Butterflies are not bullets

Butterflies aren’t bullets. You can’t aim ’em—you
just let ’em go.

— Charlie Hough

When I first started looking at the Pitch f/x data, data that gives us
an unprecedented amount of information about every single pitch that it
tracks, one of the first players that sprung to mind, one of my
favorite players of all-time, was Boston’s Tim Wakefield. You see, Wake is the only pitcher in the majors who
throws the coolest, neatest, quirkiest, most unpredictable pitch in
existence: the knuckleball. Now that we have over 1000 of Wakefield’s
pitches recorded by the Pitch f/x system, we can get a pretty good look at the

The strangest (and greatest) pitch

The knuckleball is different from all other pitches in many ways. First of all there is speed, or lack thereof: the knuckleball is one of the slowest pitches thrown on a major
league ball field. It’s not necessarily the slowest—Tim Wakefield’s curveball is slower than his knuckler, but we’ll get
to that in a minute. Another unique characteristic of the knuckleball
is the unpredictability of its movement. Nobody knows where it’s going to end up, including the
pitcher. And because of its erratic and unpredictable motion, I
believe it’s the only pitch that is not located: the knuckleball
pitcher does not aim for a certain part of the strike zone, he just,
as famed knuckleballer Phil Niekro put it, throws it at the catcher’s
mask and cheers for it on the way in.

There are other aspects that set the knuckleball apart: it’s hard to
catch; batters, when they do hit it, tend to make poor contact
(knuckleballers seem to be somewhat free of the constraints posed by
DIPS theory); there is no platoon split for knuckleball pitchers (or
at least it’s much smaller than the average split), and so on.

I suppose one of the most appealing things about the knuckleball to
Joe Average is that it doesn’t take a huge guy, with legs like Greek
columns and million dollar arm to throw an effective knuckler. Just
about anybody can learn to throw a knuckleball of some sort (even Wade Boggs), although, clearly, very few can learn to
control it to the degree necessary for it to be a useful major league

Getting the breaks

So, just how does a knuckleball break? We’ve all heard the stories
about knucklers doing incredible things and obviously they do. Now,
with the pitch data available from mlb.com, we can begin to see what
is really going on.

The chaotic glory of the knuckleball is best shown with the
movement plot that I’ve

in the

This type of plot shows the vertical and horizontal movements of a
pitch relative to a hypothetical spinless pitch. These “movements”, which are
caused by the spin that is imparted to the ball by the pitcher, are useful, along with pitch speed, in
identifying the different pitch types.

This graphic compares the movement plot of Tim Wakefield with recent
Cy Young recipient C.C. Sabathia. First, let’s have a look at
Sabathia’s repertoire (left-hand plot). The big left-hander throws
three distinct pitches: a fastball with average speed of 94 mph (red
points), a changeup at 86 mph (green) and a hard curve at 81 mph
(light blue). Each pitch type has a fairly well-defined movement,
i.e. they look like fairly contained clusters in the movement plot.

Now look at what Wakefield’s pitches are doing: the knuckleball is
that huge splotch of green points that don’t seem to have a consistent
break at all. They tend to break in any direction, or perhaps not at
all. Crazy. Well, we all knew that the break of the knuckleball is
unpredictable, but seeing this plot really drives the point home,
doesn’t it?

As you can see, the large majority of Wakefield’s pitches are
knuckleballs, but he does throw a, ahem, fastball (red points, 75 mph)
and a very occasional curve (blue points, 60 mph). As we’ll see
shortly, Wakefield generally avoids these secondary pitches, unless
he’s behind in the count.

Changing speeds

Another curious thing about the knuckler is that it changes speeds—by itself! A typical pitch loses about 10% of its original
speed while on its way to the plate. The knuckleball also loses about
10% of its speed on average, but the variation from pitch-to-pitch is
larger than for other pitches. As an example, the plot on the right
shows the percent loss in speed for Wakefield’s knuckler (green
points) and for Sabathia’s curve (light blue). So, the knuckleball is
not only dancing left and right, up and down; it’s also speeding up
and slowing down as it comes into the batter!

