# 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 has just published a book of aphorisms called Spirited Ejaculations of a New Enthusiast.

Guest
tangotiger

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.

Guest
tangotiger

include = exclude

Guest
Barkey Walker

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.

Guest
tangotiger

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?

Guest

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

Guest
tangotiger

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.

Guest
Barkey Walker

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.)

Guest

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.

Guest
tangotiger

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%.