Boston Red Sox pitcher Josh Beckett put together an amazing postseason performance this year to help the Sox to a World Series victory. He won Game 1 of the Division Series against the LA of Anaheim Angels with a 4-hit shutout. He took MVP honors in the American League Championship Series, winning Game 1 and Game 5 against the Cleveland Indians. He then topped it all off with a Game 1 victory against the streaking Colorado Rockies, who fell to the Red Sox in a four-game sweep. Beckett’s outstanding postseason was merely the cherry on top of a fine regular season which put him in contention for the AL Cy Young Award.

I decided to take a look at Josh Beckett through the lens of PITCHf/x for several reasons. One, he is an outstanding pitcher and as such is interesting to analyze. Two, he’s known as basically a two-pitch pitcher: fastball, curveball. Granted, they must be two very good pitches, but that’s unusual for a top-flight starting pitcher. Three, I was inspired by some of the discussion between Eric Van and Alan Nathan at the Sons of Sam Horn message board after his dominant Division Series shutout. Van and Nathan identified three types of fastballs among Beckett’s pitches in that game, and I was curious if I could or would see the same thing. Finally, I wanted to try out a few new ideas regarding pitch classification, and Beckett seemed like as good a vehicle as any.

First, the scouting report on Beckett. As I mentioned earlier, Beckett is basically a two-pitch pitcher. He has a mid-nineties fastball and an excellent curveball. He also mixes in a changeup and supposedly has a slider. To quote Dugout Central, “Beckett hasn’t used his slider much in the second half. It’s an inconsistent pitch with average break to it.” In the 1530 pitches recorded by the PITCHf/x system, about half the pitches Beckett threw this year and weighted more heavily toward the second half, I find no evidence that Beckett threw even a single slider.

Without further ado, I’ll present my pitch speed versus spin direction graph showing Beckett’s pitch types. (For more detail about how I derive those parameters, read my article about Jonathan Papelbon.) Then, I’ll discuss how I arrived at the pitch classification shown. Pitch speed is in mph, measured 50 feet from the plate, and spin direction is the direction of the spin axis of the pitch in degrees, as seen by the batter and catcher, with the direction of corresponding spin-induced movement to a right-handed batter noted at the bottom of the graph.

Beckett Pitch Speed vs. Spin Direction

Beckett’s curveball is easy to identify. It’s a classic curveball, running 75-80 mph. I won’t spend much more time on the curveball, since for pitch classification purposes it’s typically the easiest pitch to identify, and Beckett’s is no exception. I will note the absence of sliders on the graph. The closest Beckett comes is a few slurvy curveballs, but given their slow speed and sub-110-degree spin direction, I don’t see any reason to try to split them off as a separate pitch type. They move like normal curveballs from any other pitcher.

Separating the changeups from the fastballs is where it starts to get a little interesting. Beckett doesn’t throw many of them, less than 10% of our sample, totaling 135 pitches. Speed-wise, his changeup shows quite a bit of variation, ranging from 83-93 mph. Clearly the slower pitches are changeups, but as we get up around 90 mph and into the low nineties, how can we tell the changeups from the fastballs? In Beckett’s case, it’s quite helpful to look at the data on a start-by-start basis. Almost every start has a clear separation of pitches into three groups by speed, with the changeups in the middle group.

Beckett Pitch Speed vs. Time

I’ve highlighted the middle speed group in red. The x-axis in this graph is pitch sequence recorded by PITCHf/x throughout the season, which roughly corresponds to time, such that each of Beckett’s starts is compressed into a vertical line of the pitches that were recorded at various speeds. With the exception of a few pitches, it’s quite easy to separate the fastballs, changeups, and curveballs using this graph alone.

On a side note, I don’t know the reason for the almost 6-mph variability in Beckett’s top fastball speed from start to start. Perhaps an avenue for further investigation, possibly already covered by Joe P. Sheehan’s article or Josh Kalk‘s error correction, in any case, an avenue I will bypass for now.

If you adjust the pitch speeds by normalizing the average fastball speed for each start to the overall average fastball speed and adjusting other pitches from that start by the same amount, you get the following pitch speed vs. spin direction graph:

Beckett Normalized Pitch Speed vs. Spin Direction

You can see that within a given start, Beckett’s fastball speed is very consistent in the (normalized) 93-97 mph range. This is true for all three types of fastballs, which is quite unusual. Typically, a pitcher’s two-seam fastball will be a few miles per hour slower than his four-seamer, and a cutter may be even a few mph slower than that. For those pitchers, pitch speed can be an important clue in determining pitch type. That’s one reason that the pitch speed vs. spin direction graph is such a favorite of mine.

