# The Hardball Times

## Fastball, slider, change-up, curveball—an analysis

by John Walsh
December 20, 2007

Fastball, slider, curveball, change-up—these are the tools of the pitcher's trade. The weapons he takes with him to the thousand yearly battles with opposing hitters. Much of my recent work has been devoted to trying to understand the different characteristics of these pitches: how they move, how fast they are thrown, who throws them, and so on. In this article, I want to explore how these different pitches are used, which situations call for which pitch, and which pitches get the desired results most often.

The first hurdle to overcome for a study like this is classifying a large number of pitches. The pitch data that I work with, provided by the Pitch f/x system, does not identify the pitch. However, there is enough information on pitch speed and movement to enable us to do a pretty good job of classifying pitches. Thus far, I've managed to classify around 90% of the 310,000 pitches recorded by Pitch f/x in 2007. See the Resources section below for details on pitch classification.

Let's remind ourselves of the basics of these pitches. The graphic on the right shows the horizontal and vertical movement for the four pitch types. By the way, here is the key to the pitch type labels:

```FB: fastball
SL: slider
CU: change-up
CB: curveball
```
As always, the movement variables are defined relative to a hypothetical pitch without spin and the viewpoint is that of the catcher. The darker zones show the typical movement of the pitch. These plots are for right-handers only. For a left-hander, the plots would look like these reflected in a mirror.

Here's a table showing the average movement and speed values, in inches and mph, respectively, for the four pitch types:

```+-----------+--------+-------+-------+------+
| PitchType | NP     | speed | horiz | vert |
+-----------+--------+-------+-------+------+
| FB        | 164816 |   91  |  -6.2 |  8.9 |
| SL        |  48190 |   84  |   0.7 |  3.7 |
| CB        |  34274 |   77  |   5.2 | -3.3 |
| CU        |  30831 |   82  |  -7.4 |  6.0 |
+-----------+--------+-------+-------+------+
```
This table includes both right- and left-handed pitchers. I've reversed the sign of the horizontal movement for lefties, making it possible to average all pitchers together.

As we knew, the fastball is thrown hardest and most frequently, followed, in both categories, by the slider. Change-ups and sliders are actually thrown with similar speeds, although the change-up tends to run into a right-handed batter, while the slider moves (slightly) away.

###### When to throw what

Now that we have a sizable sample of each pitch type, we can investigate a bit how each type was used. For example, let's look at how pitchers varied their selection depending on the handedness of the batter:

```+------+------+------+------+------+
| L/R  | FB%  | SL%  | CB%  | CU%  |
+------+------+------+------+------+
| Opp  | 0.59 | 0.14 | 0.11 | 0.16 |
| Same | 0.59 | 0.21 | 0.13 | 0.05 |
+------+------+------+------+------+
| All  | 0.59 | 0.17 | 0.12 | 0.11 |
+------+------+------+------+------+
```
These numbers confirm (and quantify) what we already knew: pitchers tend to throw more sliders and curves and fewer change-ups, when they have the platoon advantage (pitcher and hitter of the same hand). In any case, pitchers throw a majority of fastballs (59% of pitches thrown) no matter what side of the plate the batter is standing on.

We can also look at how pitch selection varies depending on the count:

```+------+------+------+------+------+
| Cnt  | FB%  | SL%  | CB%  | CU%  |
+------+------+------+------+------+
| 3-0  | 0.84 | 0.05 | 0.03 | 0.08 |
| 3-1  | 0.80 | 0.10 | 0.03 | 0.07 |
| 2-0  | 0.75 | 0.11 | 0.04 | 0.10 |
| 3-2  | 0.66 | 0.17 | 0.08 | 0.09 |
| 1-0  | 0.63 | 0.15 | 0.08 | 0.13 |
| 2-1  | 0.64 | 0.16 | 0.08 | 0.13 |
| 0-0  | 0.63 | 0.15 | 0.12 | 0.09 |
| 1-1  | 0.53 | 0.19 | 0.13 | 0.14 |
| 0-1  | 0.52 | 0.20 | 0.15 | 0.12 |
| 2-2  | 0.51 | 0.21 | 0.16 | 0.12 |
| 1-2  | 0.48 | 0.22 | 0.19 | 0.11 |
| 0-2  | 0.51 | 0.21 | 0.18 | 0.09 |
+------+------+------+------+------+
```
I've placed the rows in this table in order of how advantageous the count is for the hitter, 3-0 being the best hitter's count and 0-2 being the worst. Now look at the fastball percentage: there is an almost perfect progression from lots of fastballs (84% on 3-0) down to about 50% fastballs on the worst hitter's counts.

What's clearly happening is that when behind in the count pitchers will try to throw a strike to move the count in their favor. Presumably, the fastball is the easiest pitch to control, so that's the pitch they choose. When they are ahead in the count, the cost of throwing a ball is reduced, so they can try the fancy stuff.

A possible exception may be given by the 0-2 count, where the fastball percentage goes back up a tick, instead of continuing downward. I wonder if pitchers are employing a little game theory here: throwing a few more fastballs than expected in order to confound the batter.

