The Physics of “Late Break”

Mariano Rivera had some of the best late break of any pitcher in recent memory. (via Chris Connelly)

There are a couple of persistent myths about pitching that are finally on the wane.  Since the early days of baseball, many have argued that curveballs don’t actually curve but just appear to do so.  Another legend is the rising fastball.  Thanks to technologies like PITCHf/x and Statcast, we now know these two tales, while charming, are simply folklore.

In this article, I hope to add “late break” to this collection of pitching fairy tales.  I guess I should be more careful.  I don’t want to say “late break” doesn’t exist but instead try to convince you that all break is late break. The term “late break” is simply redundant.

This point has been addressed by others including the founding father of physics and baseball.

Does a curve ball then travel in a smooth arc like the arc of a circle? Yes. Does the ball “break” as it nears the plate? Yes.  Neither the smooth arc nor the break is an illusion but a different description of the same reality.”
— Robert Adair, The Physics of Baseball

To begin to understand what I mean by “all break is late break,” I’m afraid I need to ask you what I’m sure you’ll say is a “trick question.”  At the right is a sketch of a pop-up on a planet where they play baseball, but there is no air to interfere with the behavior of the ball.  So, the ball is only under the influence of the gravitational force. 

In the sketch, I have labeled the position of the ball every half second during its flight.  The red arrows are the velocity at two of the positions.

The question:  Compare the size of the gravitational force at each image of the ball.

Think about it for a minute before I give you the answer, even though you won’t like it…The gravitational force exerted on the ball is the same throughout the entire flight!

You probably said the force dropped as the ball went up and the force at the very top of the flight was zero–most people do.  That’s because people often confuse the force on an object with the motion of the object.  Force and motion are related, but very distinct, concepts.  The speed of the ball actually is the largest at the bottom and drops to zero at the top, but that is the speed of the ball, not the force on the ball.

Why is this confusion so common?  I suspect it is because we all know the force on an object is intimately connected with the motion of the object.  The connection between force and motion is Newton’s Second Law, which says that the force on an object isn’t responsible for the motion of the object, but instead the force causes changes in the motion of the object.

Let’s use this idea to focus on just the fall of the pop-up as shown at the right.  In the images at the right, I have indicated the forces as green arrows and the velocity of the ball as red arrows.  Notice the green arrows at each image are the same size, while the red arrows grow as the ball falls and speeds up.

Notice that the force, while itself unchanging, is constantly changing the motion of the ball.  That is, the ball speeds up as it falls, and the distance it travels during each half-second interval increases. The increase in distance is pretty small between the top two images of the ball and relatively large between the bottom two images. So, force changes the motion of the ball, but it takes some time for these changes to accumulate and become dramatic.

Now that we’ve mastered how force and motion work for pop-ups, let’s apply the same idea to a pitch on the airless planet.  Below, is a sketch of a pitch only influenced by gravity.

The ball is shown about every 0.05 seconds as it travels from right to left on its way from the pitcher to the plate.  The constant gravitational force (green arrows) pulls downward on the ball, changing the ball’s motion.  After all, if gravity wasn’t doing its thing, the ball would just stay at the same height moving along the black dashed line.  So, the blue line is the trajectory created by all the accumulated changes in motion caused by the gravitational force.

A Hardball Times Update
Goodbye for now.

Here’s the point.  Since the time intervals are so short for a pitched ball, it takes quite a large fraction of the flight time for the changes caused by the force to accumulate to the point where the hitter can distinguish between the motion without any force and the motion under the influence of the force.  From this sketch, it appears that it takes nearly half the flight time for the ball to deviate significantly from the no-force trajectory.

So essentially, all break is late break.  There is little deviation in the motion of the pitch early in its flight, and the largest changes in motion occur as the pitch nears home simply due to the basic physics of Newton’s Second Law.  Hence the term, “late break” is redundant if not completely wrong.  That is to say, all break is late break.

Now, let’s head back to Earth, where there is plenty of air and everyone has played enough slow-pitch softball to easily compensate for the change in motion of the pitch due to gravity.  After all, gravity works the same way regardless of whether the pitcher throws a fastball, slider, curve, or change.  So, dealing with gravity isn’t a big issue for hitters.

