Q&A: Alan Nathan on the Physics of Pitching

What is the relationship between spin axis and the backup slider? Alan Nathan knows the answer. He also knows why fastballs move more than curveballs and why split-finger fastballs drop. A physics professor emeritus at the University of Illinois, Nathan is an expert not only on nuclear physics, he is the man behind The Physics of Baseball

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Nathan on velocity and break:
“In principle, it would be possible to throw a curveball 100 mph. It’s not the physics that prevent you from doing that. What’s preventing you is that it is biomechanically hard to do. You’re trying to get on top of the ball and put topspin on it, and to do that you’re probably sacrificing speed. But there’s no reason, in principle, that if you were able to spin a 100-mph pitch with topspin you would get even more downward movement.

“You actually see more movement on fastballs than you do, typically, on curveballs. Defining movement as how much the ball deviates from a straight line with the effect of gravity removed, you get a lot of movement from fastballs. People don’t normally think of there being a lot of movement from fastballs, because the upward movement you’d get from backspin on a fastball means the ball doesn’t drop as much as it would just purely from gravity. But there’s a significant amount of upward movement. Rapidly spinning balls moving at high speeds have a lot of movement on them.

“All fastballs in fact, drop. Look at PITCHf/x data; look at the release point versus where it crosses the front of home plate. It’s always lower when it crosses the front of home plate, but it would be even lower if there were no backspin. Backspin keeps the ball up in the air longer. We call that movement, even though the batter doesn’t really perceive it as movement. It looks more like a straight line to a batter, but the ball is falling and it would fall even more if there were less spin on the ball. That’s exactly what a split-finger fastball is doing. A split-finger fastball is holding the ball in such a way as to reduce the amount of backspin. The ball doesn’t fall because of any action of the spin, it falls because of gravity.”*

On why two-seam fastballs sink and four-seam fastballs don‘t: “It has to do with how the spin axis is oriented. With a four-seam fastball, the ball has almost perfect backspin, and maybe a little bit of sidespin that makes the ball tail. With a two-seam fastball, the spin axis is tilted in such a way that there’s more sidespin, so there’s more tail on it, less backspin, and therefore it sinks. It sinks because there’s less backspin.

“It’s not because of the seams per se. I think it has to do with the finger action of the pitcher’s hand on the ball that orients that spin axis the way it does. I don’t know exactly how they do it, but I do not believe it’s the seams that are causing that ball to move differently, It really has to do with how the pitcher applies pressure with his middle and forefinger, which are the last two fingers to touch the ball as he releases it to orient that spin axis.

“Once again, I’m relying on laboratory experiments that seems to show that all other things being equal, a four-seam pitch and a two-seam pitch, if the spin axis were oriented exactly the same, would break exactly the same.”

On if fastballs can rise; “A fastball could rise in principle, It could actually rise if you could get enough spin on it. The easiest way to show that is take a Styrofoam ball or a ball that has the same size as a baseball but is much lighter, and throw it with backspin, and you could make it rise. The reason why you can make that rise is because it weighs a lot less than a baseball — gravity isn’t not pulling down on it as hard. With a baseball, you would have to get much more spin on it in order to make it rise. Probably, it’s physically impossible. From a physics standpoint it’s possible, but biomechanically it’s hard for a pitcher to do.”

On the impact of seams: “The NCAA baseball has higher seams, and the higher seams certainly affect the aerodynamic properties of a ball. Laboratory experiments have been done where you set the two balls spinning at the same rate and look at how much movement there is. The data show that there’s more movement with the high-seam ball. Moreover, a pitcher can get a different grip on the high-seam ball. I think you can grip the ball better and probably put more spin on it as a result. For both these reasons, there will be more movement with a high-seam ball.

“It is also true is that there is less air resistance on the flat-seam ball, on the major-league ball. That is fairly well known, but it’s only been well know recently, at least from laboratory experiments. Straying a little bit from your question, there is a move afoot among NCAA coaches who are lobbying to change the NCAA baseball from a raised-seam to a flat-seam ball in order to get back some of the home runs that were lost when they went to the BBCOR bats.”

On scuffed baseballs:
“The seams do matter for movement, but the direction of the movement doesn’t depend too much on the seams. If the ball is spinning rapidly, the seam orientation is changing so rapidly that whatever forces arise due to the air flowing over the seams sort of averages out to zero because they’re so rapidly changing directions.

“The key to throwing a scuffed ball is to have the scuff on the spin axis. If you think of the North Pole of the Earth, the Earth is spinning around and the North Pole remains fixed. If you look at the North Star, which is located right on the spin axis of the Earth, the North Star doesn’t move. It’s always in the same location even though the Earth is spinning, because it’s sitting right on the spin axis. The idea of a scuffed ball is to orient the scuff so it’s right on the spin axis.

“For example, if you were throwing a four-seam fastball — a perfectly overhand four-seam fastball — you would want to have the scuff mark on one side of the ball, either the left side or the right side depending on which way you want the ball to break. The physics that govern the movement of a scuffed ball are exactly the same physics that lead to the movement of a knuckleball. In the case of a knuckleball, it’s the air flowing over the seams, but since the ball is not rotating rapidly — it might be rotating very, very slowly — unlike ordinary pitches where the ball is rotating rapidly and the effect of the seams average out, the knuckleball does not. In the case of a scuffed ball, where the scuff is located right on the rotation axis, it also does not.”

