## Converting GO/AO to GB%

Because pitcher ground-ball percentages (GB%) are available at FanGraphs and because they strip away the influence of the defense behind a pitcher, they are (to the best of this author’s knowledge) the best available means of adjudging a pitcher’s ground-ball “profile.”

That said, ground-out/air-out ratios (GO/AO) are still more widely available than pure ground-ball percentages — and are, for example, the only grounder-related number Major League Baseball publishes at its site. So it’s not entirely out of the realm of possibility that one could find himself in such a situation as he had access to the one (i.e. GO/AOs) and not the other (GB%s)*.

*In press boxes, for example, stat sheets featuring GO/AO — but NOT GB% — are frequently available.

With a view towards learning more about the relationship between the two metrics, I found both the GB% and GO/AO for the 90 or so pitchers from 2010 with at least 162 innings pitched. Plotting the two against each other (and using a logarithmic best-fit) we get the following:

That’s pretty impressive, it seems, so far as correlation goes.

Using the equation you see there, I computed the expected ground-ball percentages (xGB%) for our 90 qualified pitchers using just their GO/AO ratio.

And here are the laggards:

The expected and actual figures are close enough for this author’s liking — and the fact that the equation mostly holds up in the extremes is satisfying.

Finally, for the sake of reference, here’s a table with approximate equivalencies for GO/AO and GB%:

Note that these equivalencies only hold — so far as I know — for major-league pitchers. That Chris Balcom-Miller, for example, posted a 2.13 GO/AO in 108.2 IP at Low-A Asheville last season does not necessarily mean that he induced grounders on 52% of balls in play. (It should be noted, however, that Chris Balcom-Miller is a future star and you would do well to draft him for your fantasy team or whatever this very second.)

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Carson Cistulli occasionally publishes spirited ejaculations at The New Enthusiast.

### 35 Responses to “Converting GO/AO to GB%”

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1. tangotiger says:

Carson, a groundout to airout ratio means:

g/a

A groundball percentage means:
g/(g+a)

So, in order to convert a ratio into a percentage, you do:
ratio/(ratio+1)

A g/a of .5 means a gb% of 0.33. A g/a of 2 means a gb% of 0.67, and so on.

However, in MLB, they include lineouts from the numerator and denomiator in the g/o ratio. But, they are included in the gb%. So, a gb% is actually:
g / (g + a + l)

Furthermore, in g/a refers only to outs, while gb% refers to all contacted balls. So, you’d have to convert the go to a gb by saying doing go/.75 = gb. And so on.

***

All to say: I don’t doubt the best-fit of the equation you found.

I do think that we can come up with a different equation that is grounded (no pun intended) in logic. And you can then do a best-fit against that equation.

• tangotiger says:

include = exclude

• Barkey Walker says:

What he did is fine wrt theory. GO/AO is an odds ration, when he takes the log, he then has a log odds ration. This is typically the response in an logit. Now, he puts it on the independent side, but hey.

The main change this suggests is in the error model, but with such high counts, it won’t matter, GB% is binomial which converges to normal in the region these pitchers are in.

• tangotiger says:

Right.

If you have a g/a ratio of .500, 1, 2 the ln of that is going to give you: -.69, 0, +.69. So, perfectly symmetrical. Which matches what the g/(g+a) would give you of .333, .500, .667, respectively.

But, the actual equation for gb% is g/(g+a+l). Would the ln(g/a) still necessarily hold as a core part of the conversion?

• Colin Wyers says:

Tango, it’s G/A, not G/F. LD should be included in AO.

• tangotiger says:

Following up:

To convert the ratio to a rate, if we had the exact same parameters in both, we’d do:

g% = g/(g+a) = .x*ln(g/a) + .5

That x would approach 0.25 as g/a approaches 1. And in MLB, x would range from .24 to .25.

So, if we used all contacted balls, then a best-fit equation would come in at something like .25*ln(g/a) + .5.

But, as noted, the ratio actually uses only outs, and excludes lineouts. The rate uses all contacted balls.

Carson’s best-fit, using observed data, changes that .25 coefficient to .18. It changes the intercept from .5 to .38.

My question is if someone here would like to try to come up with an equation without relying on individual data, and simply use some logic to the process. To presume that 20% of batted balls are line drives, that 25% of those are lineouts, and so on.