For Beckett, however, pitch speed is nearly useless in determining what types of fastballs he throws. In Van and Nathan’s Sons of Sam Horn discussion, they identify three types of fastballs: a four-seamer, a two-seamer, and a cut fastball, and in that October 3rd start the three types are fairly readily identifiable. In many of his other starts, however, the differences among them are not as obvious.

We can see a hint of the three groupings in the normalized pitch speed vs. spin direction graph, but it’s far from clear. The spin rate vs. spin direction graph proves to be a little more helpful. Spin rate is shown in revolutions per minute (rpm).

Beckett Spin Rate vs. Spin Direction

In order to see what’s going on with the fastballs, let’s zoom in on that section of the graph.

Beckett Spin Rate vs. Spin Direction for Fastballs

The divisions between the fastball groupings are somewhat arbitrary, but I believe they are generally well representative of reality. There is a dense cluster of pitches in the middle of the graph between 210-220 degrees, which is an appropriate spin direction for a four-seam fastball from a pitcher with a 1 o’clock delivery. Two-seam fastballs should have a greater spin direction, reflecting the sidespin commonly applied to the ball using the two-seam grip. The cluster of pitches around 230-240 degrees appear to be two-seamers. Finally, there is a small tail of pitches with spin direction of less than 200 degrees and slightly lower spin rates. These appear to be the cut fastballs. Some of them can clearly be identified as cutters if you look at the pitches on a start-by-start basis. You might argue a little with the exact delineation between pitch types here, but I think I’ve nailed it pretty closely. I can’t imagine try to hit a 95-mph fastball from Beckett while trying to decide whether it would hop, sink, or cut.

Finally, I wanted to add in a couple novelties and solicit your feedback on whether these new methods of presenting the data are helpful. These ideas mainly have their genesis in various discussions about the PITCHf/x data presentation topic at Tom Tango and Mitchel Lichtman’s The Book blog.

First, here is a graph of pitch time vs. spin direction. The horizontal axis is the same as for most of the graphs above. The vertical axis shows the time, in seconds, for the pitch to travel from shortly after the pitcher’s release point until the ball crosses the front of home plate. (In the PITCHf/x coordinate system, this is from the initial measurement point at y=50 feet to the final measurement point at the front of home plate at y=1.417 feet. The origin of the coordinate system is at the point of home plate, and the plate is 17 inches, or 1.417 feet, deep.) You could make a graph showing the time for the pitch to travel any other distance you wanted to see. The main point of this graph is to illustrate what the pitches look like on a time scale rather than the more familiar speed scale. Just over a third of a second to hit a Beckett fastball–wow!

Beckett Pitch Time vs. Spin Direction

Next, I revisit the traditional PITCHf/x vertical and horizontal “break” parameters, pfx_x and pfx_z, or as Tom Tango has at least temporarily convinced me to call them, the horizontal and vertical spin movement. This graph shows the spin-induced movement of the pitches, in inches, between the y=40 feet point and the front of the plate, from the perspective of the batter/catcher.

Beckett Vertical Spin Movement vs. Horizontal Movement

For comparison, take a look at Josh Kalk’s algorithmically generated player card for Josh Beckett. He has a lot of good data there that you may find interesting, although he does not separate Beckett’s fastballs by type. But the main point of the preceding graph was to contrast with a graph which Tango and MGL have asked for, the spin plus gravity movement, i.e., the deviation of the pitch from a straight line, which I present below.

Beckett Vertical vs. Horizontal Spin plus Gravity Movement

This graph includes all the information of the traditional pfx_z vs. pfx_x graph, but it also shows that slower pitches drop more because the force of gravity has longer to act on them. Some of Beckett’s curveballs break down almost three feet when the effect of gravity is included.

That’s all for now. I hope to take a further look at some of this data when I get a chance.

Here’s a link to Part 2 of my Josh Beckett analysis.


Building on the previous pitch identification work I did for Eric Gagne, let’s take a look at how he uses his pitches.

Here are some strike zone charts showing where he locates his pitches against left-handed hitters and right-handed hitters. I’m experimenting with the formatting of these charts, so let me know if there are things I can do to improve that. The graphics are a little small, but I thought it was more important to contrast the general patterns of lefty versus righty than to see the exact result for a specific pitch.

The strike zone is shown as a box, including one radius of a baseball on each side of the plate, and the top and bottom of the zone are a general average not adjusted per batter in these charts. The location is plotted where the pitch crossed the front of home plate.

Let’s begin with the curveball.