In truth, the variation in speed is small in absolute terms: the
spread in the average velocity (which is what matters to the batter)
is only around 2-3 mph. Still, perhaps when you’re putting all your
concentration into following the dancing floater as it comes in
towards you, the variation in speed is one more thing to worry about.

A loss of tactics?

Before a “normal” pitcher throws a pitch, he and his catcher must make
a couple of choices. They must agree on the type of pitch and the
location. Fastball in, slider away, split in the dirt, that kind of
thing. They make these decisions based on several factors: who is
batting, the count and number of outs, the score, what pitches are
working for the pitcher that particular day, etc. This choice of
pitch is a kind of cat and mouse game between pitcher and batter: the
batter tries to anticipate what the pitcher will throw and the pitcher
in turn tries to figure that out and throw something different.

A Hardball Times Update
Goodbye for now.

When Tim Wakefield is on the mound, all of those tactics go out the
window. Well, most of them, anyway. About 80% of Wakefield’s pitches
are knuckleballs. There really isn’t any element of surprise,
except for the surprise of seeing a pitch seem to defy the laws of physics—the batter doesn’t try to guess what the pitcher is doing and
the pitcher isn’t trying to outsmart the batter. Wakefield just
throws the knuckler right down the middle, 80% of the
time. He’s content to let chaotic air flow, or God, fool the batter
and not worry about pitch selection or location.

Think about that for a minute: with the knuckleball, the whole battle
between pitcher and batter is vastly simplified. You ever hear
anybody say that Doug Mirabelli, who is Wakefield’s personal catcher,
“called a great game today”? Of course not, because he really isn’t
calling very many pitches. Now, we’ve all seen the knuckleball catcher struggling to corral
these knuckleballs, but in some ways, Mirabelli has it easy:
instead of studying video of opposing batters and noting their
weaknesses and strengths, he can go out and party all night (or stay
home and read spy novels—I do not know where his preferences lie),
because the “game plan” is just to throw a flock of knuckleballs down
the middle.

In another sense, of course, Mirabelli has it anything but easy. He’s
got to catch the damn thing, which is not exactly child’s play: Joe Torre once said that you don’t
catch a knuckleball, you defend against it. And Mirabelli has to try
to throw out opposing basestealers, who seem to be starting their
slide into second while Wakefield’s butterflies are still wending
their way towards home plate. Unsurprisingly, Wakefield is generally among the American
League leaders in stolen bases allowed.

When to throw something else

I throw 90% knuckleballs. The other 10%
are prayers. I probably could throw other pitches. The only reason I
don’t is that I love pitching in the major leagues.

As mentioned above, Wakefield throws a knuckleball about 80% of the
time. Of the other pitches, about three-fourths of them are fastballs and
one-fourth are curveballs. Now Wakefield’s fastball, as we saw above,
comes in at around 75 mph, so its effectiveness clearly depends on it
not being a knuckleball.

So when does Wakefield decide to change gears and throw something
other than the knuckler? The table below shows how often Wake throws
a particular kind of pitch depending on the count. So, when the count is 0-0, Wakefield throws the
flutter-ball 88% of the time, the fastball 10% and hardly any curves
at all.

Pitch Selection for Different Counts
| Cnt  | NP  | KB%  | FB%  | CB%  |
| 0-0  | 349 | 0.88 | 0.10 | 0.02 |
| 0-1  | 156 | 0.92 | 0.02 | 0.06 |
| 0-2  |  83 | 0.90 | 0.02 | 0.07 |
| 1-0  | 138 | 0.78 | 0.20 | 0.02 |
| 1-1  | 123 | 0.91 | 0.06 | 0.03 |
| 1-2  |  97 | 0.87 | 0.02 | 0.11 |
| 2-0  |  44 | 0.52 | 0.41 | 0.07 |
| 2-1  |  55 | 0.62 | 0.36 | 0.02 |
| 2-2  |  78 | 0.96 | 0.04 | 0.00 |
| 3-0  |  16 | 0.31 | 0.38 | 0.31 |
| 3-1  |  21 | 0.48 | 0.52 | 0.00 |
| 3-2  |  35 | 0.54 | 0.40 | 0.06 |

