July 5, 2007

Schrodinger's Bat

Searching for the Gyroball

by Dan Fox

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"Hmm. How should I answer that question? I knew this question was coming today. And I was preparing some optional answers for this particular question. Should I say, 'I have that ball?' Or I could say, 'Which particular ball are you referring to?' Or 'Which ball are you calling a gyroball?' Overall, if I have the chance, I will pitch that ball."
--Red Sox pitcher Daisuke Matsuzaka, answering a reporter's question during his first press conference after arriving in Fort Myers for spring training.

If you Google "Matsuzaka and gyroball," you'll get over 68,000 hits. Wade through those links and you'll find everything from the early supposition that the pitch breaks as much as three feet and two different directions from the mound to the plate, to denials that Daisuke Matsuzaka even throws the pitch, to claiming that he has thrown it but only occasionally and somewhat accidentally. Given the wide range of opinion on the subject, I thought a quantification of his pitches might add to the ongoing discussion.

This week we'll break down Dice-K and the 586 pitches he's thrown this season as tracked by the PITCHf/x system. Those pitches cover six of his 16 starts as shown in the following table.

Start              Pitches   IP  H  SO  BB ER
4/17 at Toronto        105  6.0  3  10   3  2
5/9  at Toronto        102  7.0  5   8   3  1
5/25 at Texas           85  5.0  7   6   3  5
6/5  at Oakland         55  7.0  7   8   2  2
6/22 at San Diego      126  6.0  5   9   5  1
6/27 at Seattle        113  8.0  3   8   1  1

As you can imagine, this sample should give us a pretty good indication of what he's throwing, and when he's throwing it. The June 5^th start at Oakland unfortunately recorded only 55 of his 130 total pitches for the evening, but for the other five starts we're only missing a total of six pitches.

1. What Does He Throw?

This of course is the central question related to the gyroball. Unfortunately, it's also the most difficult. Matsuzaka has an impressive repertoire that is said to contain six or seven different pitches. With all of that noise, a pitch like the gyroball that he might throw only experimentally could easily be lost. But as we have with Felix Hernandez, Tim Wakefield, and Chad Gaudin, we'll first take a visual inspection at the movement on his pitches classified by velocity.

As we may have expected, this graph is a little more complex than that for Hernandez with his three tight groupings, although we can still detect some clusters that provide the clues we need to classify Dice-K's pitches. In the upper left, we see faster velocities with positive vertical and negative horizontal movement. In the lower right, we see slower pitches with greater horizontal and negative vertical movement. Respectively, these are obviously fastballs (staying up in the zone and tailing in to right-handers) and curveballs (dipping down and away from right-handers).

Then it gets more complicated. The remainder of the pitches to the right of zero on the x-axis are smeared out in a kind of downward arc, and they also run the gamut from 80 to over 90 miles per hour, as indicated by the various colors of the data points. Still, it's possible to detect two groups here--one that moves a little less horizontally but is thrown mostly in the 85-90 mph range (shown in orange and purple), and one with sinking movement that is thrown at 80-85 mph (in green). Likewise, to the left of zero on the x-axis and underneath the mass of fastballs we see a rather spread-out group of pitches in terms of movement that are primarily from 80-85 miles per hour. What we have then are five basic groupings that include fastballs, curveballs, and two kinds of harder breaking balls that move away from right-handed hitters.

We can make some further sense of the jumble by plotting horizontal movement versus starting velocity as shown below.

Now we can see that the pitches thrown at less than around 86 mph with negative horizontal movement fall into two groups--a group that breaks less but that is thrown between 82-86 mph, and one that breaks a little more and is thrown between 78-81 mph. The first of those we can identify as the changeup, and the second as likely a combination of different pitches we can group together as his forkball/splitter.