###### Performance by pitch type

Now that we have some idea about pitch selection, let's have a look at what happens to these different pitches. The following table shows how often a particular kind of pitch resulted in a ball, called strike, foul ball, swinging strike or ball in play.

```+-----------+-------+---------+-------+-----------+---------+
| PitchType | Ball% | Called% | Foul% | Swinging% | InPlay% |
+-----------+-------+---------+-------+-----------+---------+
| FB        |  0.36 |    0.19 |  0.19 |      0.06 |    0.19 |
| SL        |  0.36 |    0.14 |  0.17 |      0.13 |    0.20 |
| CB        |  0.40 |    0.19 |  0.13 |      0.11 |    0.16 |
| CU        |  0.40 |    0.11 |  0.14 |      0.13 |    0.21 |
+-----------+-------+---------+-------+-----------+---------+
| All       |  0.37 |    0.17 |  0.17 |      0.09 |    0.19 |
+-----------+-------+---------+-------+-----------+---------+
InPlay - includes home runs
```
There's lots of interesting information to be gleaned from these numbers, so let's take it one step at a time. First of all, looking at Ball%, we see that the slider is about as easy to throw for a strike as the fastball, so perhaps pitchers should go to the slider a bit more often when down in the count. Obviously, these are general trends and each particular pitcher will weigh his own strengths and weaknesses (and those of the batter) when making his pitch selection.

Perhaps the biggest surprise in these numbers, at least for me, is the low percentage of swinging strikes on fastballs. The image of the mightly slugger swinging through a blazing fastball goes all the way back to Ernest Thayer's "Casey at the Bat", written over a century ago. But what we see above tells a different story — if you want to get a swinging strike, the fastball (on average) is the worst pitch for the job. Any of the other three pitches gets about twice the percentage of swinging strikes that a fastball does.

You might be wondering about 3-0 counts—as we saw above, 3-0 counts lead to a lot of fastballs, and since many batters will take the 3-0 pitch, that will reduce the swinging strike percentage for fastballs. This is true, but the effect is very small, due to the small number of pitches thrown on 3-0. I've made the above table excluding 3-0 counts and there is no material difference.

It's interesting to note the fraction of pitches taken, given by the sum of Ball% and Called%. The curveball is taken most often (59%), while the slider is taken least often (50%). The InPlay% is highest for the change-up and lowest for the curve, with a fairly large difference between the two.

I'm not offering reasons for these differences, because I don't have any. I thought the numbers were interesting, though. I will offer a plausible reason for the Foul% numbers that we see: my hypothesis is the faster the pitch, the greater the chance of fouling it off.

But what happens to the balls in play? Are particular pitches more susceptible to the home run? (Mr. Fastball, I'm looking at you.) What about hits in general? Does batting average on balls in play (BABIP) depend on pitch type? Let's have a look:

```+-----------+-------+-------+-------+-------+-------+
| PitchType | NP    | AVG   | BABIP | SLG   | HR%   |
+-----------+-------+-------+-------+-------+-------+
| FB        | 31704 | 0.330 | 0.304 | 0.521 | 0.037 |
| SL        |  9433 | 0.310 | 0.286 | 0.481 | 0.033 |
| CB        |  5577 | 0.310 | 0.290 | 0.471 | 0.029 |
| CU        |  6594 | 0.319 | 0.295 | 0.502 | 0.035 |
+-----------+-------+-------+-------+-------+-------+
| All       | 53308 | 0.323 | 0.298 | 0.506 | 0.035 |
+-----------+-------+-------+-------+-------+-------+
```
These are now only pitches where the ball was put into play. It's interesting that the worst numbers across the board belong to the most frequently thrown pitch: the fastball. Overall, the balls put into play off the curveball seem to do the least damage of the four.

As I suspected, the highest home run rate comes against the fastball—after all, the fastball has relative rise, which should result in more fly balls and, hence, more home runs.

What about BABIP, or batting average on balls in play (excluding home runs)? As you may know, there is an ongoing debate in the saber world about how much control a pitcher has over BABIP. I believe that pitchers do have some measure of control, but less than is commonly believed, maybe. What we don't know is what gives some pitchers the ability to limit BABIP. Might it be related to the type of pitches he throws?

From the above table, it looks like fastball pitchers would have a higher-than-average BABIP, while pitchers who throw lots of breaking stuff might show lower BABIP values. However, we also know that BABIP will depend on the flyball tendencies of the pitcher, which, in turn will depend somewhat on pitch selection.

In other words, this is a complicated business, one that I will perhaps tackle at a later date. But, there may be an important link between BABIP and pitch type.

