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June 21, 2007

Schrodinger's Bat

Gameday Meets the Knuckleball

by Dan Fox

"The knuckle ball will ultimately replace the spit ball and may be even more effective than the famous twist."
--Clark Griffith as quoted in The Sporting News, May 7, 1908

"Me watching Niekro pitch was like a young artist inspecting his first Picasso. I examined him very closely. His knuckleball seems to wobble up there, moving three or four times in a small pattern. Wilhelm's swishes up to the plate in swinging arcs. My knuckleball gets up there in a hurry and breaks more sharply and erratically, but only once. When it's working, I mean."
--Jim Bouton in Ball Four

The 216 raised stitches on a baseball offer a world of possibilities to the man on the mound. Around 1905, as Rob Neyer tells us in The Neyer/James Guide to Pitchers, Eddie Cicotte and Nap Rucker were playing together for Augusta in the South Atlantic League. It was then that Cicotte, with or perhaps without Rucker's help--the details are sketchy--came up with a grip and release that realized one of those possibilities. Cicotte further refined the pitch in 1906 at Indianapolis with teammate Ed Summers, who is credited with the fingertip grip. Cicotte would later give him half the credit for inventing the knuckleball.

It is often the case in science where the pervading intellectual climate foments ideas that are "in the air" allowing for the nearly simultaneous "discovery" of a theory. Something like this probably also happened with the knuckleball, as it is also the case that Lew Moren needed a new pitch after being sent back to the minors in 1905, and came back to Philadelphia with the knuckler in 1907. He enjoyed great success and was also acclaimed as its inventor. What is not in dispute is that Cicotte went on to be the first pitcher to have sustained success with the pitch and that the pitch has been thrown continuously and with success ever since.

As Neyer points out, the popularity and the usage of the pitch has changed over time. Cicotte may have been the pre-eminent master of the pitch, but plenty of other pitchers employed it as a part of their arsenal throughout the Deadball Era, often lumping it in with other "slow ball" deliveries. In the 1920s, Eddie Rommel (requiring a replacement for his banned spitter), Jesse Haines, and Fred Fitzsimmons all used it to great effect as starters. Nevertheless, the knuckler was soon relegated primarily to the status of a secondary pitch in the 1930s and 1940s. One exception often cited was the mid-1940s Washington Senators who featured four knuckleball pitchers including Roger Wolff, Emil "Dutch" Leonard, Johnny Niggeling, and Mickey Haefner. At the same time, however, it was being thrown at least occasionally by a larger percentage of pitchers and became a kind of fad. In 1952 Hoyt Wilhelm was brought up to the Giants by Leo Durocher as a reliever and from there until Phil Niekro came along in the late 1960s, the idea caught hold that knuckleballers were best suited for relief work. That pattern continued for the most part through the 1970s. Neyer credits September 8, 1981 as a turning point of sorts. Charlie Hough started against the A's, pitched well, and went on to leave his relief career behind him; he had made 415 relief appearances before that.

All of which brings us to more or less the present day. Today knuckleballers are generally frowned upon in the bullpen where passed balls are more costly. One recalls Bob Uecker's famous dictum that "the way to catch a knuckleball is to wait until the ball stops rolling and then to pick it up." Today's reigning knuckleballer---a crown passed from Tom Candiotti (who Neyer rates as having had the sixth-best knuckler of all time)--is clearly Tim Wakefield. Wakefield has in fact broken the modern stereotype by making 141 relief appearances in his 15-year career, and even closing for the Red Sox in 1999, notching 15 saves. Still, he's primarily been a starter, and that fact has allowed the PITCHf/x system to capture five of his 2007 starts. We'll take a closer look at the pitch using the same four questions we applied to Felix Hernandez last week.

But first, before moving to Wakefield, we should at least touch on the physics involved in the pitch. It turns out that the key to the knuckleball is not that the pitch doesn't spin or rotate, but that it does so very slowly. A theoretical pitch that does not rotate at all (a real pitch thrown with no rotation will take on some spin as the forces act on it) will not veer, as a study done in 1975 by R. G. Watts and E. Sawyer in the American Journal of Physics mentions, but will instead move in a direction consistent with the Magnus Force generated by the air flow over the orientation of the stitches. Those like Wakefield who have mastered the pitch throw it such that it spins from one quarter to one-half rotation from the time it leaves the pitcher's hand to when it arrives at the plate. That slow rotation presents differing stitch configurations as air flows over the ball that in turn generates transient regions of higher and lower pressurem, resulting in forces acting on the ball. The forces push the ball one direction, and then as the stitch configuration changes, unpredictably push the ball in another direction.

As many backyard experimenters have proven to themselves, if the pitch is thrown too hard, the ball will not dance as much since the forces don't have enough time to act on the ball. The faster air stream keeps the ball in a straighter line. As a result, most professional knuckleballers throw the pitch between 65 and approximately 73 miles per hour.