• Barkey Walker says:

I don’t understand where “That x would approach 0.25 as g/a approaches 1. And in MLB, x would range from .24 to .25.” comes from.

I think the more interesting thing to do would be to show that of the residual, some of it is explained by, i.e. the UZR of the players (obviously infield UZR should move a point to the right and outfield UZR should move it to the left.)

• Colin Wyers says:

You can rewrite GB% as:

GO + GB_H /(GO + GB_H + AO + A_H)

Where GB_H is ground ball hits and A_H is air ball hits.

GO+AO is going to cover something like 60% of all BIP. You could, if you wanted to get clever, do this instead:

GO + GB_H /(GO + GB_H + AO + HR + A_H_BIP)

So now you only have to worry about estimating GB_H and A_H_BIP. The question then becomes how well we trust the estimate of GB_H and A_H-BIP given to us by the batted ball stringers.

• tangotiger says:

I think this would be the basic point, right? That we’d estimate GB_H and A_H based on GB_O and A_O.

Basically, taking the factual information of g/a ratio of outs only and translate that in a simple equation into a g/(g+a) rate of contacted balls. So, if you see someone with a 1:1 g/a out ratio, you can then say that’s a GB contacted rate of 38.3%.

• I’m entirely prepared to bow to your wisdom. Let there be no mistaking.

Two questions:

1. MLB really excludes lineouts? Isn’t that a bizarre choice? It seems to me as though the advantage of GO/AO is that you can bucket all GB outs on the one hand and all line outs and fly outs in the other, and that way classification becomes less of a problem.

2. My main concern here, as you might guess, is just having a quick-reference sheet, so to speak. Even if the process I’ve used ISN’T the most logical way of getting to the answer, it still “works,” yes, as a quick reference?

3. Pun not intended AT ALL? Not even, like, 10%?

• tangotiger says:

Colin is saying lineouts are included. I agree with you that it would be highly bizarre to exclude them.

I agree with you that your equation does the job, and for that, it’s good. I was more asking as a technical exercise, that instead of relying on sample data, can we get to the same place without the individual player data, and just use league-wide data.

Pun: no, not at all. I was just writing, and then I stopped when I realized what I said.

• Colin Wyers says:

Tango’s mistaken, I think – AO should include fly balls, line drives and popups.

Lesse here – on MLB.com, Cain is listed with 248 AO. From Retrosheet, I come up with 178 fly ball outs. If I include PU and LD, I get 283…

Hrm. Okay, maybe I’m the one mistaken here.

• Colin Wyers says:

No, I spotchecked a few player – looks like LD outs are excluded. I concur that it’s extremely odd for them to do so, and I don’t know if that’s been done historically.

2. Mario Mendoza says:

ouch

• No, not really. That’s how the Tiger rolls. He’s just interested in doing good work. That’s why he’s so valuable to the community.

• tangotiger says:

That ouch was for me?!

Here’s an easy way to read my comments: if you can read ambiguity into whatever I’m saying, then read mostly nice ambiguity in there, with a hint of “but maybe he is being an a\$\$hole”.

• Nathaniel Dawson says:

Ahh, but that little bit of “a\$\$hole” makes people want to really think about what they’re doing and delve further into their methodology to make sure they’re looking at everything and haven’t missed anything. That bit of “niceness” enables them to accept an alternative explanation if they find it better fits reality. And, if they still come up with a better answer, they have no problem with saying so, without worry that it devolves into stubbornness between people instead of enlightenment.

You really have a gift for challenging people without being belligerent. It’s allowed people to really examine things and come to a greater understanding of baseball, without letting egos get (too much) in the way of enhancing our knowledge of baseball.

3. Dash says:

Carson, congratulations on having your post commented on by tango and Colin. You’re on the saber-radar! Does this mean they’ll start reading your NotGraphs posts, too?

4. Matt says:

I read the comments, and then my brain exploded. Awesome stuff guys.

• Just an FYI, FanGraphs is in no way liable for brain-explosions and does not offer replacement brains or treatment of any kind for said explosions. But, please, DO seek medical attention, immediately.

• Matt says:

I can’t… I need to find out when 27 is old.

• joser says:

Wait, now you’re giving medical advice? D’oh!

5. Charles Saeger says:

Typically, the GO/AO ratios have double plays counting as two ground outs. They do on BB-Ref.com; they did in the old Elias Analysts. Stupid, I am aware.