You can see that as a general trend, Wakefield will throw fewer
knuckleballs as he falls behind in the count. When the count is 3-0,
for example, Wake throws the knuckler 31% of the time, with the
rest being roughly split equally among fastballs and curves.

All Red Sox fans know the sinking feeling when
Wakefield gets behind in the count and is forced to throw his 75 mph
heater. We start to feel queasy at the prospect, we squirm in our
chairs and get ready to turn away in horror when Wake’s fastball gets launched
into low earth orbit to come crashing down on the Massachusetts Turnpike like meteorites from
space. The Boston Police have been known to halt traffic on the Pike
when Wake goes to a three-ball count: the populace must be protected.

One way to beat the knuckler

Mark Ellis was having a hard time against Wakefield in a
this season.
He had struck out swinging on knuckleballs his first three trips
to the plate. As he strolled to the plate for the fourth time
against the wily Wakefield, he was formulating Plan B in his mind (this is pure conjecture on my part).
Wake’s first pitch was a knuckleball (it almost always is, as we have
seen) that was just a hair outside. He followed with two straight
curveballs (!), both taken by Ellis, to bring the count to 2-1. Wake
confounds again by throwing the fastball and Ellis again takes it:
strike two.

So, there is some strategy going on here, after all. After making
Ellis look foolish with the knuckler in the first three at bats, Wake
throws only one knuckleball in the first four pitches. Ellis is
hoping for a knuckler at this point, his Plan B depends on
it. Wake obliges by throwing the knuckleball at 2-2 (as expected, see table
above) and it flutters towards the inside part of the plate. Ellis
executes a slight but perceptible rotation of his front shoulder
towards the plate.

The butterfly caresses him gently on the left biceps
and Ellis trots down to first base—perfect execution of Plan
B. The normally unflappable Wakefield has some words with the home plate umpire,
but to no
avail. Wakefield usually hits quite a few batters, partly because
nobody knows where the damn pitch is going, but also because batters
are more than happy to take first base in exchange for a slight
tingling sensation on their shoulder.

Drilling down to pitches

With a reasonable sample of pitches thrown by Wakefield, we can start
to look at what happened on any given thrown pitch. Let’s first look
at the frequency of balls, strikes and balls put in play.

Pitch Results for Tim Wakefield
| PitchType |    NP  | Ball% | Called% | Foul% | Swinging% | InPlay% |
| KB        |   995  |  0.35 |    0.17 |  0.17 |      0.10 |    0.20 |
| non-KB    |   200  |  0.30 |    0.30 |  0.09 |      0.05 |    0.25 |
| MLB Ave   | 279106 |  0.37 |    0.17 |  0.17 |      0.09 |    0.19 |
Called, Foul, Swinging - types of strikes

The first two rows show Wakefield’s pitches, divided into knuckler and
non-knuckler categories. To give you some idea of typical values, the
last row shows the MLB average for all pitch types. The first
interesting thing to note is that the knuckleball, by these measures, looks
a lot like an average MLB pitch. I wasn’t expecting that at all.

The other curious thing regards the non-knuckleball pitches: twice the rate of
called strikes and half the rate of swinging strikes. You’d think
batters would unload early and often on a 75 mph fastball, but they
are clearly surprised by many of these non-knucklers, letting 30% of
them pass over the plate unmolested. On the other hand, when they do
swing, they don’t miss often.

But what happens once the ball is put into play? Well, we’re going to
be hampered a bit by low sample size, but let’s have a look anyway.