1. What Does He Throw?

Tim Wakefield throws the knuckleball. (That was easy.) He actually throws not just a knuckleball but also a fastball and curveball. Gameday tracked his starts from April 6th at Texas, April 18th and May 10th at Toronto, May 26th back in Arlington, and June 6th at Oakland, a sample which includes 461 pitches. As we did last week, we'll use visual inspection to try and detect these three pitches.

image 1

That's a mess when contrasted with the three compact regions we saw for Hernandez. What can be detected here, however, is a region of higher velocity pitches in the upper left-hand corner, and a small region of low velocity in the lower right-hand corner. The fastball is the former and the curveball the latter. That hodge-podge of everything else in between is the knuckler. It turns out there is an easier way to separate the pitches. The graphs below plot the starting velocity on the y-axis and the horizontal and vertical breaks on the x-axis.

image 1

image 1

Now things appear more clearly. In the first graph the cluster of pitches in the upper left corner are those thrown at 73.1 miles per hour, and above (one pitch to Hank Blalock in the sixth inning of the April 6th start was recorded at 91.6 miles per hour and does not appear on the graph) the horizontal breaks between about -2.4 inches and -7.9 inches, indicating pitches that move into right-handed hitters when thrown by a right-hander like Wakefield.

In the lower right-hand corner we see a cluster of pitches thrown between 58.6 and 63 miles per hour that break between 3.2 and 9.9 inches, indicating these slower pitches break in to a left-handed batter.

In the lower graph the same pattern is repeated with the cluster of higher velocity pitches exhibiting a vertical break of between 7.8 and 12.7 inches, while the slower variety break between -12 and -4 inches. The remainder of pitches on both graphs form a nicely clustered band between 65 and 71 miles per hour. In both graphs then top cluster are the fastballs, the middle the knucklers, and the bottom the curveballs.

By running an algorithm that isolates these bands we can then create the following pitch profiles for Wakefield using the same definitions as last week.


Pitch Type       Count    Break   Start     pFX    Vert   Horiz      BA     RPC     RPG
Knuckleball        376    15.64   68.07    7.78    2.10    1.68   -3.16   -1.04    6.46
Fastball            55     8.43   75.91   12.14   10.74   -5.50   16.93   -0.69    6.72
Curveball           30    24.27   61.16   11.54   -8.40    7.62   -8.84   -0.98    6.65

The interesting thing here is that the Break length value, defined as the greatest distance the pitch acquires from the straight line drawn from the release point to the plate, is on average over 15 inches for Wakefield's knuckleball. This jives with the description of the knuckleball by Adair, where he shows an example variation of 11 inches and in another source that noted that knuckleball traveling at 72 mph have been known to move off the straight line by as much as 18 inches.

At first the larger Break length may seem counterintuitive, since the knuckleball has the lowest average horizontal and vertical movement of the three pitches in the table above. The reason for this is that the knuckler, unlike a traditional pitch, moves in either and sometimes both directions, so the effect is largely cancelled out. If we instead average the absolute value of the movement we get values closer to five inches for each. But this doesn't do the pitch justice either since all three measurements--Break, Vert, and Horiz--are simply point in time snapshots of the pitch, with the Break at its greatest divergence from the straight line, and Horiz and Vert with respect to the final location. As such, they don't capture the wobbling and change in direction. In order to adequately plot a knuckleball on a computer screen, one would need multiple measurements of break length all along the pitch trajectory.

This table also tells us that he throws the knuckleball 81% of the time, the fastball 11.9% of the time, leaving the curveball for the other 6.5% of his pitches.

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 further by looking at how often he's thrown each pitch by start and batter handedness.


Date        Stand         Total    KB      FB      CV
6-Apr         L              49   89.8%    8.2%    2.0%
              R              38   86.8%    0.0%   13.2%
18-Apr        L              23   95.7%    0.0%    4.3%
              R              75   76.0%   18.7%    5.3%
10-May        L              17   64.7%   29.4%    5.9%
              R              57   71.9%   15.8%   12.3%
26-May        L              22   81.8%   13.6%    4.5%
              R              65   83.1%   10.8%    6.2%
6-Jun         L              64   87.5%    9.4%    3.1%
              R              51   78.4%   13.7%    7.8%
Total         L             175   86.3%   10.3%    3.4%
              R             286   78.7%   12.9%    8.4%

Generally speaking he'll throw his fastball equally to lefties and righties, and against righties also mix in his curveball. Against lefties he avoids throwing the curveball at almost all costs. Although the curveball percentages are indeed low, his percentages this year may in fact be higher than in the past since it was reported in spring training that Wakefield was working on the curve: "It could be a very important pitch to my repertoire if I used it a little more."

Next, let's take a look at when he throws each pitch in terms of the inning.