Gagne Curveball Location

Gagne faces about an equal number of lefties and righties, so the first thing we can see is that he uses his curveball much more against righties (19% of pitches to RHH) than against lefties (11% of pitches to LHH).

He works away from righties and in to lefties with the curve and has pretty good success getting righties to chase the curve down and away.

Next, let’s look at fastballs.

Gagne Fastball Location

Gagne throws approximately equal numbers of fastballs to lefties (56%) and righties (51%). He likes to work away to both lefties and righties but seems a little more willing to come inside to lefties. He gets a lot of foul balls and contact in the zone with his fastball and, other than a few high pitches, not a lot of balls chased out of the zone.

Moving on to changeups…

Gagne Changeup Location

Gagne throws the changeup about equally to lefties (30%) and righties (25%). He clearly likes to keep his changeup down and away to both lefties and righties. It looks like he has pretty good success with that, but when he gets up in the zone with the change, it starts to get hit, particularly against lefties. We’ll see in a moment if the numbers bear that out, but the strike zone charts certainly look that way.

Finally, let’s look at the sliders.

Gagne Slider Location

Gagne doesn’t throw many sliders, 2% of pitches to lefties and 5% of pitches to righties. The few he throws to lefties are inside, same as with the curveball, perhaps moreso. With righties he works down and away with the slider, mostly missing the zone. It looks more like a show-me pitch than anything.

It would be interesting to learn on what count he throws the slider, or any of the other pitches for that matter, but I haven’t compiled that information yet.

Here are the results by pitch type and batter handedness in tabular format.

Fastball 66 38 31 10 17 5 7 0.227 0.318 60%
Changeup 31 10 12 17 9 11 13 0.550 0.650 66%
Curveball 15 9 4 2 4 0 0 0.000 0.000 56%
Slider 2 0 2 1 1 0 0 0.000 0.000 67%

Fastball 44 22 45 9 23 11 17 0.324 0.500 71%
Changeup 28 8 14 17 6 3 6 0.333 0.667 63%
Curveball 23 15 7 7 2 2 2 0.500 0.500 59%
Slider 10 2 2 1 0 1 1 1.000 1.000 38%

CS=called strike, SS=swinging strike, IPO=in play (out), IPNO=in play (no out), TB=total bases, BABIP=batting average on balls in play (including home runs), SLGBIP=slugging average on balls in play (including home runs).  For Strk% all pitches other than balls are counted as strikes.

Clearly, my earlier hunch was right: Gagne’s changeup gets tattooed when he gets it up in the zone against lefties. Also, it does look like the slider is mainly a show-me pitch to righties.

As the regular season ends and the playoffs approach, I’m looking at a few of the playoff-bound pitchers, and I want to share the results for one of those pitchers–Eric Gagne.

I begin with identifying his pitch types, and as time permits, I’ll move on from there in further posts. I was able to identify four main pitch types that Gagne has thrown this year in the 39 games (of 54 total) for which we have PITCHf/x data recorded.

The graph I find most helpful in quickly identifying pitch types is pitch speed versus spin direction. For more detail on the methodology, read my post on Gagne’s teammate Jonathan Papelbon.

Gagne Pitch Speed vs. Spin Direction

Gagne’s pitch mix is about 53% fastballs, 28% changeups, 15% curveballs, and 4% sliders.

His fastball looks like a classic four-seamer delivered from about 1 o’clock and running 89-95 mph. I don’t see any evidence of a two-seam fastball, but he could probably hide a handful of them in there without me being able to spot them as a unique pitch.

His changeup is interesting. He calls it a Vulcan changeup because of the V grip he uses, and there are some definite similarities to a split-finger or forkball pitch in terms of the significant sidespin, inclined about 50 degrees more than his fastball. Speed-wise his changeup ranges from about 80-87 mph.

His other major pitch is a curveball, hitting about 67-73 mph with good topspin, and also thrown from about a 1 o’clock delivery.

His occasional slider seems very inconsistent. It runs about 82-86 mph, but its spin axis is all over the place, ranging from 120 degrees (great sidespin) to 210 degrees (no sidespin at all other than that from the 1 o’clock delivery).

There are five pitches out of total of 601 in our PITCHf/x dataset for Gagne that I could not classify into the aforementioned four pitch types. Three of them appear to be data collection errors based on unrealistic release points, and I’ve eliminated them from the dataset. Before I discuss the other two pitches further, here are two additional graphs: pitch speed vs. spin rate and spin rate vs. spin direction.

Gagne Pitch Speed vs. Spin Rate

Gagne Spin Rate vs. Spin Direction

On these two graphs you can see two unidentified pitches as well as additional details about the four main pitch types.