Armed with these two graphs and a perusal of a few general descriptions of his repertoire from analysts, scouts, and a discussion with our own Will Carroll, we can build the following pitch profiles:

Pitch             Count    Pct   Break   Start     pFX    Vert   Horiz      BA    RelC    RelG
Four-seamer        338     56%    3.51   92.54   13.19   11.63   -5.94   36.83   -2.02    5.35
Slider              93     16%    6.88   84.19    5.81    3.80    3.60  -13.47   -2.19    5.49
Cutter              61     10%    6.26   88.51    5.44    5.13    1.28   -8.17   -2.29    5.47
Curveball           39      7%   12.23   78.71    7.43   -1.41    6.73  -15.38   -2.15    5.80
Forkball/Split      32      5%    8.83   83.96    7.04    2.45   -5.83   14.35   -2.24    5.63
Changeup            19      3%    9.12   80.24   10.66    3.35   -9.92   23.73   -2.05    5.75
Unknown              4      1%    5.50   85.88    6.69    6.69   -0.19   -2.73   -2.13    5.34

In perusing those profiles we're able to identify six different pitches:

• Fastball: This is the group of red and purple pitches identified in the first plot. He throws his fastball with an average velocity of 92.5 mph and over half of the time (56 percent), exactly in tune data from Inside Edge on his ESPN player card. There were reports that he throws both a four-seam and a two-seam fastball, but the evidence for the latter is lacking. As discussed in the profile on King Felix and shown comparatively on my blog, a good two-seam sinker will have a vertical movement in the range of two to seven inches, whereas Matsuzaka (as evidenced by the first graph above) throws most of his fastballs (81 percent) with a vertical movement of 10 or more inches and averaging over 13. Still, there are a subset of 18 pitches that could possibly be classified as two-seamers, since they had an average vertical movement of 5.8 inches and were thrown at just 90 miles per hour. However, they weren't included in the table and subsequent analysis because of the small sample and uncertainty of the identification.
• Slider: These are the slower of the two overlapping hard breaking balls shown in the first graph. Dice-K throws his slider 16 percent of the time, with an average velocity of 84 mph. It moves into left-handed hitters (3.6 inches on average) but not as much as the curveball. It also drops more than the cutter, an average of just 3.8 inches more than a theoretical reference pitch with no spin.
• Cutter: As mentioned above, his cut fastball overlaps with his slider, making exact identification difficult. Here we've identified 10 percent of his pitches as cutters, and being those that are faster (88.5 mph), move a little less horizontally (1.3 inches), and don't drop as much (5.1 inches) as his slider. Together, the slider and cutter make up 26 percent of his total pitches, which generally conforms to Inside Edge, which identifies only the slider and has him throwing it 22 percent of the time.
• Curveball: The curveball is easier to identify since it has the largest movement in to left-handers both horizontally (6.7 inches) and vertically (-1.4 inches). Here we see he throws it seven percent of the time, while Inside Edge has it as nine percent.
• Forkball/Splitter: Of the two groups of pitches identified in the second plot, those that range between 82 and 86 mph (for an average of 84) and that move a little less horizontally (-5.8 inches) are ones we're grouping together as forkballs and splitters. You can see that these sink an inch more than the changeup, with a vertical movement of just 2.45 inches bettering the drop of the best sinking fastballs thrown by the likes of Derek Lowe and Roy Halladay, albeit with less velocity. It's likely the case that the majority of these pitches are in fact forkballs, with Matsuzaka gripping the pitch deeper in his fingers than a traditional split-fingered fastball. Announcers will often simply call it the splitter. I confirmed my hypothesis by examining video of a subset of pitches under this classification, and the split-fingered grip is obvious on many of the pitches as he takes his windup. It should be noted, however, that he also possesses a hard sinker with left to right movement, a so-called shuuto. Although these pitches are thrown in very different fashions, their profiles would be similar, so a few of these pitches are possibly sinkers. Under this classification he throws the forkball/splitter five percent of the time.
• Changeup: Like his forkball, his changeup has similar action moving down and away from left-handed hitters. We've identified that second group of pitches in the second plot as changeups, and he throws them with an average velocity of 80 mph. In addition to the slower speed, they differ from the forkball in that they don't sink as drastically (3.35 inches of vertical movement), but move away from a lefty much more (-9.9 inches). Inside Edge calculates that he throws the changeup seven percent of the time, while we have at three percent. This is a reasonable difference if Inside Edge is grouping the forkballs with the changeups, since they do look very similar. The video inspection also showed that a minority of the pitches we're classifying as a forkball or splitter are probably changeups that are overthrown, and so don't move as much.

