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Alan Nathan is Professor Emeritus of Physics at the University of Illinois at Urbana-Champaign. After a long career doing things like measuring the electric and magnetic polarizabilities of the proton and studying the quark structure of nucleons, he now devotes his time and effort to the physics of baseball. He maintains an oft-visited website devoted to that subject: go.illinois.edu/physicsofbaseball.

In response to a question posed to me yesterday about late break on a fastball, here is my reply:

I'm not sure I really have much to say about the subject of late break. What I do have to say is summarized in the figure below (click to expand), showing Mariano Rivera throwing his cutter.

The solid curve is the actual trajectory, taken from PITCHf/x data. The dotted curve is a straight line projected from the release direction. The two curves look pretty nearly identical until about 20 feet from home plate, which is just about the point of no return for the batter. The ball deviates from the straight-line path at that point and ends up with about 0.5 feet (6") of movement, so the pitch that looks like it might hit the corner ends up 6" off the plate (and breaks the bat of a left-handed hitter, a rather common occurrence for Mo).

So, did the ball break late? No, it did not. The break is actually continuous, starting from when the ball is released. However, in this case the break was so little that the ball did not show any appreciable deviation from a straight line until the point of no return.

What does physics have to say about this? Physics says that the amount of break (assuming a constant force that causes the break) is proportional to the square of the flight time. Or in our case, proportional to the square of the distance from release. In the present case, the total deflection of the ball from 50 feet to 20 feet is about 35 percent of the total break from 50 feet to zero feet. The latter is 6", so the former is about 2". If you look very carefully at the trajectories in the figure, you should be able to see that there might be about a 2" difference between the solid and dotted curves at 20 feet. PITCHf/x tells us that essentially all pitches should have this behavior: Namely, the deviation from a straight line between 50 and 20 feet will be about 35 percent of the deviation between 50 and zero feet.

So, what is late break? In my view, late break actually means "not much break," meaning that the difference between no break and actual break is small enough at 20 feet that the batter can't perceive it. That is, 35 percent of the total break is too small to perceive. The Rivera pitch is an example of that.

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matrueblood
3/26
This is actually really interesting, though. The corollary conclusion might be, "A pitch that breaks less deceives best," since a batter will perceive so much less movement until after the point at which they have to decide to swing. This is why so few pitchers actually do well with the Matt Clement/Carlos Marmol-style sweeping, two-foot breaker. The batter can see that that pitch is going to end up in la-la land, no matter where it starts. But a slider with less movement, even thrown at the same (maybe even a bit slower) speed, has a better chance of inducing an ill-advised swing.
SixToolPlayer
3/26
This is kind of the impetus for the Perry Husband idea of pitching "tunnels" to which Trevor Bauer subscribes.
jfranco77
3/26
Or, alternatively, all pitches break late, because "break is proportional to the square of the flight time" and our brains think linearly, not exponentially.
backbrush
3/27
Fascinating article! More from Professor Nathan please.

So when Stephen Strasburg talks about working on developing "later movement" -- as he has this Spring Training -- he actually means working finding the right amount of movement, and potentially reducing the movement, so the pitch is more effective.

harrypav
3/27
we'll actually be covering this topic at The Post this season. We've already discussed the visualization technique we're going to use, so look for it (we'll surely show it here, too).
leleutd
3/27
"Physics says that the amount of break (assuming a constant force that causes the break) is proportional to the square of the flight time. Or in our case, proportional to the square of the distance from release."

This isn't strictly true, correct? Generally a pitched ball loses around 10% of its velocity by the time it reaches the plate. Since the velocity is declining (presumably at a consistent rate between different pitches), it spends more time traveling the last 15 feet to the plate than the first 15 feet from the pitcher's hand.

Second question: could there be a difference in the amount a pitch slows as it travels to the plate, depending on different rotational profiles? Does more spin on the curve (cmp to less spin) cause additional friction, slowing the ball more?
kmg1016
3/27
And to add to Travis's point/question, as the ball slows, wouldn't the spin have a greater impact on the ball's "finish" as it approaches the plate than it did when the ball was traveling at a higher rate of speed, thus giving the ball "late break"?

For those who haven't yet seen this, it's a can't miss presentation on Rivera from the NY Times a few years back: How Mariano Rivera Dominates Hitters
harrypav
3/27
for the record, Alan contributed to that Rivera piece (as did I and the rest of the CGC gang) ... and what you've said pretty much encapsulates how I think late movement manifests.
redsoxin2004
3/27
Thanks for the presentation. Great stuff. Helps also explain why his cutter is more effective than most (fastball spin vs. slider).

a-nathan
3/27
Responding to some of the questions:

Travis, 1st point: Yes, what you say is true and that adds to the effect of more movement later than earlier in the trajectory. To a good approximation, the force on a spinning baseball is proportional to velocity (v). The flight time is proportional to 1/v. So, deflection is proportional to 1/v. As the ball slows down, you get more deflection.

Travis, 2nd point: The dependence of the air drag on rotation rate is not well established experimentally, although it is a known effect for golf balls. The latest data I have seen for baseballs do not show much of an effect.

kmg1016: See my answer to Travis. Thanks for pointing out the NYT piece. The video presentation they put together is pretty fantastic.

I don't think any of the stuff I just described (slowing down, spin-dependent drag) plays any appreciable role in the question of "late break". The PITCHf/x data tell us that the ball follows very closely to a parabolic trajectory. That is an experimental fact. That necessarily means the break is continuous, with about 67% of it coming in the last 20 ft. I won't quibble about whether the 67% might really be 70% due to these other factors.