I’ve tentatively labeled the two unidentified pitches as a slurve and a forkball. The “slurve” pitch was thrown with a speed on the borderline between the curve and slider groupings. Its spin direction makes it look almost like a curve, but its slow spin rate makes it look almost like a slider. My best guess is that Gagne was attempting to throw a curveball but gave it a little more slider action than normal.

The pitch I’ve labeled “forkball” looks quite a bit like his other changeups except for the fact that it has a spin rate of only 500 rpm, and that’s reminiscent of a forkball or split-finger pitch. It doesn’t quite fit with the sliders given its spin direction of 224 degrees. We’ve already seen that Gagne is inconsistent with the amount of sidespin he gets on his slider, but this would be sidespin in the wrong direction for a slider. Given his changeup grip, it wouldn’t surprise me to see him throw a changeup that looks pretty forkball-ish.

If you want to compare my data with the work of others, you can check out the player card that Josh Kalk generated for Eric Gagne using his clustering algorithm and data normalization. Below is my graph of vertical “break” vs. horizontal “break” with the pitch types labeled according to my classification. Josh’s algorithm lumps what I call sliders in with Gagne’s changeups.Gagne Vertical Break vs. Horizontal Break

I realize the above graph is not presented in a terribly intuitive fashion in terms of what the vertical break, particularly, means. I have some ideas for helping to clarify that, but for now I’ll just present that graph as is.

There is a lot more that can be done with this data, but I’ve found before that if I try to do it all in one fell swoop, I don’t publish anything, so I’ll start with this.

Update: Part 2 of the series on Gagne.

There’s some very informative commentary from Ike at his blog on how the reconstruction algorithm of PITCHf/x works and how that affects measurement error in the data.

He also has a couple of previous posts on the PITCHf/x topic.

It’s nice to see a fellow Sooner and, as best I can tell, a fellow OU Physics alum writing on this topic.

Some of the other PITCHf/x analysts out there are looking at the hitting aspects or other things that can be divined from the data, but I’m still quite fascinated by the ability to classify a pitcher’s pitches. I know that’s not the be-all-end-all of baseball or of PITCHf/x, but I’m learning so much about the game from pursuing this angle, I may camp in this corner for a while.

I decided to take a look at one of my favorite players–who happens to have had quite a resurgence in the second part of this year–Royals’ former and once-again wunderkind Zack Greinke.

I split the data into three parts. The first part was his first seven starts this year, in which he compiled a 5.71 ERA on the strength of 49 hits, 11 walks, and 19 strikeouts in 34 2/3 innings. This performance resulted in his banishment to the bullpen in hopes of salvaging something from 2007 for Greinke. We only have one start recorded in PITCHf/x from this period. In this start, his fastball was recorded at 87-93 mph. Other than noting that fact, I’ve chosen to ignore the rest of the data from this start.

The second part was his relief performance, which lasted from May 10 to August 20, and for which he have 295 pitches recorded by PITCHf/x. In 38 relief appearances, he compiled a 3.54 ERA on the strength of 43 hits, 15 walks, and 55 strikeouts in 53 1/3 innings. In the data we have, his fastball as a reliever ran in the 92-98 mph range. Here’s the speed versus spin direction chart:

Greinke Speed vs. Spin Direction

As a reliever, he threw 67% fastballs, 24% sliders, 5% changeups, and 4% curveballs. The fastball and changeup groupings are pretty obvious. I used the spin rate parameter to help me separate the sliders and curveballs. I won’t reproduce that graph for his relief outings, but suffice it to say that the curveballs are the pitches with slower speed, higher spin rate, and lower spin direction.

What’s interesting to me is comparing the reliever graph to the same graph for his return to the starting rotation, which began on August 24. We have PITCHf/x data for four of his five starts since then, missing only his September 15 start at Cleveland. In all five starts, he’s compiled a 1.71 ERA on the strength of 21 hits, 8 walks, and 15 strikeouts in 21 innings.

Greinke Speed vs. Spin Direction as a Starter

His fastball still has a lot of pop in the 91-97 mph range. It will be interesting to see if he can keep that life on his fastball as he stretches out beyond 4 or 5 innings at a time. He’s also using his changeup a bit more: 75% fastballs, 15% sliders, 8% changeups, and 3% curveballs.

Here’s the spin rate vs. spin direction graph for his starter outings. I’ve labeled the x axis to show how the spin direction corresponds to break to a right-handed hitter. A pitch that broke straight down would have a spin direction of 0 degrees, break away from a righty corresponds to 90 degrees spin direction, break up (or a “rising” fastball) corresponds to 180 degrees, and break in on a righty’s hands corresponds to 270 degrees. So the spin direction tells us which way the pitch will break, and the spin rate tells us how much the pitch will break.

