Aaron number, and .041 for OBAxSLG).

To scale your number to batting average, you'd have to do something like:

0.88 x OBA x SLG + .15

which is not very satisfying.

I personally really like the Aaron number for its simplicity and power.

**Posted 4:19 p.m.,
November 24, 2003
(#4) -
****Sweet
**

*I personally really like the Aaron number for its simplicity and power.*

Me too, especially since ZIPS projects Hee Seop Choi to have one over .300. (*grin*)

I'll do my best to popularize this on BP and elsewhere.

**Posted 4:27 p.m.,
November 24, 2003
(#5) -
****tangotiger
**

Just to give you some quick calculations, this is what OBA/2 + SLG/4 gives you:

OBA... SLG... Aaron

0.300 0.300 0.225

0.320 0.350 0.248

0.340 0.400 0.270

0.360 0.450 0.293

0.380 0.500 0.315

0.400 0.550 0.338

0.420 0.600 0.360

0.440 0.650 0.383

0.460 0.700 0.405

**Posted 4:31 p.m.,
November 24, 2003
(#6) -
****studes
(homepage) **

You know, calling it "the Aaron number" would be an appropriate honor for its creator. Which calculation are you talking about, though? His first, or the 0bp/2+slg/4 calculation?

**Posted 4:36 p.m.,
November 24, 2003
(#7) -
****tangotiger
**

I'll let Aaron put his stamp on his own metric. I'm just offering my recommendation.

**Posted 4:52 p.m.,
November 24, 2003
(#8) -
****AlanJordan
**

"So what does Aaron do? He simply divides the number by 4. Does that give you a better scale?

.....Anyway, then I simply ran a regression of Aaron's number against my number. The r was 0.999, which is about as close to perfect as you can get."

Tango OPS correlates .999 to the Linear Weights rate stat whether you divide by 4 or not. Multiplying by a constant or adding a constant have no effect on r.

What about correlating it to something based on BaseRuns, wouldn't that be better than linear weights?

**Posted 5:09 p.m.,
November 24, 2003
(#9) -
****tangotiger
**

*Tango OPS correlates .999 to the Linear Weights rate stat whether you divide by 4 or not. Multiplying by a constant or adding a constant have no effect on r.*

I know.

I could have easily have said I ran the correlation prior to Aaron dividing by 4. I didn't mean to imply that dividing by some number led to the correlation.

*What about correlating it to something based on BaseRuns, wouldn't that be better than linear weights? *

No, for a player, Linear Weights is the better measure. Custom LWTS (generated from BaseRuns) would be even better, but when you look at 15,000 players, I doubt that custom LWTS will show any appreciable difference.

**Posted 5:11 p.m.,
November 24, 2003
(#10) -
****tangotiger
**

I also mentioned that:

*1 - 1.7 * OBP + SLG has such a strong correlation to Linear Weights Ratio*

as opposed to

(1.7*OBP+SLG)/4.

**Posted 5:50 p.m.,
November 24, 2003
(#11) -
****Aaron Gleeman(e-mail)
(homepage) **

Hey fellas -

Tango, thanks for linking me. Nice to see that I have stumbled onto something useful/interesting.

As for the name...

I was thinking of going with the "Aaron's Baseball Blog Average." Not that catchy, but the acronym is ABBA, which isn't bad.

Any other suggestions?

**Posted 6:04 p.m.,
November 24, 2003
(#12) -
****studes
(homepage) **

Abba? You want Mike Piazza "Dancing Queen" jokes for the next six months? kidding...

I personally like "the Aaron number". Catchier. Sure to sell on Madison Avenue. Maybe you can even trademark it!

Cheers,

Dave

**Posted 6:06 p.m.,
November 24, 2003
(#13) -
****Aaron Gleeman(e-mail)
(homepage) **

Yeah, I'm not all that excited about the ABBA stuff, but what would the acronym for "The Aaron Number" be? ABBA at least has some sort of name recognition and it "sounds" normal when you use it, like EqA or something.

**Posted 6:32 p.m.,
November 24, 2003
(#14) -
****Aaron Gleeman(e-mail)
(homepage) **

Okay, as long as I'm babbling...

What about:

TAN = **T**he **A**aron **N**umber

or

AaN = **Aa**ron **N**umber

or

ABBA = **A**aron's **B**aseball **B**log **N**umber

Can I get some votes?

**Posted 7:55 p.m.,
November 24, 2003
(#15) -
****David Smyth
**

Without going into any real detail, I think that the best choice in this area is probably something I have posted before, which is OBA*SLG*34, which is on the R/G scale, which is more satisfying than the BA scale, which has nothing to do with anything, really. In choosing one of these simplified OPS "competitors", you have to not only look at the overall R squared results, but also the results for the best and worst hitters in baseball, and the overall scale they determine. It is very difficult to find a batter who is significantly out of whack with OTS, given normal speed. You can do the +1 technique to determine where OTS falls short in theory, but for some reason it seems to balance out quite well for real players.