On bullet spin and back-ups sliders:
“There are certain types of pitches that can be thrown in which the ball can break in an unexpected way, not because of a scuff, but simply because of how the spin axis is oriented and relative to the seams. There is a famous case that was looked at pretty carefully a few years ago, Freddy Garcia’s split-finger fastball. There were several cases of this where the ball broke in the wrong direction. It was thrown with the same kind of orientation as a two-seam fastball, so you’d expect it to tail. But instead of tailing, it actually broke in the opposite direction. A lot of effort was put into trying to understand why it did what it did. I think we sort of understand it, at least qualitatively. It had to do with how the seams were oriented for this particular pitch. It seems to be not one that’s thrown very often, and iit could have even been a scuff on the ball, but there wasn’t obviously a scuff on the ball.

“When a slider is thrown, the spin axis is oriented in the forward direction, unlike other pitches where it’s perpendicular to the forward direction. A pure gyroball is one that is thrown with so called bullet spin. A gyroball basically doesn’t break, In fact, there’s no movement to it.

“A slider is oriented in such a way that the spin axis actually passes right through a seam. If the spin axis is already slightly forward and it passes through a seam and the batter sees this red dot. That is the red dot skilled hitters — at least ones with good eyes — can see. They know the pitch coming at them is a slider.

“If the ball is not released properly so that the spin axis is oriented much too much in the forward direction, there will be very little movement on the pitch. That’s a backup slider, or at least this is what people have told me. It’s called a backup slider because the catcher moves over to try to catch it. He’s expecting it to break, and has to back up because he sees it is not breaking, Generally speaking, it is a mistake pitch. It’s a slider that doesn’t slide.

“The reason why it doesn’t slide is not because it’s not spinning. It’s because the spin axis has been oriented too far forward, probably due to the fact the pitcher released the ball a little bit later than he should have. Because of the motion of his fingers, the spin axis ended up being like that of a spiral football.”




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David Laurila grew up in Michigan's Upper Peninsula and now writes about baseball from his home in Cambridge, Massachusetts. He authored the Prospectus Q&A series at Baseball Prospectus from February 2006-March 2011 and is a regular contributor to several publications. His first book, Interviews from Red Sox Nation, was published by Maple Street Press in 2006. He can be followed on Twitter @DavidLaurilaQA


24 Responses to “Q&A: Alan Nathan on the Physics of Pitching”

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  1. Bip says:

    I love this.

    People often look at a straight fastball and say “that pitch won’t be successful, it has no movement.” In reality, it appears to me that fastballs with lots of rise are hard to discern from others just by looking at them, but you can see the difference in the results.

    Exhibit A: Clayton Kershaw. Kershaw had the most valuable fastball in baseball by a wide margin this year. That is partly due to his velocity (21st among starters, 6th among lefty starters) but he also has effectively the most vertical “rise” on his fastball of any starter. That is despite having almost no horizontal movement, which is what people often point to when they say a fastball has a lot of movement.

    Exhibit B: Koji Uejara. Though he is more known for his splitter his fastball rates well above average as well. This is definitely partly because of the excellent way his pitches play off one another (i.e. the Tim Wakefield effect), but if his fastball was really a 89 mph nothing-ball he throws 50% of the time, then no secondary pitch could make it look good. His fastball is exceptional in one way though: it is 2nd among relievers in rise. This probably plays right into Uehara’s repertoire, as his secondary pitch is another type of fastball with different velocity and much less rise. This difference in vertical movement, paired with the fact that the pitches probably look identical until the last second, is how he is so effective with a 89 mph fastball.

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    • Isaac Newton says:

      Did you skip the paragraph about rising fastballs? He said a rising fastball is physically possible, it would just require more backspin than we have seen from a biomechanical standpoint. In other words, they haven’t found any one who throws a fastball that rises. Hence the statement that all fastballs fall.

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      • Simon says:

        He’s obviously using rise to mean the backspin which prevents the ball from falling as much as one would expect from gravity. But then, I think you knew that.

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      • Bip says:

        I use the word “rise” because I am used to pitch fx measurements, which calculate movement relative to a ball affected by only gravity. Therefore fastballs have positive vertical movement according to those measurements, which I just refer to as “rise”.

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  2. DAVID M. says:

    Re: two-seam vs. four-seam:

    “I don’t know exactly how they do it, but I do not believe it’s the seams that are causing that ball to move differently, It really has to do with how the pitcher applies pressure with his middle and forefinger, which are the last two fingers to touch the ball as he releases it to orient that spin axis.”

    This is correct. The seams itself don’t create the movement, but they allow a pitcher to put pressure on one side of the ball as you release. You can thrown a two-seam or a cut fastball just by applying more pressure with either your index finger or middle finger as you release…using a 2-seam grip just lets you do that much more easily than a four-seam grip.