Greinke Spin Rate vs. Spin Direction as a Starter

Here’s the vertical break vs. horizontal break displayed in inches.

Greinke Vertical vs. Horizontal Break as a Starter

I’m excited to see Zack Greinke back on top of his game, and I hope he can stay there for years to come.

So far we’ve classified the pitches for four pretty orthodox pitchers: Joba Chamberlain, Jonathan Papelbon, Edinson Volquez, and Greg Maddux. It’s time to try someone a little more novel.

Like Josh Kalk, I’ve been thinking about ways of automating the pitch classification process, although he’s much further along that process than I am. One thing I have wondered is whether such a system can ever be developed that will handle all pitches from all pitchers, or whether we will have to restrict it to mainstream pitchers and pitches only. So I’ve been thinking about pitchers who might be exceptions to various rules that seem to apply well to everyone else.

Take Chad Bradford, for instance. Could a pitch classification system handle a pitcher who throws underhand? He plays in a home park, Baltimore, that doesn’t have the PITCHf/x system running, but we have 188 pitches recorded for him in other parks, and that seems to be enough to figure out his repertoire.

The scouting information on Bradford couldn’t be much muddier for a guy who doesn’t throw very many different pitches and uses the same basic delivery for all of them. One scouting report says he throws a fastball, a slider, and an occasional changeup. The Sporting News says he “throws in the high 80s and has a solid changeup and curveball.” Another article (of which I seem to have lost track) said he threw a two-seam sinking fastball. The Washington Post says he throws an 83-mph fastball, a slider, and a changeup. The Post article is well worth reading if you’re interested in Bradford. Everyone seems to agree he has three pitches, but they can’t agree what they are. Surely we can tell if we dive into the data we have.

Let’s start with what is becoming my traditional pitch classification graph, pitch speed versus spin direction. (As usual, I have normalized the start_speed parameter to y0 = 50 feet.)

Bradford Speed vs. Spin Direction

I’ve not labeled the slow breaking pitch in the graph because, as we will discuss later, it’s name is not so clear. I have color-coded his three pitches and circled the groupings, and now I’ll go through the process I used to determine those groupings and the pitch types.

There are two pretty obvious groupings, one containing the fastballs and the other some sort of slower breaking pitch. There are several questions to answer. First, are the multiple pitches hiding in the cluster on the upper right, and if so, what are they? Second, what is the 65-70 mph pitch? None of my usual secondary graphs were very illuminating on these questions.

To help answer the first question, I went to another pair of graphs I like to see, the same speed vs. spin direction plot from above but split out for right-handed and left-handed hitters.

Bradford Speed vs. Spin Direction to Righties

Bradford Speed vs. Spin Direction to Lefties

The first thing I notice is that lefties don’t get many of the slow breaking pitches in the lower left corner of the graph, and righties don’t see pitches slower than 76 mph on the right side of the graph. That implies that there are at least two distinct pitches in our grouping on the right side, since I see no reason to believe Bradford would purposefully throw his already-slow fastball even slower to lefties on occasion. Most probably this is a changeup. We can’t tell from this graph whether righties also see some changeups from Bradford or whether 76 mph is really the cutoff between fastballs and changeups.

For that, we move to another plot that exposes a limitation in our data. This graph shows Bradford’s pitch speeds (normalized to y0 = 50 feet) throughout the season, recorded when the Orioles visited a park equipped with PITCHf/x and Bradford happened to pitch. The x-axis lists the pitch id number from my database, but that corresponds closely to time, with pitch #1 at the beginning of the season and pitch #637,220 occurring on September 12.

Bradford Speed vs. Time

Here we can see on a game-by-game basis that Bradford clearly throws three different speeds of pitches. Our overall speed data is being clouded by two games in Boston on July 31 and August 1, with pitch speed on average 3.5 mph slower than in other parks. Fenway Park’s PITCHf/x system is the source of all sorts of measurement errors, so this does not come as a surprise.

Now that we’ve separated the three groups of pitches, can we tell what they are? First, it’s reasonable to classify the mid-speed pitch as changeup since it has similar spin to the fastball only thrown a little slower. But is the fastball a regular four-seam fastball or a two-seam “sinking” fastball as some people suggested? And is the breaking pitch a slider or a curveball?