So what does that leave for the gyro? Not much. What remains are four pitches that are unidentified, and the possibility that we've lumped a few gyroballs in with other pitches. The four unidentified pitches averaged almost 86 mph, dropped about five inches more than his typical fastball but less than his two-seamer, and basically did not break horizontally (an average of -0.2 inches). Alan Nathan, a physicist from the University of Illinois, has written about three possible variations of the gyroball, and these four unidentified pitches roughly fit what he illustrates as a "gyroball with lift force" which would drop more than a fastball but would have no horizontal break. But of course it could be that these are simply sliders that didn't slide (backup sliders), or cutters that didn't cut, or even batting practice fastballs. One of the other variations, described as a "gyroball with side force," would have the same horizontal movement as a cut fastball or slider but would probably sink a little more than the cut fastball we've identified. Even if what we've identified as his cutter is really a gyro, no one thinks he throws it nearly that often, making it almost certain that the vast majority of these pitches are really cut fastballs.

In any case, it doesn't appear from this analysis that there is much room for a gyroball. Absent other evidence, we'd have to tentatively conclude that Matsuzaka, as he has claimed, does not include it as a regular part of his arsenal at this time. Its inclusion in his psychological arsenal is another matter entirely.

2. When Does He Throw It?

We've already answered the basic question of how frequently he throws each pitch, but let's break that down by looking at how often he's thrown each pitch by batter handedness.

Type     Fastball Cutter  Slider  Fork/Split  Curve  Change
           (FB)    (CFB)   (SL)    (FK/SPL)    (CV)    (CH)
Left        53%     11%     10%      13%        6%      7%
Right       61%     10%     20%       1%        7%      1%

As you would expect, he favors his slider against right-handers and his forkball against lefties. He also goes to his changeup more frequently against lefties, and avoids both the forkball and changeup against right-handed hitters.

Next, let's take a look by inning:

Inning      FB     CFB     SL   FK/SPL    CV      CH
1           69%     7%      8%     1%      7%      6%
2           65%     7%     13%     0%     10%      1%
3           51%    10%     24%     3%      5%      4%
4           54%    14%     13%     8%      4%      3%
5           49%    11%     19%     8%      7%      1%
6           46%    11%     16%     9%      5%      5%
7           48%    10%     12%     7%      0%      7%
8           59%     0%      0%     0%      5%      0%

Even more than King Felix, Matsuzaka relies on his fastball in the first two innings, and then works in his slider, cutter, and forkball the second and subsequent times through the order.

Finally, let's take a look at the counts at which Dice-K throws his six pitches.

Vs Left
Count       FB     CFB      SL    FK/SPL    CV      CH
0-0         58%      6%      4%     13%     13%      6%
0-1         48%      7%     19%     11%      4%     11%
0-2         62%      0%     15%     15%      0%      8%
1-0         48%     13%     17%     13%      9%      0%
1-1         40%      5%     10%     15%     15%     15%
1-2         50%     15%      5%     15%      0%     15%
2-0         38%     15%     15%     23%      0%      0%
2-1         60%      7%      7%     20%      7%      0%
2-2         44%     22%      6%     11%      0%     17%
3-0        100%      0%      0%      0%      0%      0%
3-1         67%     22%     11%      0%      0%      0%
3-2         67%     25%      8%      0%      0%      0%

Vs Right
Count       FB     CFB      SL    FK/SPL    CV      CH
0-0         56%     10%     17%      0%     15%      0%
0-1         56%     12%     16%      4%     10%      0%
0-2         63%     16%     22%      0%      0%      0%
1-0         52%      3%     24%      0%     14%      7%
1-1         74%      0%     21%      0%      0%      3%
1-2         42%     22%     28%      3%      6%      0%
2-0         64%      7%     21%      0%      7%      0%
2-1         80%     13%      7%      0%      0%      0%
2-2         70%      7%     22%      0%      0%      0%
3-0        100%      0%      0%      0%      0%      0%
3-1         67%      8%     25%      0%      0%      0%
3-2         68%     11%     21%      0%      0%      0%