Results for Balls in Play
| PitchType |   NP  | Hit%  | HR%   | BABIP | OPS   |
| KB        |   197 | 0.315 | 0.025 | 0.297 | 0.822 |
| non-KB    |    49 | 0.265 | 0.020 | 0.250 | 0.673 |
| MLB Ave   | 53505 | 0.323 | 0.035 | 0.298 | 0.829 |

Again, we see the knuckler not very different from the average
pitch. I was actually expecting the HR% for knucklers to be higher
than average and the opposite for BABIP. I was expecting a lower
BABIP number for the knuckleball, since knuckleballers are generally known
to give up fewer hits on balls-in-play than conventional pitchers.

However, we are plagued by a small sample size here: the one standard
deviation uncertainty in the knuckleball BABIP is .032, i.e. the true value
could easily be much lower (or higher) than what we see here. As for
the non-knucklers, although Wake had great success with them this year, the
sample is so small as to preclude any general conclusions.

If it don’t break, then hammer it!

As is evident from the movement plot above, some knucklers
have very little “knuckle” to them and they end up near the middle of
that plot, i.e. little or no movement.

Now, it’s possible that the ball breaks more than once on its way to
the plate, but we can’t tell that from the Pitch f/x data. All we know
is that the ball was headed somewhere when it left Wakefield’s hand
and it ended up very close to that spot.

Some of these pitches that show little movement may have wiggled left,
shimmied right and then fluttered back over the center of the plate,
while the batter could only blink in wonder. Others, without a doubt,
really do go straight in and get clobbered.

With the Pitch f/x data, though, we can compare the results on balls
in play for pitches that broke a lot and for pitches that broke very
little. We’ve already seen that the sample size is getting small, but
let’s forge bravely onward anyway.

I’ve divided the knuckleballs into three groups with small, medium and
large breaks (see graphic on right) and I’ve determined the results on
balls put into play for each group. This table gives the numbers:

Knuckleball Results for Different Amounts of "Knuckling"
| Break  | NP | Hit%  | HR%   | BABIP | OPS   |
| Small  | 47 | 0.383 | 0.021 | 0.370 | 0.979 |
| Medium | 71 | 0.338 | 0.028 | 0.319 | 0.873 |
| Large  | 79 | 0.253 | 0.025 | 0.234 | 0.684 |

Gee, BABIP really follows the expectations according to the amount of
break, doesn’t it? Pitches that broke little had a high BABIP of .370, while
pitches with large knuckling movement had BABIP of only .234. This may
be fortuitous, though, since the uncertainties on these BABIPs are quite
large, due to the small sample size. Still, it is rather
suggestive, isn’t it?

On the other hand, we don’t see the astronomical home run rate that I
was expecting on the low-movement knucklers. Folks, these are 65 mph
pitches that are presumably coming in straight—I would
have expected more than one in 47 balls in play to go out of the
park. Perhaps these pitches really are wiggling around on the way to the plate, before ending up where they were
originally headed.

I want more data

This looks like a promising area for further research, but we’re going
to need more data. I’d like to get five times as many knuckleballs to
look at, but will Tim Wakefield pitch long enough to reach that goal?

I’m pulling for him, no doubt, but I’m also pulling for another guy to
stick in the big leagues, a 23-year-old reliever for the White Sox, a guy by the name of Charlie Haeger.

References & Resources
Further reading:

  • The Knucklebook by Dave Clark is a fun read, with some physics, instruction, history and interviews. Clark also runs the
    Knuckleball HQ web site.

  • The Diamond Appraised by Craig Wright and Tom House is a classic of sabermetric thinking. Wright devotes a chapter to knuckleballers, and finds that the pitch is likely underused.
  • This is getting to be a habit, but I’m going to plug The Neyer/James Guide to Pitchers yet again. Neyer penned the chapter devoted to the history of the knuckleball as well as compiling a list of 70 major league pitchers who threw the pitch.
  • A Game of Inches by Peter Morris also contains much information about the early history of the knuckler.

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