The thing any pitcher has got to develop—the biggest single item in

his whole stock of trade—is control! And by control I don’t mean

the ability to put the ball over the plate somewhere between the

shoulders and knees; I mean the ability to hit a three-inch target

nine times out of 10, the sort of control that lets you put the ball

in the exact spot you want it, and to play a corner to the split

fraction of an inch.

—Babe Ruth

How well can a pitcher locate his pitches? Here’s what I mean: set up

a dartboard at home plate and have your typical major league pitcher

fire his fastball, a real game fastball, not a batting-practice

cookie, at the target. How often will the pitch smash though the

little red bulls-eye? How often will he miss the dartboard completely?

I have a hunch that pitchers actually have less control over where

their pitches end up than is commonly believed, so that is what I’m

going to investigate today.

Scott Kazmir has had a tough time getting the ball over the plate, even withthe count 3 balls and no strikes. (Icon/SMI) |

Here’s where my hunch comes from: back when I was just a cub reporter

at The Hardball Times, one of my early pieces was a lightweight

musing about the 3-0 count. I looked at which batters

never swung on 3-0 (Piazza was one, I remember), who swung most often

(Sammy Sosa), stuff like that. There was one stat I came across,

though, that really surprised me: the high percentage of 3-0 pitches that

were balls and, obviously, directly resulted in a free pass. Try to

guess what that percentage is before reading the next paragraph.

###### The automatic strike—Not!

OK, what was your guess? My guess would have been around 15 percent.

The fact is that pitchers throw a ball on 3-0

fully 35 percent of the time. Think about that: most of the time the

batter is taking all the way and the pitcher knows it—all he

has to do is lay one over—and he misses more than one-third of

the time.

Well, that doesn’t really square with the notion of control that you

hear about from TV commentators, newspaper writers and blog authors.

“Painting the corners,” “on the black,” “pin-point control,” these are

the descriptions we hear constantly, but they seem to contradict the

finding of 35 percent balls on 3-0 pitches. Let’s investigate a bit further.

First of all, let’s see if I might have neglected some important

effect in analyzing the Retrosheet data for results on 3-0 pitches.

I’ve removed intentional walks, of course, but you might argue that

many players are semi-intentionally walked, especially after the

pitcher falls behind 3-0. I re-did the above, this time only

considering cases when first base was occupied. The thinking there is

that with first base occupied, the pitcher is much less likely to

pitch around a batter. The data show that there was no difference

with a runner on first; the ball percentage was still 35 percent.

What about selection bias, you say? That is to say, pitchers that go

to 3-0 counts often will be wilder than the average pitcher. So, we’re

not estimating the accuracy of the average major league pitcher, but a

wilder sub-sample. Well, it turns out that there is a small selection

bias: The average walk rate (unintentional walk per batter faced) for

the pitchers in the 3-0 sample (8.4 percent) is slightly larger than

the major league average (7.9 percent). I’m not going to try to

correct for this bias, but I think it’s safe to say that an unbiased

analysis would show a 3-0 ball percentage over 30 percent.

###### Who can get it over and who can’t

What about individual pitchers? I think we should see a wide variation in

3-0 ball percentage among pitchers, just as we see a wide variation in walk rate.

I can break down the 3-0 ball percentage according to pitcher easily enough. The following

table shows the 10 pitchers with the lowest ball percentage on 3-0

counts for the 2006-2007 seasons.

Lowest Percentage of Balls on 3-0 Counts, 2006-2007 +----------------+------+-------+ | pitcher | NP | B_pct | +----------------+------+-------+ | Haren_Danny | 56 | 0.179 | | Blanton_Joe | 69 | 0.217 | | Suppan_Jeff | 54 | 0.222 | | Moyer_Jamie | 76 | 0.224 | | Bedard_Erik | 63 | 0.238 | | Peavy_Jake | 52 | 0.250 | | Webb_Brandon | 67 | 0.254 | | Vazquez_Javier | 58 | 0.259 | | Glavine_Tom | 87 | 0.264 | | Westbrook_Jake | 52 | 0.269 | +----------------+------+-------+ (min 50 pitches)

A pretty good list of pitchers, which can roughly be divided into two

groups: the guys with good stuff **and** good control (Haren,

Bedard, Peavy and Webb) and the guys who throw strikes, but are more contact

pitchers than strikeout guys (Blanton, Suppan, Moyer, Glavine and Westbrook).

