KNUCKLEBALLS

Rod Cross May 2013

RA Dickey is renowned as the only pitcher in Major League baseball who throws a knuckleball almost exclusively. He was especially successful in 2011 and 2012. He has made a slow start in 2013. A knuckleball is thrown at relatively low speed and with very little spin. It is difficult to hit since the ball tends to change direction in flight as a result of the fluctuating aerodynamic side force on the ball. That force varies with the angle and location of the seam. The same thing happens with a rapidly spinning ball, but if the side force varies rapidly from positive to negative many times during the flight, the average effect is zero. With a knuckleball, the side force might vary in sign only once or twice on its way to the batter, with the result that the ball starts moving to say the left, then starts moving to the right and might then end up moving up or down, depending on the way the ball is spinning.

It is not easy to pitch a ball with no spin or even with very little spin. It is more natural to throw or pitch a ball by bringing the fingers down the back of the ball as it comes out of the hand, in which case the ball is thrown with backspin. That’s how pitchers throw a fastball. Dickey grips the ball by digging his fingernails into the ball just behind the seam, and holding the ball between his thumb and third finger, something like in the attached drawing. If he pushes forward as he releases the ball, so that the forces F1 and F2 are about equal, then there will be very little spin.

Usually, a knuckleball rotates one to three times on its way to the batter, and the ball usually spins about an approximately vertical axis – that is, with side spin. Sometimes, the ball spins about a different axis, depending on which fingers push the hardest.

To demonstrate that it is not all that difficult to pitch a knuckleball, this QuickTime video shows an example where I threw a knuckball and filmed it at 300 fps. The hard part is to throw it accurately, relatively fast and consistently well. I cheated by throwing a very light polystyrene ball with string glued to the ball to simulate a raised seam. However, the physics of the problem is exactly the same, regardless of the mass or diameter of the ball, and that is what I was interested in. The video shows that the ball didn’t follow a simple curved path. Rather, the ball curved first in one direction and then in the opposite direction. Sometimes, a slowly spinning baseball curves in only one direction, but on this occasion it didn’t. It depends on how the seam is aligned and how the spin axis is aligned and how fast the ball is spinning. This video shows that some of my knuckleballs curved in only one direction. The ball curved 24 cm sideways after traveling a distance of 6 m to the length of string stretched across the front of the camera. In this case, the curve can be explained by the smooth patch on the left side of the ball, which is equivalent to having an illegal rough patch on the opposite side. As the ball rotates, no part of the seam enters the smooth patch. The seam is highlighted by a dashed line drawn along the seam (ie string).

Can YOU hit a knuckleball ?

This first movie shows a knuckleball headed your way. I stopped the movie when the ball was ¾ of its way to the “home plate”. Have a guess where the ball crossed the home plate. Then check your guess here.

Even Dickey has trouble pitching “good” knuckleballs. If the ball curves in only one direction, then the batter can usually connect with the ball since it doesn’t curve as far as fast-spinning balls, and it is slower than most other types of ball. That makes it easy to predict where the ball is headed.

Dickey’s pitching statistics are surprisingly similar to many other top pitchers. Batters choose not to swing at about 50% of all pitches. When they do swing, they get about 35% of those pitches into play, foul about 40% of pitches and miss the remaining 25% of pitches. Missing the ball completely is therefore fairly common. With fast pitches, batters have trouble with the speed and the relatively large curve of the ball in flight. With knuckleballs, the main problem is that the ball tends to curve a few inches away from the direction that the batter thinks it is headed. The following diagram shows the problem. The bird’s eye view shows an example where the ball curves horizontally to the left and then curves slightly to the right. The lower view is an example where the ball curves slightly upward at the end of its path.

The diagrams above are consistent with how the catcher reacts to a knuckleball. The batter and the catcher both tend to make the same mistake when predicting the path of a knuckleball. They presumably base their predictions on the path of the ball over the first 40 feet or so. Based on that prediction, the batter swings his bat at the expected point of arrival, and the catcher moves his glove to the same point. Meanwhile, the ball rotates slowly and presents a different seam pattern to the flow of air around the ball, so the force on the ball changes in magnitude and direction. If the side force is big enough and acts for long enough, it can cause the ball to curve a few inches away from the expected path. As a result, the batter misses the ball and the ball can hit the edge of the catcher’s glove rather than land in the middle of the glove.

The following stills from MLB.TV show two examples where the batter and the catcher both made the same mistake when facing a Dickey knuckleball. In both cases, the batter missed the ball by an inch or two and the ball hit the edge of the catcher’s glove. For some strange reason, batters swing under the ball much more frequently than over the ball, despite the fact that knuckleballs tend to swerve randomly in all directions - up, down and sideways.

Slow motion QuickTime video of the problem faced by batters and catchers can be seen by clicking on the next two images.

Further information on this on-going research project can be found on Alan Nathan’s web site at http://baseball.physics.illinois.edu/

And for those of you who read Danish, there is a translation by Mille Erikson at

http://www.zoobio.fr/edu/2016/10/25/knuckleballs-rod-pa-tvaers-af-maj-2013