What about grounders and fly balls? Do certain pitch types preferentially induce particular batted ball trajectories? The answer is, yes, to some degree. The following table tells the story:

```+-----------+-------+-------+-------+-------+-------+
| PitchType | NP    | G     | L     | F     | P     |
+-----------+-------+-------+-------+-------+-------+
| FB        | 31732 | 0.428 | 0.194 | 0.289 | 0.077 |
| SL        |  9593 | 0.446 | 0.186 | 0.269 | 0.084 |
| CB        |  5633 | 0.481 | 0.185 | 0.252 | 0.068 |
| CU        |  6547 | 0.479 | 0.185 | 0.255 | 0.068 |
+-----------+-------+-------+-------+-------+-------+
G - ground ball
L - line drive
F - fly ball
P - pop up
```
As we might expect, we get more fly balls and fewer grounders on fastballs, which tend to have a large upward movement (relative to the hypothetical spinless pitch, remember). Actually, the best pitch to induce a ground ball when one is needed is the sinking fastball. Noted ground ball artists such as Brandon Webb, Derek Lowe and Chien-Ming Wang all specialize in the sinking fastball.

Now, distinguishing the sinking fastball from a normal rising fastball using the Pitch f/x data is a bit tricky. But we can do a reasonable job simply by calling any fastball with a vertical movement less than six inches a sinking fastball. Here now is the above table showing batted ball types for each pitch, including now the sinking fastball (sFB):

```+-----------+-------+-------+-------+-------+-------+
| PitchType | NP    | G     | L     | F     | P     |
+-----------+-------+-------+-------+-------+-------+
| FB        | 25377 | 0.388 | 0.199 | 0.315 | 0.087 |
| sFB       |  6355 | 0.591 | 0.173 | 0.185 | 0.036 |
| SL        |  9593 | 0.446 | 0.186 | 0.269 | 0.084 |
| CB        |  5633 | 0.481 | 0.185 | 0.252 | 0.068 |
| CU        |  6547 | 0.479 | 0.185 | 0.255 | 0.068 |
+-----------+-------+-------+-------+-------+-------+
```
Look at how the sinking and rising fastballs have such different batted-ball outcomes now: the groundball percentage of the sinker is 59%, higher than any other kind of pitch (not surprisingly). And the rising fastballs are at the other extreme: only 39% ground balls, lowest of any pitch type.

We see the same tendencies with the line drive as well, although the differences are not as stark. Curious.

###### What have we learned?

I don't know about you, but I've learned a lot researching this article. I didn't realize the averge fastball was thrown comfortably above 90 mph. I can remember, not all that long ago, when 90 mph was considered throwing hard; now it's below average.

The change-up, despite was you sometimes read, is not the slowest pitch thrown (the curveball is). I read recently a claim that somebody's change-up was 20 mph slower than his fastball—no way! The average difference between fastball and change-up is 9 mph. I haven't checked, but I'm confident that nobody has a 20 mph difference between the two pitches.

Pitchers throw the change-up three times more often when facing an opposite-hand batter, but throw the fastball equally as often, regardless of the handedness of the batter. This is not a good stategy, as you will see when you read my article on platoon splits for different pitch types in the Hardball Times Basebll Annual 2008 (plug!).

Fastballs appear to have the worst BABIP and sliders the best, although a rigorous link between BABIP and pitch type needs more study. A quick look at batted-ball types, though, reveals that a larger proportion of line drives come off rising fastballs.

I could go on, but this seems like a good place to pause. There is plenty more to think about, now that we have lots of pitches classified by pitch type. Keep an eye out for more of this stuff as the offseason progresses.

References and Resources

Classifying Pitches

There are two distinct tasks involved in classifying pitches: 1) for each pitcher, separate his pitches into clusters of distinct pitch types; 2) determine the pitch type for each cluster. The first part is accomplished using a standard clustering algorithm known as k-means. The algorithm uses three Pitch f/x quantities — speed, horizontal movement and vertical movement — to divide the pitches into different clusters. The only "intelligent" input that I must give is the number of pitches that any given pitcher has.

I determined the number of pitches that any pitcher has by visual inspection of movement/speed plots for about 400 pitchers. That sounds like a lot of work, but in only took me a couple of hours once I had written a program to flash a series of plots on my screen, allowing me to quickly judge how many pitchers a particular guy throws.

Once the pitches have been clustered into distinct groups, we now have to determine what kind of pitch each cluster is. The first step is to find the average speed, horizontal and vertical movement for all pitches in each cluster. Next, I call the pitch with the highest speed the fastball.

I assume the remaining pitches are slider, curveball or change-up. Splitters actually work like change-ups and are usually labeled change-up. Fastball variations (2-seamer, cutter) usually are labeled fastball. As we gain more experience with the Pitch f/x data, I expect we'll be come up with more sophisticated classification techniques.

Once the fastball is identified, I know generally where to look, in terms of speed and movement, for the other pitcher types. For example, I know that on average a change-up is about 10% slower, has around 30% more horizontal movement and 35% less vertical movement than the fastball. I have determined similar profiles for sliders and change-ups.

Of course, each pitcher is different and nobody will have pitches that match up exactly with the average pitch profile. So, for each pitch I calculate a number that tells me how close it matches each of the three possible pitch types. I then simply classify the pitch according to the best match.

John Walsh dabbles in baseball analysis in his spare time. He welcomes questions and comments via e-mail.