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    • Bip says:

      I think the seam actually does matter a bit though. I hope I can explain why in a way that someone can understand it:

      The two pitches get their name from the number of seams that will pass over the ball in one rotation. So if you are watching the ball coming at you (orthogonal to the axis of rotation) you would see four different seams go up for each rotation of the four-seam fastball, and two for the two-seamer.

      This important because the number of seams going by creates more or less friction against the air, which is what creates movement. The four-seamer has more seams going by, which means more friction, which means more movement. For a fastball, the friction is greatest under the ball, which pushes the ball up, similar to how an airplane wing works. That one reason why two-seamers “sink” more, even though sink in this case actually means less rise.

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      • DAVID M. says:

        I think you’re right – I should be less absolute in my statement. The seams make a difference, particularly in terms of vertical movement like you said.

        I was thinking more purely in terms of the horizontal movement, where the seams facilitate the movement rather than create it. If I’m reading the article correctly, the horizontal movement is created by changing the spin axis, not by the friction created by the seams.

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      • Alan Nathan says:

        While what you say may make some sense physically, it is not supported by laboratory data. The data involve projecting the ball at a given speed, with a given spin, and the spin axis oriented in the desired way. Then the full trajectory is measured, from which one can obtain the movement. The data show not much difference in movement with the other parameters held fixed (assuming the ball is spinning rapidly). All data have experimental uncertainties and I don’t recall off-hand how much uncertainty there is in this result. However, new measurements are planned with even better precision that should settle this issue once and for all.

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  3. tz says:

    Do they still sell TracBall sets?

    I remember pitching with the styrofoam balls that came with the set. You can definitely make those rise with any amount of backspin.

    Loved the article.

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  4. Brandon says:

    I know more things about the thing I love than I did before I read this article.

    Terrific article, 1/1 rating according to my qualifications.

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  5. bob says:

    My understanding is that you need much more spin on a baseball to make it rise, compared to a hypthetical baseball-size Styrofoam ball with the same air resistance and spin forces, because the baseball has more inertia and therefore has greater resistance to a change in direction. While it’s true that gravity does not pull down as hard on a Styrofoam ball lighter than a baseball, that can’t be the whole explanation for why a lighter ball is easier to curve, since all objects fall at the same speed in a vacuum.

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    • Matt says:

      While acceleration due to gravity is constant (in a vacuum), the downward force caused by gravity’s pull is correlated to the mass of the object. Gravity DOES pull down equally on a styrofoam ball and a baseball, but the resulting force is different because of the different masses. Therefore, an object with more mass will require a greater upwards force (caused by spin) to counteract the greater downward force caused by gravity, so the difference in mass can explain this difference. (Although the seams, ball surfaces, etc. certainly play some role as well.)

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  6. japem says:

    This topic has always fascinated me. Can we get a sequel about hitting?

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  7. TF12 says:

    My dad bought me the Physics of Baseball by Adair when I was a kid. I used to refer to it when I would struggle. I always felt that if you knew why the ball did certain things it was easier to make adjustments.

    I saw it mentioned above but I gripped my breaking ball off of two seams. Basically inside the horseshoe. Every coach hated that grip, but for me it made the ball feel smaller in my hand and I felt like I had more leverage and pull when spinning the ball.

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  8. Park Chan Ho's Beard says:

    I’d be interested to know how much spin a pitcher would have to put on his four seamer to keep it from dropping at all, i.e. completely counteracting the gravitational force. Does anyone know how to solve this? And can it be expressed in simple rpm’s needed to keep the ball perfectly “straight”?

    And, what are the rpm’s of an average four seam fastball? I.e. how close are mlb pitchers to having their fastballs go perfectly “straight”?

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    • Bip says:

      I don’t know the answer, but I do know that even if this ball was thrown with this RPM, the friction of the air slowing down both the forward motion of the ball and the rotation of the ball would cause the ball to leave this state almost immediately and begin to drop.

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    • Michael Richmond says:

      Throwing a ball faster will help it to rise, and adding more backspin will help it to rise. The two effects build on each other, so there is no unique answer. One combination that would counteract the gravitational force is a speed of 110 mph and rotation rate of 3500 RPM. You can read about this and other aspects of the physics of thrown baseballs at

      http://spiff.rit.edu/richmond/baseball/traj_may2011/traj.html

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  9. Alan Nathan says:

    Hot off the press: Earlier today the NCAA D1 Baseball Committee approved the use of flat-seam baseballs for championship play (not sure what that means exactly) starting in 2015. See http://www.ncaa.com/news/baseball/article/2013-11-05/di-committee-changes-flat-seamed-baseballs-2015-championship. According to recent measurements, that should add as much as 20 ft to a long fly ball.

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  10. Matt says:

    Truly fascinating. Great work, as always.

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  11. GoodasGoldy says:

    Great article. The part on finger pressure reminded me of interesting discussion Sutton or Glavine gave about Greg Maddux. They said his success came from his developing a very advanced feel for finger pressure which enabled him to throw the same pitch with varying degrees of break in either direction just with slight alterations of his finger pressure.

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