Inning             KB       FB      CV
1                80.0%    14.1%    5.9%
2                89.6%     7.5%    3.0%
3                86.2%     6.9%    6.9%
4                84.4%     9.1%    6.5%
5                78.1%    15.1%    6.8%
6                83.3%     7.4%    9.3%
7                66.0%    25.5%    8.5%

Here the pattern appears to be to work the fastball a little more in the first inning perhaps as he gets the feel of the knuckler, rely on the knuckleball to get through the next three innings, and then use the fastball and curveball a little more the second and third times through the order.

Finally, let's take a look at the counts at which Wakefield throws his three pitches:

Vs Left
Count               KB       FB      CV   Total     Pct
0-0                 40        5       2      47   26.9%
0-1                 19        0       0      19   10.9%
0-2                 12        0       2      14    8.0%
1-0                 16        4       0      20   11.4%
1-1                 19        0       0      19   10.9%
1-2                 16        0       1      17    9.7%
2-0                  7        1       0       8    4.6%
2-1                  5        1       0       6    3.4%
2-2                 10        0       0      10    5.7%
3-0                  1        2       1       4    2.3%
3-1                  3        1       0       4    2.3%
3-2                  3        4       0       7    4.0%
Total              151       18       6     175
Pct                86.3%    10.3%    3.4%

Vs Right
Count               KB       FB      CV   Total     Pct
0-0                 72        6       3      81   46.3%
0-1                 29        0       3      32   18.3%
0-2                 13        1       3      17    9.7%
1-0                 25        9       2      36   20.6%
1-1                 21        2       2      25   14.3%
1-2                 17        0       4      21   12.0%
2-0                  9        4       3      16    9.1%
2-1                  9        7       1      17    9.7%
2-2                 22        0       0      22   12.6%
3-0                  2        1       2       5    2.9%
3-1                  1        6       0       7    4.0%
3-2                  5        1       1       7    4.0%
Total              225       37      24     286
Pct                78.7%    12.9%    8.4%  100.0%

Vs Left
Count              KB       FB      CV
Ahead            94.0%     0.0%    6.0%
Even             86.7%    10.8%    2.4%
Behind           76.2%    21.4%    2.4%
Two Strike       85.4%     8.3%    6.3%

Vs Right
Count              KB       FB      CV
Ahead            84.3%     1.4%   14.3%
Even             88.9%     6.7%    4.4%
Behind           56.8%    33.3%    9.9%
Two Strike       85.1%     3.0%   11.9%

When you add it all up, a left-hander should expect nothing but a diet of knucklers when behind in the count--not that knowing it's coming makes it any easier to hit--and should expect fastballs one out of five times when ahead in the count. With two strikes, Wakefield will occasionally try and sneak a fastball and even an occasional curve by an unsuspecting hitter. Clearly, he'll work right-handers a bit more with the curve when ahead in the count, and uses it occasionally as a two-strike pitch. When behind he'll try the fastball a third of the time and "only" throw the knuckler half the time.

3. Where Does He Throw It?

Like last week, we'll take a quick look at where he locates his pitches.

image 1

image 1

In general there are too few non-knuckleballs to really discern much of a pattern. He does attempt to throw his fastball on the outside corner to both lefties and righties, as you might expect. On a percentage basis he also seems to throw his curve up and in to right-handers almost as much as he locates it low and away.

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                      KB      FB      CV   Total    Pct
Ball                         52       5       3      60   34.3%
Ball In Dirt                  4       0       1       5    2.9%
Called Strike                25       7       0      32   18.3%
Foul                         33       0       0      33   18.9%
In Play                      27       5       2      34   19.4%
Swinging Strike              10       1       0      11    6.3%
Total                       151      18       6     175
Pct                         86.3%   10.3%    3.4%

Against left-handers he does sneak his fastball in there for a strike 39% of the time he throws it, but one would have thought that his swinging strike percentage on the knuckler, which sits at just 6.6%, would have been higher. But as researchers such as Tom Tippett have found, even when batters do put the ball in play against a knuckleball (as lefties do 39% of the time they swing at it against Wakefield) they don't fare as well as against other pitchers.

Vs Right-Handers
Outcome                      KB      FB      CV   Total    Pct
Ball                         85       5       8      98   34.3%
Ball In Dirt                  2       0       0       2    0.7%
Called Strike                36      14       4      54   18.9%
Foul                         39       5       1      45   15.7%
Foul Tip                      2       0       0       2    0.7%
In Play                      33      11       9      53   18.5%
Pitchout                      0       1       0       1    0.3%
Swinging Strike              27       1       2      30   10.5%
Swinging Strike (Blocked)     1       0       0       1    0.3%
Total                       225      37      24     286
Pct                        78.7%   12.9%    8.4%

Against right-handers Wakefield gets called strikes on his fastball at the same rate as against port-siders (39%) but right-handers don't put the knuckleball in play quite as often at 32%. Despite wanting to use his curveball as a possible two-strike option, he's only gotten four called and two swinging strikes with it against righties this season.

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