As an aside, in terms of pitch classification algorithms, do we really care what the names of Bradford’s pitches are or how he pronates his wrist? Shouldn’t a mathematical description of how the pitch moves be sufficient? I think the answer to the latter question is probably yes, but pitch classification can be interesting beyond just the search for a universal classification system. It’s interesting to learn about a particular pitcher’s approach, and for that description, it helps to know what the pitcher is attempting from his perspective.

How do we determine whether a fastball is a four-seamer or a two-seamer? The classic four-seamer, if thrown from the 12 o’clock position, would have only backspin, which would show up on our graph as a spin direction of 180 degrees. If the pitcher drops down to a 3/4 delivery, the four-seamer gets a little sidespin component, and the spin direction shifts to the neighborhood of 210 degrees. For example, we saw Volquez’s four-seam fastball right in this area, in the range from 200-220 degrees, and Papelbon’s four-seamer was in a similar range of spin directions, 195-225 degrees.

The two-seam fastball is thrown with the fingers along the seams, with the middle finger applying pressure to the ball to produce sidespin. If the two-seamer were thrown from the 12 o’clock position, we would expect to see a spin direction greater than 180 degrees by an amount dependent on how much sidespin the pitcher applied to the ball. From a 3/4 delivery, the spin direction would shift over to a greater angle by another 30 degrees or so. Greg Maddux’s two-seamer had spin directions in the range 215-265 degrees (a wide range consistent with his reputation of varying the movement on his fastball), Papelbon’s two-seamer was at 210-235 degrees, and Volquez’s two-seamer was at 220-245 degrees.

For an pure underhand pitcher with a delivery from 6 o’clock, the classic four-seam fastball with pure backspin (now switched to pure topspin by the change in delivery) would have a spin direction of 0 degrees (equivalent to 360 degrees). For a more realistic delivery from 5 o’clock, which appears to be consistent with pictures I can find of Bradford’s motion, the spin direction would shift back by about 30 degrees to 330 degrees. If Bradford were applying pressure to the ball to produce the sidespin of a two-seamer, that would tend to move the spin direction back toward 360 degrees because of the direction that the human wrist pronates. Instead, we see a spin direction of 295-330 degrees, consistent with a delivery between 5 and 6 o’clock and little or no sidespin applied to the ball. Therefore, I conclude he is throwing a four-seam fastball.

This conclusion squares with one we could have made via logic alone, without regard to the data. Pitchers generally attempt to throw their fastball as hard as they can, which is accomplished with the four-seam grip. They use different grips and accept slower speeds for the purposes of movement or deception. Because of his underhand motion, Bradford gets plenty of sink on his fastball without needing to sacrifice speed to put sidespin on the ball. Here’s the chart of vertical and horizontal movement.

Bradford Vertical vs. Horizontal Break

His fastball sinks 5 to 12 inches, which is just incredible–almost as much downward break as a Barry Zito curveball! His fastball also moves in on the hands of a right-hander by 7 to 13 inches, which is comparable to the best two-seam sinkers thrown overhand from guys like Brandon Webb and Derek Lowe. You wonder why right-handers can’t hit this guy? My guess is that’s why. And it’s all attributable to the spin direction, which in turn comes from the underhand delivery, and not to the speed of the pitch, which is only in the low 80’s.

Finally, we come to the last question for this post: Is that a curve or a slider? It has the horizontal break of good curveball, and sometimes a little more. It has a vertical break somewhere between a typical slider and curveball. Which is it? We already know that Bradford’s unorthodox delivery can significantly affect the movement on a pitch. For the answer, we turn back to the spin direction graph. Bradford’s breaking pitch checks in with spin directions in the range of 75-130 degrees. That’s not too different than an overhand curveball delivered from the 1 o’clock position, although not a perfect fit.

A curveball with pure topspin delivered from the 12 o’clock position has a spin direction of 0 degrees. Dropping down to the 1 o’clock position shifts the spin direction to 30 degrees. However, the pronation of the actual human wrist can’t deliver pure topspin to the ball without also imparting some sidespin that pushes the spin direction up to higher angles. For example, Maddux’s curve lands in the 50-100 degree range of spin direction, Volquez throws his curve at 35-80 degrees, and the few curves we saw from Papelbon ranged from 40-80 degrees.

A theoretical underhand 6 o’clock curveball delivered with pure topspin (now switched to pure backspin by the change in delivery) would have a spin direction of 180 degrees. Coming back up to the 5 o’clock position would shift the spin direction back up to 150 degrees. The sidespin imparted by pronation would move us back toward 180 degrees; however, and we don’t see Bradford’s breaking pitch around 180 degrees.

So Joe Slider, our blog turns its lonely eyes to you.
Woo, woo, woo…
What’s that you say, Kerry Robinson?
Slidin’ Joe has left and gone to the plate.
Hey, hey, hey…hey, hey, hey!