The odd man out is Vazquez whose strikeout and walk numbers would put him

in the first group, although he hasn’t achieved the same level of success due to a

persistently higher BABIP than expected.

The bottom 10, the guys who had trouble throwing a strike even when

they were just trying to groove one down the middle, are shown in this

table:

Highest Percentage of Balls on 3-0 Counts, 2006-2007 +-------------------+------+-------+ | pitcher | NP | B_pct | +-------------------+------+-------+ | Wright_Jamey | 59 | 0.508 | | Chacon_Shawn | 54 | 0.500 | | Trachsel_Steve | 72 | 0.500 | | Kazmir_Scott | 81 | 0.494 | | Davies_Kyle | 63 | 0.492 | | Jackson_Edwin | 60 | 0.483 | | Billingsley_Chad | 54 | 0.463 | | Hernandez_Orlando | 50 | 0.460 | | Lackey_John | 59 | 0.458 | | Carmona_Fausto | 60 | 0.450 | +-------------------+------+-------+ (min 50 pitches)

As we would expect, lots of high-walk guys here. A couple are

considered potential future superstars (Kazmir, Billingsley), one (Lackey) is

an established star and some of the

others have enjoyed periods of success (Jackson, Snell and

Carmona). The other guys are just wild, except for maybe

El Duque, who may be more of a nibbler. In any case, the point here is that some pitchers can barely

throw a strike 50 percent of the time, even when there is little danger of

the batter even swinging at the pitch.

So, looking at the percentage of balls thrown on 3-0 counts can give

us some qualitative insight to how much control a pitcher

has. However, we can do better by looking at the PITCHf/x data, which,

as you know, tells us the precise location for every recorded pitch.

###### PITCHf/x helps us quantify

The graphic on the right shows what happened on some 1,800 three-oh pitches to

right handed batters in 2007. Look at how badly some of these pitches, a

**lot** of these pitches, missed the center of the strike zone.

So, let’s try to quantify how close these pitches came to their

presumed target.

I’m going to simplify things a bit by looking separately at accuracy

in the horizontal and vertical directions. What I’ve done is take all

3-0 pitches, and thrown away anything that is not classified as a

fastball. I figure if a pitcher is throwing something other than the

fastball, he’s probably afraid the batter might swing on 3-0 and he’s

unlikely to be aiming down the middle.

I then calculate two quantities for this sample of pitches: the mean

and the standard deviation of the horizontal position. The mean, of

course, just gives us the average location of the pitches, which

should be zero (the center of the plate). The standard deviation is a measure of the **spread** in the

horizontal location of the pitches, or, in other words, of the average accuracy with which these pitches

are thrown—in short, the standard deviation is the quantitative measure of control that we

are looking for. Oh, one more thing: I additionally break down the data by pitcher and batter handedness.

The following table shows the results for horizontal movement:

Mean and standard deviation of 3-0 pitches, horizontal direction (inches) +--------+------+------+------+------+ | throws | bats | NP | avgX | sdX | +--------+------+------+------+------+ | L | L | 208 | -2.0 | 7.9 | | L | R | 602 | 1.8 | 9.0 | | R | L | 1121 | -5.5 | 8.1 | | R | R | 993 | 0.8 | 8.5 | +--------+------+------+------+------+

Here’s how to read this table: each row corresponds to one

pitcher/batter hand combination: left-handed pitcher vs. left-handed

batter, etc. The column avgX shows the average horizontal location of

3-0 fastballs, in inches. I’m using the usual PITCHf/x coordinate

system: zero is the center of the plate and positive values means the

pitch is on the outer half for a right-handed batter. The column labeled sdX is the

standard deviation in inches.

