Taking control

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.

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