6. Steven says:

OMG, Carson actually almost contributed something useful for a change….almost…

7. tangotiger says:

1999 on MLB.com for Greg Maddux
g/a = 1.78

On B-R.com:
g/a = 1.68

***

On B-R.com:
294 GB outs (including 14 DP) ; 14 GB errors
140 FB outs (including 5 SF); 2 FB errors
40 Line outs; 1 Line error

So, how do we get to 1.78 or 1.68? If we count everything:
ground outs: 294 + 14 (for the 2nd out) + 14 (for the fake out) = 322
air outs: 140 + 2 + 40 + 1 = 183

322/183 = 1.76

Well, that’s pretty close. Let’s take out the errors.

ground outs = 308
air outs = 180

308/180 = 1.71

Getting closer to Sean’s.

What if we remove lineouts and remove the errors?

ground outs = 308
air outs = 140

308/140 = 2.20

Nope, we took too much off the bottom. Let’s take out the extra out on DP in the numerator.

ground outs = 294
air outs = 140

294/140 = 2.10

Not right either.

Let me just ask Sean and Cory, and I’ll report back.

• tangotiger says:

On MLB.com’s page, Maddux has 306 ground outs and 171 “air” outs.

To get to 306, that would mean either counting the errors as outs, or counting DP twice. Either way, you get to 308, or close enough.

To get to 171 though? If you keep the lineouts, but remove the SF, you get to 175. I guess that’s close enough too.

I only checked Maddux 1999. If someone else wants to check someone else, go ahead. I’m asking the guys at MLBAM for confirmation.

8. UncleCharlieVT says:

This sounds hard to do. Instead why don’t you just invent a time machine, go back to to 1987, watch and score all of Jamie Moyer’s starts and compare them with the record. If you don’t like watching games at Wrigley, I guess this is just a bad idea.

9. yanatan16 says:

Here’s a derivation of an approximate formula for GB% given GO/AO and constants derived from a large population:

Consider the goal GB% := g/(g + a). If we had R=g/a, then 1/(1+1/R) = R/(R+1) = g/(g+a) = GB%. Thus, we now have simplified the problem to converting GO/AO to R=g/a.

For now, let g:=grounders, a:=BIP-g, go:=grounder outs, and ao:=BIP outs – go. Then go = g * f_g, the fielding rate on grounders, where f_g := 1- BABIP(g). And ao = a * f_a, f_a := 1 – BABIP(a). We can then see that GO/AO * (f_a/f_g) = g / a = R! But now what if ao isn’t exactly a * f_a?

Ok, so my proposal is figure out (in a large population) the constants f_a:=mean(a)/mean(ao) and f_g:=mean(g)/mean(go), now defined as the conversion rates from a to ao and g to go (whatever they may be). Then let c = f_a/f_g. Now our function is:

GB% = 1/(1+1/(GO/AO * c)).

It is approximate because f_a and f_g are calculated for a population instead of for a player, but I think this is necessary, because Carson’s motivation is trying to find GB% given not enough information, so we are unlikely to have the information available to find the constants either. And because we don’t really know what ao and go are, this allows us to find the conversion rates without having exact knowledge of the definitions of ao and go.

10. Bob says:

Thanks for the research, Carson (and Tango, et. al., as well).

What struck me immediately was the high quality of hurlers at BOTH extremes of the GB/FB spectrum. Advantage groundballers—but not by much.

Makes me wonder if this is at all a one-year fluke, or if flyball outliers are historically, and consistently, as successful as their groundball-heavy brethren.

• Nathaniel Dawson says:

Not a one-year fluke. Over the past 9 years since Fangraphs has data for batted balls, there’s little difference in ability to prevent runs between groundballers and flyballers. It seems there is a slight advantage for groundballers, but not a particularly significant one. I’ve often wondered if that has been constant over the different eras of baseball. Did groundball pitchers have a significant edge in the 60’s, when run scoring was so low that the value of a home run was magnified? Were flyballers better in the 70’s during an era with larger parks that had artificial turf, with a lot of speedy players patrolling the outfield? Could my logic be flawed and it was the other way around?

The vast majority of hall of fame pitchers were fly ball pitchers.

• Nathaniel Dawson says:

Knowing the limitations of our knowledge of batted ball results beyond this last decade, how do you know this to be true? Not saying I’m challenging your statement, but would like to know the basis for it.