Sorry for that, I needed a distraction. This post is getting a little long in the tooth. I now return you to “The Slider Teaches Johnny to Pronate”, already in progress…

A pitcher throwing a typical slider overhanded applies sidespin in the opposite direction of a two-seamer, as if it were trying to become a topspin curveball, which you might say it was. In the process, it also gets a significant spin component around the direction of travel, which we ignore in terms of affecting the break of the pitch. The significant sidespin of the slider would put its spin direction around 90 degrees in theory, 120 degrees if it’s thrown from 1 o’clock, but in reality the pronating wrist ends up turning more toward the backspin of the fastball than the topspin of the curveball, and our typical slider ends up at slightly higher angles than 90 or 120 degrees. Checking back on our previous pitch classifications, a Greg Maddux slider falls in the range of 130-175 degrees, and Papelbon’s slider is in the range 140-190 degrees.

If Bradford were throwing a slider from the 5 o’clock position, at approximately what angle would we expect to see it spin? If he were throwing from the 6 o’clock position and getting pure sidespin on a slider, we’d expect it to have a spin direction of 270 degrees. Moving his delivery toward 5 o’clock moves the spin direction on the slider toward 240 degrees. But then the wrist action tends to pull it back toward the fastball, maybe in the neighborhood of 280 degrees. Huh. We don’t see Bradford’s breaking pitch centered anywhere close to that.

In fact, it’s centered around a spin direction of 100 degrees, closer to the 180 degrees we’d expect from a submarine curveball than the 280 degrees we’d expect of a submarine slider, but still not a great match for the curveball. In fact, it seems to have a strong screwball component, which makes some sense out of the movement we see on the vertical/horizontal break, but makes no sense to me in terms of why Bradford would throw a screwball or screwball-like pitch rather than a curveball/slider. Screwballs are hard to throw; they’re hard on your arm, which makes no sense for Bradford, who already has to deal with back pain from his submarine delivery. Nobody reports Bradford throwing a screwball. Maybe this is because it moves more like a traditional overhand slider or curve, but more likely it’s because he doesn’t throw a screwball.

Maybe some of you can help me by finding an error in my calculations or reasoning or pointing me to a more authoritative scouting report on Bradford. Until then, I’ll have to leave his third pitch as a mystery.

Update: I’ve done more reading on Bradford and the underhand delivery, and I’m finding some support for the idea of Bradford throwing a screwball. Most people don’t call it that because it doesn’t move like a screwball from an overhander, but it appears I may not be as off base as I thought I was.

From the Sporting News: “Chad Bradford is a submariner with a tough slider and a circle changeup. Because of his delivery, Bradford essentially twists his hand to the left on each pitch, turning the ball over–almost a screwball-type action.”

Some of you who know more about pitching motions and grips might be able to make something out of the pictures in Chris O’Leary’s analysis of Bradford.

Once again, Josh Kalk has some good things brewing on his blog. He’s working on a clustering algorithm to distinguish pitch types for all pitchers, and he has player cards up for almost 300 pitchers. He’s seeking input to improve his algorithm from the first pass.

According to Josh, one of the worst performances of the algorithm was for Greg Maddux, so I thought I’d try out my tools on Maddux and see what I found in terms of pitch types.

My conclusion is that Maddux throws mostly two-seam fastballs (67%), a lot of changeups (21%), some cut fastballs (10%), and an occasional slider (1%) and curveball (1%). This more or less agrees with scouting reports, although you can find mention of Maddux throwing just about every pitch under the sun other than the knuckleball. For example, his Wikipedia article will tell you Maddux throws the splitter and the screwball, but I found no evidence for either in the PITCHf/x games in the 2007 season. On to the graphs…

Let’s start with what’s fast becoming my bread and butter, the pitch speed versus spin direction graph. I’ve color-coded the pitches in this graph based on my conclusions from all the data. I don’t claim that they are all easily identifiable based solely on this first graph. (All pitch speeds are normalized to y0 = 50 feet.)

Maddux Speed vs. Spin Direction

The curveball is the easiest to identify. At 70-76 mph, it is the slowest pitch, and it’s the only one with topspin, with a spin direction of 50-100 degrees.

The slider is also fairly easy to distinguish, although I had to work a little at the exact boundaries between it and the cutter and changeup. The slider runs 79-83 mph, with mostly backspin and a little sidespin, corresponding to a spin direction of 120-180 degrees.