As explained many times before in many places, the air exerts forces on a pitch that depend upon the speed and spin of the ball.  The batter has little idea as to the speed or spin of the ball during the initial motion of the pitch.  In addition, the forces the air exerts will not have had enough time to accumulate to the point change in the motion of the ball will give the batter much of a hint.

So, the trick to having highly effective “late break” is to disguise the speed and spin of the pitch from the batter for as long as possible.  The most common way this works is for pitchers to deliver their different pitches with identical deliveries and similar early trajectories.  This idea is called tunneling.

This is also Alan Nathan’s argument, which he described in terms of trajectories and batter perception when he examined the secret to Mariano Rivera’s success.  Rivera’s cut fastball is so effective because “all break is late break.”

Well, it’s time for me to give you a break, though that’s probably a little too late.  I’ll conclude by sharing some thoughts of Nobel Prize winner Richard Feynman regarding the beauty of a flower.  Instead of just stealing the quote, I modified it to my devious ends.

I have a friend who’s an artist a pitcher and has sometimes taken a view which I don’t agree with very well. He’ll hold up a flower throw a pitch and say, ‘Look how beautiful it is,’ and I’ll agree. Then he says, ‘I, as an artist a pitcher, can see how beautiful this is, but you as a scientist take this all apart and it becomes a dull thing,’ and I think that he’s kind of nutty…science knowledge only adds to the excitement, the mystery and the awe of a flower pitch. It only adds.”

David Kagan is a physics professor at CSU Chico, and the self-proclaimed "Einstein of the National Pastime." Visit his website, Major League Physics, and follow him on Twitter @DrBaseballPhD.
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Eli Ben-Poratmember
6 years ago

Great work as usual, David. The question I’ve always had with respect to “Late Break” is this: Say we posit that 20% of the movement of an average fastball occurs in the first half and 80% occurs in the second half, is it possible for pitchers, based on their unique release point, spin rpm and spin axis, to shift this ratio to 10%/90% or 30%/70%. Theoretically, if more of the movement as a percentage of all movement, as compared to the average, occurs in the second half, this could qualify as “late break”.

David Kagan
6 years ago
Reply to  Eli Ben-Porat

I believe that if you compare Kershaw’s typical trajectories for his fastball versus curve ball, you’ll see his curve start with a slight upward trajectory which quickly peaks and begins heading downward. His fast ball is heading downward from the moment of release. The point is that they are released from nearly the same spot and trajectories cross early in their flight on the way to the plate. The difference between the two trajectories is small for an elongated period because of the crossing trajectories. Is this the kind of thing you are driving at?

Jetsy Extrano
6 years ago
Reply to  Eli Ben-Porat

Let’s set a baseline of 25% / 75%, since that’s what you’d expect from the physics of a simple constant force, integrating to a parabolic arc.

Then what’s the mechanism to get a different split? The force must increase in magnitude, or decrease, or change direction. Well, you lose spin and lose speed during flight, can you get late break out of that plus the details of the aerodynamics? I dunno.

The first question I’d ask is are you looking to get late break out of spin deflection plus gravity, or are you relying on additional aerodynamics.

6 years ago

Nice job with the images, they really help. As an aside, I wonder if the suspected smoother baseballs this year have not been as much of a problem for pitchers who rely more on just change of speeds than any “break”.

6 years ago

While I appreciate the physics and theory discussed in this piece, I am not certain it fully dispenses with the notion of ‘late break,’ or even fully comprehends what is meant by that term. As I understand it, late break refers to the appearance of sudden lateral and or vertical movement of the ball as it gets closer to the plate. While it is obvious that the forces at play–initial velocity, gravity, drag (magnus effect)–are all in action the entire flight of the pitch, I am not convinced the combined effect of all of those forces, particularly drag, cannot be realized closer to the plate. Most breaking pitches, especially cut fastballs and sliders, but also curve balls, appear to have an asymmetrical flight path where most of the lateral or vertical movement occurs in the 10-20 feet before the plate. It seems your argument is that the trajectory is a consistent arc or curve that is relatively symmetrical from the time the ball leaves the pitchers hand to the time it crosses the plate–the movement in the first 30+/- feet (obviously with a pitcher’s arm length and kick-step this distance goes down, but for argument sake consider it close to the actual 60’6″) is mirrored in second 30+/- feet before the plate. If this is true in every instance than clearly you are right late break does not exist. However, to the extent the horizontal flight path or vertical trajectory of the ball is asymmetrical, then late break not only seems possible, but in many instances seems likely. I guess, in summary, I would argue that the spin and velocity of the ball are creating a magnus effect that generates greater movement over time, and that it is possible for there be significant break at a late point in the flight path when the forward velocity of the ball decreases relative to the air currents moving around one side of the spinning ball. Thoughts.