**Posted 8:16 p.m.,
November 24, 2003
(#16) -
****Aaron Gleeman(e-mail)
(homepage) **

*ABBA = Aaron's Baseball Blog Number*

As usual, I'm an idiot. That should be Aaron's Baseball Blog AVERAGE.

C'mon, I need an opinion. I'm running this on my blog tomorrow and I don't have a name for it yet!

Another possibility is AGA = Aaron Gleeman Average

**Posted 9:32 p.m.,
November 24, 2003
(#17) -
****jto
**

what about AOPS Aaron's OPS?

**Posted 9:39 p.m.,
November 24, 2003
(#18) -
****Michael Humphreys
**

Gleeman Production Average? ("GPA")

Aaron Hitting Average? ("AHA") (Ahah!)

Aaron's Batting Average ("ABA") (too lawyerly?)

**Posted 9:46 p.m.,
November 24, 2003
(#19) -
****Aaron Gleeman(e-mail)
(homepage) **

Hmm...I think I like GPA. Definitely the leader in the clubhouse. Sounds good, doesnt have anything to do with a bad music group and it is a "grading" system.

**Posted 10:04 p.m.,
November 24, 2003
(#20) -
****jto
**

GOPS= Gleeman's OPS?

**Posted 10:43 p.m.,
November 24, 2003
(#21) -
****Tangotiger
**

Yes, I like aOPS and gOPS. The name will at least convey something, unlike the millions of other TLA out there.

TLA = three letter acronym

**Posted 11:03 p.m.,
November 24, 2003
(#22) -
****jto
**

Thanks Tango. I'm glad you liked my suggestions. Oh, and jto stands for James T. Ondrey if you need to credit "naming" aOPS or gOPS to me in your blog Aaron :) haha j/k. keep up the great work everyone!

**Posted 11:37 p.m.,
November 24, 2003
(#23) -
****studes
(homepage) **

Count me as someone who's sick of acronyms. That's why I like "the Aaron number." That's classy. Sort of like the Richter Scale, the Laffer Curve and the Doppler Effect. Giving it an acronym will ensure that it gets lost in the sabermetric haze.

**Posted 2:32 a.m.,
November 25, 2003
(#24) -
****DCW3
**

"Aaron Gleeman's Offensive Number, Yo!" : AGONY

Otherwise, maybe "the Gleeman number." "The Aaron number" sounds too much like it would be 755.

**Posted 7:07 a.m.,
November 25, 2003
(#25) -
****Tangotiger
**

heh... never associated Aaron to Hank Aaron.... I think "The Aaron Number" is better in that case, as it gives Gleeman his credit, and maybe better name recognition because of Hank.

**Posted 10:12 a.m.,
November 25, 2003
(#26) -
****tangotiger
**

Aaron has updated his site, with this GPA, along with the league leaders. To really show this off, I'm going to take Aaron's list, and include his EqA.

GPA EqA Player

0.425 0.420 Barry Bonds

0.364 0.362 Albert Pujols

0.363 0.345 Todd Helton

0.340 0.341 Gary Sheffield

0.328 0.325 Jim Edmonds

0.321 0.322 Brian Giles

0.317 0.321 Jim Thome

0.316 0.310 Richard Hidalgo

0.314 0.308 Luis Gonzalez

0.314 0.312 Lance Berkman

0.340 0.337 Top 10

GPA EqA Player

0.340 0.338 Carlos Delgado

0.339 0.341 Manny Ramirez

0.328 0.326 Alex Rodriguez

0.323 0.325 Trot Nixon

0.317 0.325 Jason Giambi

0.316 0.318 Frank Thomas

0.314 0.316 David Ortiz

0.314 0.317 Bill Mueller

0.312 0.318 Jorge Posada

0.308 0.310 Magglio Ordonez

0.321 0.323 Top 10

Except for Todd Helton, which we expected, that's a huge BINGO!

**Posted 11:04 a.m.,
November 25, 2003
(#27) -
****Sylvain(e-mail)
**

Hey Aaron,

Great idea and nice picture on your website ;-)

Hope the use of the GPA will spread on the web.