Maddux’s three main pitches are a bit tougher to separate. Let’s start with the changeup, whose most prevalent characteristic is its slower speed 78-83 mph, with similar spin direction to the fastballs. It has a spin direction ranging from 190-270 degrees, from mostly backspin to mostly sidespin.

Next, let’s go to the fastballs, the cutter and the two-seamer. From the speed vs. spin direction graph, you can tell that there are probably two separate fast pitches, but it’s hard to tell exactly where the line between them would go. Also, we can see another interesting fact. Usually the harder fastball is a four-seamer on the left, with more backspin (i.e., closer to 180 degrees), and the slower fastball is a two-seamer on the right, with more sidespin (i.e., shifted somewhat toward 270 degrees). Maddux doesn’t have that arrangement. His harder pitch is on the right, which is where the two-seamer should be. Based on scouting descriptions of Maddux’s repertoire, his main fastball is in fact a two-seamer, and he also throws a cut fastball. A cut fastball is usually a little slower than a four-seamer or two-seamer, so that correlates with our mystery pitch on the left half of the fastball grouping. In addition, the cut fastball typically has some slider-like characteristics, so it makes sense that the cut fastball would be found toward the slider side of the spin direction (i.e., toward 180 degrees and lower angles). So I think there’s good evidence to believe we’ve identified a two-seam fastball and a cut fastball on the graph.

Finding the boundary between the two will take us on a tour through some other graphs which will also help us define the changeup a little better and reaffirm our identification of the slider and curveball.

First, let’s visit an old standby graph, the speed versus horizontal break.

Maddux Speed vs. Horizontal Break

In this graph, the curveball is clearly evident again, as the slowest pitch with the most break away from a right-handed hitter. There is a group of pitches 78-83 mph also with a positive horizontal break, although slightly less break than the curveball. This, of course, is a signature of the slider. The changeup group is pretty readily identifiable here as the pitches 78-83 mph with negative horizontal break (in toward a right-hander). We can see some thinning out between the two-seamer group on the right and the cutter on the left of the fastest pitches. The boundary between the two is very smeared and hard to delineate on this graph. At least some of that smearing may come from the fact that we have three different y0 initial distances represented in our data set, and the closer y0 is set to home plate, the less break we will measure on the pitches.

I don’t see any evidence for a screwball on this graph.  A screwball should be a very slow pitch, like a curveball, but breaking in to a righty, opposite of the curve.  There are no pitches slower than 77 mph on the left side of the graph, hence, no sign of a screwball.

Next on tour comes the speed versus spin rate graph. It turns out that spin rate is a very useful parameter in helping us separate two-seamers from cutters and changeups.

Maddux Speed vs. Spin Rate

The two-seamer generally has a faster spin rate, mostly in the 1500-2500 rpm range, but with some significant tails at both ends. The cutter and the changeup have slower spin rates, mostly in the 500-2000 rpm range. There is some overlap between the spin rates of different pitches, but it is a helpful tool in our pitch classification tool box.

Another graph we can make is spin rate versus spin direction, and this one is useful mainly for identifying two-seam fastballs that might otherwise look like borderline changeups. I didn’t find it very helpful in telling the other pitches apart.

Maddux Spin Rate vs. Spin Direction

It’s possible there are some splitters hiding out on the extreme right edge of this graph in what I’ve labelled as changeups. If there was a separate grouping hanging out farther to the right, as Papelbon’s splitter did, I’d tend to believe they were splitters, but at this time, apart from any other evidence, I don’t see a reason to believe they aren’t all just changeups.

Finally, we can look at vertical break versus horizontal break. This is the graph presented in Josh Kalk’s player card for Greg Maddux. You can see the great big blog that his algorithm couldn’t separate. I’ve nicely color-coded the pitches, so you can see there’s some order left-to-right, but they’re still pretty much a mess.

Maddux Vertical Break vs. Horizontal Break

Ugh! Other than the curveball, I wouldn’t try to pick anything out of that graph alone. However, it was useful in identifying a few more two-seamers that were trying to masquerade as changeups.

So that’s the story on Maddux and his five pitches. The speed vs. spin direction graph once again comes through as the star, but this time it needed more help from its friends.

Of course, there are more interesting things in the data, for Maddux or for any pitcher, beyond just classifying their pitch types. Which pitches does Maddux prefer to throw to lefties or righties? Answer: he throws the cutter more to lefties (15%) than to righties (6%), and with righties he relies more on his two-seamer instead. Which pitches does he throw in various counts? How does he locate them? Which pitches get swings and misses and which ones see more contact? Which pitches turn into home runs most often? Et cetera. These will be left as an exercise to the reader.

Or, what the heck, do what I do and move on to another topic before this one is even cold.

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