6 years ago
Reply to  msch

Yeah, this.

Oort Cloud
6 years ago
Reply to  msch

Yeah. Late movement is later movement as in late relative to a typical breaking ball. No solecism or redundancy, really. All break cannot be late because, by definition, the typical break would “on time.”

Can a pitcher control whether a pitch breaks early or late in its trajectory? If so, late break very much exists.

V Grof
6 years ago

It’s a little hard to understand the first paragraph of this article. The two persistent myths are….??? “Curve balls do really curve” or “it’s only an illusion that curve balls curve”. ?????? Which is the myth??

Second myth (maybe easier to understand what exactly is the persistent myth) – “Rising fast balls actually rise” or “Rising fast balls only appear to rise”. ??? More likely that “Rising fast balls actually rise” is the persistent myth in this case.

The discussion on “Late break” is clear, however.

6 years ago

Thanks for the article, Dr. Kagan. Please tell me if (or how) I’m mistaken…

Considering drag, I believe there can be a relatively “late breaking” curveball. If:

Drag reduces velocity continuously to home plate.
Drag increases with velocity squared.
Vertical break is proportional to spin velo and inversely proportional to velo (Vs/Vt = spin factor).


As a 12-to-6 curveball’s initial velo is increased, drag increases. Therefore, delta Vt will be greater (between pitcher and catcher) than for a pitch with a slower initial velocity. Since drag is proportionate to V^2, The relative slowing of the ball will give more time for gravity to act, creating a more dramatic non-linear drop as the ball gets closer to the catcher (compared to a lower velocity curve).

Assuming spin velocity (Vs) is constant throughout the pitch and Vt will decrease over time due to drag, the lift coefficient of the curveball will become greater (in the case of topspin, greater downward movement) over time. The rate of downward movement will increase more over time for a high top-spin curveball than for one with a lower spin rate.

These two reactions will create the effect of a late breaking curveball.

I hope I’m not off by too much – been a long time since my college aerodynamics class.

David Kagan
6 years ago
Reply to  dbminn

“A little knowledge is a dangerous thing!” Of course, you are correct – the speed of a pitch drops by about 8% on the way to the plate, so the drag would drop be about 16% because it depends upon the square of the speed. Also, the lift does depend both upon the speed of the ball which drops and the spin of the ball which doesn’t change. You do remember your class!

The aerodynamic forces on the ball do indeed drop as the ball gets closer to the plate while the force of gravity remains constant. Nonetheless, I believe my argument that it takes time for the change in motion caused by the force to accumulate still holds even if some forces are changing themselves. So, I think we are saying the same thing i different ways.

6 years ago
Reply to  David Kagan

Thanks for the reply and the article!

6 years ago
Reply to  David Kagan

Explain a knuckle ball then. I know from catching one, that it appears to wobble on the way towards you. As it nears you the wobble appears to increase, then the ball suddenly darts in some unpredictable direction. Seems like late break cause by aerodynamic forces to me.

Jetsy Extrano
6 years ago
Reply to  TZ

Yup. A knuckleball does have a changing force on it! The force can totally change direction during the flight.

A pitch that’s got gravity and Magnus force, though, doesn’t have that kind of change going on.

So you are correct and you also support the overall argument at the same time.

6 years ago

Let’s say two pitchers throw a 95 mph fastball, identical spin rate but different release points but pitcher A’s tilt 0 degrees pitcher B let’s say 20 degrees What is the effect on the movement. Mariano sawed bats off with “late movement” sideways not drop. So i’d like to see some comparisons on pitchers using cutters or sliders. You are correct when address drop but late movement at the pro level should only be looked at on FB over 85 mph on the horizontal plane.

Walker Wentworth
6 years ago

How do your models account for the impact of the seams?

Jetsy Extrano
6 years ago

In particular I wonder about “swing” deflection as used in cricket bowling. The baseball pitch can’t get as much, but can it get enough to create an extra inch of late break on pitches that exploit this effect?