Sylvain

**Posted 3:03 p.m.,
November 26, 2003
(#28) -
****tangotiger
(homepage) **

Just for those who are interested in my other comments on this subject, you can go to the above link, and also look for these posts: #72 and several starting at #136

I also made some comments at http://www.battersbox.ca

**Posted 9:51 p.m.,
November 26, 2003
(#29) -
****Patriot
**

I cannot believe the mini-furor that has erupted over this little stat. Nobody ever claimed it was the be all and end all of player evaluation, and people want to evaluate it against that standard. EQA makes claims a lot more grandiose, and doesn't get as much grief, and it uses a scale fudge as well. This[the uproar, not the stat] is just so frickin stupid.

**Posted 10:58 a.m.,
November 27, 2003
(#30) -
****David Smyth
**

Here is the same list Tango gave, using OBA*SLG*34. The scale is RC/27. I rounded to 1 decimal place in acknowledgment that this is only a quick-style approximation.

Bonds, 13.5

Pujols, 10.0

Helton, 9.8

Sheffield, 8.6

Edmonds, 8.1

Giles, 7.5

Thome, 7.5

Hidalgo, 7.5

LGonzalez, 7.3

Berkman, 7.2

Delgado, 8.6

Ramirez, 8.5

ARod, 8.1

Nixon, 7.8

Giambi, 7.4

Thomas, 7.5

Ortiz, 7.4

Mueller, 7.3

Posada, 7.1

Ordonez, 7.1

Not bad, huh? I prefer it to the "GPA" because it's on a better scale, and is a bit easier to calculate.

I want this named after me. Even though OBA*SLG was invented by D Cramer 25 years ago, I am the one who thought to multiple by 34. Since Cramer called his stat Batter's Run Average, I going to call this one the Smyth BRA. And no, I don't wear a bra. :)

**Posted 1:46 p.m.,
November 27, 2003
(#31) -
****Tangotiger
**

The difference that I see is the "finality" of this scale. Once you put in on a run scale, you are now saying something specific. In this case, " a team of 9 hitters with an equal performance will produce these many runs per game". And, that is a b-**** thing to do.

At least, with Aaron's number, it's presented along a batting average scale, and so, it saying that there's still at least another step to convert it into runs. Since Aaron's number and Linear Weights Rate have the same standard deviation, it's actually a pretty easy thing to convert it into runs for a player, within the context of a team.

With OBAxSLGx34, since the currency is already runs, that's it. Sorry, but I don't like it.

However, whatever floats someone's boat. If David thought long and hard for a R/G scale, then by all means. And if Aaron and lovers of EqA prefer the BA scale, so be it.

**Posted 9:44 p.m.,
November 28, 2003
(#33) -
****Tangotiger
**

What does that mean exactly. That Barry Bonds created 13.30 runs, within the context of an average team, per 27 of... who's outs? His actual outs? An average player's outs given the same number of PAs as Bonds?

What is the one-line definition of OBAxSLGx34?

**Posted 6:34 p.m.,
November 29, 2003
(#34) -
****David Smyth
**

---"What is the one-line definition of OBAxSLGx34?"

Allow me 3 lines in the interest of avoiding a long, "run-on" sentence.

OTS*34 is a quick estimate, using seasonal data, of the number of absolute runs created by a batter per offensive game. An offensive game is 27 total outs by this batter, or 25.2 batting outs, or whatever the equivalent is from the dataset you are using. By "absolute" runs created, I am refering to the numbers generated by, for example, the "new" B James RC, XR, or even your own conversion from LWR of (.47*plus)-(.10*minus).

Tango, you know all this, so why are you challenging OTS*34 with such "ferocity"? Are you ticked that your objection on the grounds of batter self-interaction is, in effect, not correct?

Bottom line for me--OTS*34 is an easier quick calculation than Aaron's GPA, plus it is on a more accurate scale than BAvg. This "scale" consideration is not only preferable on simply esthetic grounds, but also if you are doing a large study and want to use a simple stat. If you use a BAvg scale and one group is better than avg by 50%, and another group is worse than avg by 50%, you can't assume that they balance out to the avg, for example.

**Posted 7:30 p.m.,
November 29, 2003
(#35) -
****Tangotiger
**

I just wanted to make sure we are talking about the same thing.

*OTS*34 is a quick estimate, using seasonal data, of the number of absolute runs created by a batter per offensive game. *

But, didn't you say earlier that you don't have the problem with the interactive effect? I still don't know what it means exactly that Bonds has 13 RC/game, in the real sense. You aren't talking about 9 Bonds interacting with himself, right? Are you talking about Bonds interacting with 8 players, and then, ..... what exactly?

*An offensive game is 27 total outs by this batter, or 25.2 batting outs, *

This is another problem. Again, Bonds may make 2.2 outs per 5 PAs, while everyone else makes 3.3 outs per 5 PAs.

I still don't know what it means that Bonds created 13 runs per game, when he himself will only have 5 PAs.