We see that in all cases sdX is similar, ranging from

about eight to nine inches, and we can call this the average accuracy (in the

horizontal direction) of these pitches. Just what I mean by “accuracy”, I’ll get to

in a bit.

The other thing to notice is that the value of avgX is not necessarily zero (the middle of

the plate), nor is it consistent for the different handedness combinations. What is going on here? Are

the pitchers not aiming for the center of the strike zone on three-and-oh pitches? That’s possible, but

there could be another explanation: When

studying the strike zone with PITCHf/x data last year, I found that the for left-handed batters the

strike zone was shifted somewhat towards the outside of the plate. The numbers in the above table are

qualitatively in agreement with the shifted strike zone.

Now let’s look at the results in the vertical direction. Things are a bit more complicated in

this case, because the vertical strike zone changes from batter to batter. Still, we can look at

the average vertical location of all 3-0 fastballs and compare that to the average center of the vertical

dimension of the strike zone. The following table shows the results:

Mean and standard deviation of 3-0 pitches, vertical direction (inches) +--------+------+-----+------+------+------+ | throws | bats | NP | avgZ | sdZ | szZ | +--------+------+-----+------+------+------+ | L | L | 208| 31.3 | 9.0 | 31.5 | | L | R | 602| 31.1 | 8.7 | 30.6 | | R | L | 1121| 30.8 | 8.8 | 30.7 | | R | R | 993| 31.0 | 9.1 | 30.7 | +--------+------+-----+------+------+------+

I’ve added an additional column, **szZ**, which is the average

vertical center of the strike zone (supplied in the PITCHf/x data

stream) for the four different cases. Here, the agreement among the

average location of the 3-0 pitches (avgZ) and the center of the strike zone (szZ)

is remarkable — the differences are always less than one

inch. In other words, these 3-0 pitches are really going, on average,

right to the center of the strike zone. This makes me feel better

about the assumption that these 3-0 pitches are really aimed down the

middle.

The standard deviation in the vertical direction is about the same as for the horizontal

direction, perhaps a shade higher. To be honest, I expected worse

accuracy in the vertical direction, because I’d always heard that a

pitcher had more control inside-outside than high-low. That appears to

be the case here, but the difference is minimal.

###### What it all means

OK, it looks like the average pitcher can locate the ball with an

accuracy of eight or nine inches, each, for the horizontal and vertical

directions. We can see what this means with a specific example. Let’s

say the pitcher decides to throw a fastball near the outside corner,

but he does not want to throw a ball. So, maybe he aims his pitch to pass over

the outer third of home plate—about seven inches from the

center of the plate and three inches from the edge of the strike zone.

How often will he hit his spot? Well, the chance of the pitch going over the outer

third of the plate (i.e. between 3 1/3 and 10 inches from the center) is

about 34 percent and there is a 20 percent chance that the pitch will pass over the **inner half** of the

plate, a true mistake pitch.

It’s actually very easy to see this while watching a game on TV

— just watch where the catcher sets up for the pitch and note

how often he must move his glove a significant amount to receive the

pitch. Sure, sometimes the ball goes straight to the mitt, but very

often the glove is moving around behind the plate quite a bit.

Announcers will rarely comment on how much a pitch missed its target

if the result (swinging strike, ground out, etc.) turns out OK. But

the level of control, or lack thereof, is easy to see if you watch (as Yogi said).

To close out, let’s try to answer our questions about the dartboard

of the opening paragraph. Based on the PITCHf/x results it appears

that a fastball thrown at a dartboard placed over home plate will hit

the bulls-eye with some part of the ball a little less than 1.5 percent of the

time. Fully 46 percent of these pitches would miss the dartboard

completely. Just think of that when they tell you about somebody’s pinpoint control.

**References & Resources**

The quote from Babe Ruth on control comes from *
Babe Ruth’s Own Book of Baseball*, which was actually ghostwritten by Ford Frick.