Vs Left      FB     CFB      SL    FK/SPL    CV      CH
Ahead        52%      8%     13%     13%      2%     12%
Even         53%     11%      6%     12%     10%      9%
Behind       56%     13%     13%     14%      5%      0%
Two-strike   54%     16%      8%     11%      0%     11%

Vs Right     FB     CFB      SL    FK/SPL    CV      CH
Ahead        60%      9%     18%      1%     11%      1%
Even         63%      7%     20%      0%      7%      4%
Behind       60%     14%     23%      1%      3%      0%
Two-strike   67%      8%     17%      2%      5%      1%

Interestingly, he throws his fastball with roughly the same relative frequency to both sides regardless of whether he's ahead, behind, or even in the count, with a slight nod to it with two strikes against righties. With two strikes against lefties, he goes to either the cut fastball or the changeup, while using his slider against right-handers to complement the fastball. Although he throws his curve more frequently when even in the count against lefties and ahead against right-handers, for the most part there isn't much of a pattern that hitters can key off of. This fact, combined with mechanics that make his pitches look very much alike, are two of the reasons why he's so tough on opposing hitters.

3. Where Does He Throw It?

As with our other pitchers, we'll take a quick look at where he locates his pitches.

The chart against left-handers shows that he prefers working away with his fastball, generally from the middle out and usually up in the strike zone. He generally avoids the inner half of the strike zone. His cutter is thrown up in the zone as well, while the forkball appears to be either down and in or low and away. His changeup varies in its location.

Against right-handed hitters, his fastball remains up, although he locates it on either side of the plate, while he tends to leave his cut fastball more on the outside of the plate. The curve is definitely thrown for strikes across the width of the zone while the forkball is thrown on the inner half. As you would expect, he throws his slider low and away, yet surprisingly he also throws it in the strike zone a good deal, even doing so frequently on the inside corner.

4. What Happens When He Throws It?

Before we close, let's take a quick look at the pitch outcomes by batter handedness:

Vs Left-Handers
Outcome            FB     CFB      SL    FK/SPL    CV      CH   Count
Ball               36%     29%     36%     55%     50%     31%    87
Called Strike      23%     29%     32%      3%     21%     13%    47
Foul               19%     13%     14%     17%     14%     19%    39
In Play            10%     25%     14%     10%      0%     19%    27
Swinging Strike    13%      4%      5%     14%     14%     19%    26

Against left-handers, he gets his greatest percentage of called strikes on sliders (32 percent), while his forkball stays out of the zone (typically down and in), and is either usually a called ball or fouled off. At 25 percent, the cutter is the pitch that is put into play most often, while his curveball is rarely fielded. Overall, his slider gets strikes over half the time (51 percent), as does his fastball (55 percent) and changeup (51 percent).

Vs Right-Handers
Outcome            FB     CFB      SL   FK/SPL    CV      CH   Count
Ball               33%     27%     32%    33%     40%     67%   121
Called Strike      16%     16%     18%     0%     44%     33%    66
Foul               24%     16%     23%    33%      4%      0%    77
In Play            15%     22%     11%    33%     12%      0%    53
Swinging Strike    11%     19%     15%     0%      0%      0%    43

Against right-handers, Matsuzaka gets called strikes 44 percent of the time on his curveball, which testifies to the fact that he throws it for strikes when ahead or even in the count. His fastball leads to plenty of foul balls (24 percent) as does his slider (23 percent), but it is the slider on which he gets the highest percentage of strikes (56 percent). The sample sizes for the forkball and changeup against right-handers are too small to really read anything into the percentages.

The Search Continues

So what if the gyroball is not all it's cracked up to be as far as Dice-K is concerned? With his vast array of pitches, he's still one of the most entertaining pitchers in baseball to watch. What's more important is that he's still having success on the field and contributing to a double-digit lead in the AL East. There's no doubt that much of the hype has been justified.