I know what you are trying to do, but I don't know what it is EXACTLY that is happeneing.

**Posted 9:04 p.m.,
November 29, 2003
(#36) -
****David Smyth
**

Sorry, but I have no idea what you are talking about, Tango. It seems that you are trying to debunk OTS*34, simply as a way to debunk the father stat RC/27. If you don't like RC/27 (because it is not on a LW basis or whatever), that's fine, but lots of people do like it and understand what it means. I am certainly not trying to claim that RC/27 is a state-of-the-art way to rank batters, but it's certainly much better than BAvg, and since it's been around for 20 years and is on a natural scale, the "interpretation" of a simple quick estimator is not a problem with the average informed fan. And the PA thing with Bonds, who cares about PAs if you are on an absolute scale?

**Posted 10:50 p.m.,
November 29, 2003
(#37) -
****Tangotiger
**

David, I have no intents other than my direct questions.

OBA*SLG/(1-OBA) is RC/27, I believe. And the reason we don't like it is because of the interaction of having 9 Bonds on the same team.

Now, you said that by doing OBA*SLG*34 that you get a result similar to the Bonds + 8 average players, as best as I understand it. And you get a result of 13 runs. But, that doesn't make sense, which is why I've been asking for a clarification.

So, I ask again: what exactly does OBA*SLG*34 represent? What does 13 RC/27 for Bonds mean? Are you saying that the definition is:

"Barry Bonds created 13 runs per 27 of his own outs, within the context of that performance occurring with 8 league average hitters"?

**Posted 11:20 p.m.,
November 29, 2003
(#38) -
****David Smyth
**

---Are you saying that the definition is:

"Barry Bonds created 13 runs per 27 of his own outs, within the context of that performance occurring with 8 league average hitters"?

I guess the answer is yes, but I'm suspicious that that is sort of a trick question.

**Posted 10:16 a.m.,
November 30, 2003
(#39) -
****Patriot
**

What 34*OTS represents is the number of runs Barry Bonds would create playing with 8 of himself, but limited to the league average number of PA/G. At least as far as I can tell. OBA*SLG=Runs/At Bat. 34 is fairly close to the league AB/G for long term ML play.

**Posted 10:49 a.m.,
November 30, 2003
(#40) -
****David Smyth
**

---"What 34*OTS represents is the number of runs Barry Bonds would create playing with 8 of himself, but limited to the league average number of PA/G."

Thanks, Patriot, I think that's correct. I think I now realize what Tango was trying to get at. He was asking what OTS*34 *does* represent, rather than what I was using it as a proxy to represent. So I guess his point is that it's an *accident* that OTS*34 works. Sure, no problem, but since it's only a quick estimator, I wasn't all that concerned about that. I think that other virtues are more important in the specific matter of a quick estimator.

**Posted 2:46 p.m.,
November 30, 2003
(#41) -
****Tangotiger
**

One of the GREAT things about putting something in a probability metric (like batting average and OBP are, and SLG is not) is that you can apply statistical probability distribution techniques. So, there are some benefits of the BA scale.

Again, a reader can prefer to look at the BA scale, and others the R/G scale.

And yes, I wanted to say that OTA*34 is a fudge, albeit, a very good one.

**Posted 3:21 p.m.,
November 30, 2003
(#42) -
****David Smyth
**

BAvg itself is a probability, but just because GPA is on the Bavg scale does not mean that it also is restricted to between 0 and 1. Plug a perfect batter (1.000 OBA and 4.000 SLG) into GPA and you get 1.45, not 1.000. So I don't see how you could apply "statistical probability distribution techniques" to GPA.

Anyway, this topic doesn't really warrant this amount of discussion.

**Posted 5:06 p.m.,
November 30, 2003
(#43) -
****Tangotiger
**

In practical terms, Barry Bonds' is really the limit here, and his BA scale corresponds just about exactly to Linear Weights rate. From that standpoint, its a GREAT tool.

**Posted 12:09 a.m.,
December 1, 2003
(#44) -
****Greg Tamer(e-mail)
**

*Plug a perfect batter (1.000 OBA and 4.000 SLG) into GPA and you get 1.45, not 1.000. So I don't see how you could apply "statistical probability distribution techniques" to GPA.*

Well, not for GPA, but you could for 1.8*OBA+SLG by first dividing all values by the highest possible attainable value, 5.8 (and not 4). Then, the maximum is now one and the minimum is zero. I'd rather see/use this than GPA.

**Posted 7:57 a.m.,
December 1, 2003
(#45) -
****David Smyth
**

Sure, Greg, but you could do the same thing with OTS or any other stat. But you then lose the value of having it be on a well-known scale.