What's the Deal With Those Weird Bats?

Torpedo in the #discourse

This past Saturday, the New York Yankees pounded the Milwaukee Brewers, winning 20-9 in a game where the Yankees hit nine home runs. In the course of the broadcast, Michael Kay of the YES Network made a passing reference to the odd shape of the bats being used by several of the younger Yankees, including shortstop Anthony Volpe, who promptly hit a home run. This exploded in the sports-media #discourse, with the usual cavalcade of accusations that this was blatant cheating, compromising the purity of baseball’s bodily fluids sacred traditions, etc. It also catapulted former atomic physicist Aaron Leanhardt to temporary fame¹ : “Lenny” was an analytics guy for the Yankees and played a key role in convincing the hitters to try this new style of bat.

In depressingly typical fashion, this broke just in time for the start of Spring term classes at Union, and the usual start-of-term chaos has kept me from having any time to write about it in a timely manner. But I can hardly let this pass unremarked, so here’s a little bit about the physics behind the “torpedo bats.”

So, how is this not a massive cheating scandal? Launching bats out of a submarine seems like a clear competitive advantage. First and foremost, it’s important to note that these bats are perfectly legal. MLB specifies the composition of the bat (a single piece of wood), a maximum length (42” or 106.7cm), and a maximum diameter (2.61” or 6.63cm), and that the bat has to be round (so no cricket bats). The “torpedo” bats in question are within the maximum width specification, but where a traditional bat is widest at the far end from the handle, these reach their widest point partway up the handle, then taper back down.

The effect is somewhat subtle for most of these, as you can see in this hastily assembled composite of pictures grabbed off websites selling baseball bats:

The top is a traditional wooden bat, the bottom is the model of aluminum bat that The Pip is using this season, and the middle is a “torpedo” bat that has appeared for sale since this story broke. You can see that the “torpedo” bat reaches its widest point about two-thirds of the way down the length, and then tapers down, where the classic bat shape is widest right before the end.

What’s the point of that? Well, when you want to talk about the physics of an extended object (anything more complicated than the point-cow approximation²), a key feature for characterizing the object is the location of its center of mass. In the simplest physical picture, the bulk motion of the object will behave like a single mass concentrated at that point.

The center of mass of a uniform object is right in the middle— the center of a sphere, say, or halfway along a straight stick. If the object isn’t perfectly regular in shape, though, the center-of-mass is pulled toward the heavier end. You can at least crudely identify the location of the center of mass by attempting to balance the object on a finger: if your finger is directly below the center of mass, it will balance there, while at any other point, the object will tip toward the side where the center of mass is actually located.

For a tapering object like a baseball bat, the center of mass is shifted toward the fat end, because there’s more wood (and thus more mass) at the point where it’s thickest. I’ve put red dots on the bats in the composite photo illustrating the basic idea. The torpedo-bat shape gets narrower at the far end, which has the effect of shifting the center of mass back toward the narrow handle somewhat. I’ve indicated that (conceptually, at least) with the blue dot in the figure above.

So, wait, how does moving that dot a little bit lead to more home runs? It’s complicated.

Come on, man, that’s a cop-out. It’s not, honestly. The whole process here is genuinely very complicated. As a general rule, once the cows stop being spheres, physics gets difficult. But I’ll take a run at explaining the idea.

Being a physicist, though, I need to break this down to a starting point where the cows are spheres. Or at least, the bat and the ball are— at bottom, the process of hitting a baseball is a collision between two moving objects, the bat and the ball. The bat is, generally speaking, 6-ish times heavier than the ball, so if we model them as two colliding spheres we expect the ball to reverse direction after the collision. The bat will slow down very slightly, and the ball bounces out at a higher speed than it came in.

If you’re dealing with spherical objects colliding in space, the only parameters that matter here are the two masses, the two velocities, and any offset between the directions of the velocity. If they strike exactly head-on, the ball just reverses direction, if the bat is below the center of the ball it kicks upward, and if it’s above the center it kicks down. The higher the relative speed of the bat and the ball, the faster the ball is moving when it leaves the bat— a hard swing at a fast pitch goes a long way, but a weak swing at a slow pitch doesn’t.

But a bat isn’t a sphere. Right, so we need to consider it as an extended object. It’s also being actively swung, pivoting about a point in the general vicinity of the wrists of the batter. The next thing we might think about as a model would be having a collision between the ball and the bat represented as a sphere at the center of mass. The speed of the center of mass of the bat is determined by the rate of rotation involved in the swing and the distance along the bat: the faster the batter is turning, the higher the speed, and the farther the center of mass is out the bat, the higher the speed.

Photo by Josh Hemsley on Unsplash

But, wait, if the torpedo shape moves the center of mass closer, wouldn’t that reduce the speed of the bat in the collision? If the speed of rotation is the same, and the collision is at the center of mass, yes. But then we have to think about what’s involved in the swing.

Swinging a bat is fundamentally about rotation— the bat is turning about a point somewhere around the wrists of the batter— which means that getting it moving is about exerting a torque to cause a rotation. The torque depends on where the batter is holding the bat and how much force they can exert, neither of which changes when you change the bat shape. The rate of rotation that results from that torque depends on something called the “moment of inertia,” which is a bit complicated to calculate, but tends to track with the distance of the center of mass from the axis of rotation.

Lowering the distance from the handle to the center of mass reduces the moment of inertia, which in turn means that the same force exerted through the same grip will lead to a slightly higher rate of rotation. You see this in quotes from users of the torpedo bats talking about how they “feel lighter”— the mass of the bat hasn’t changed but the moment of inertia has, making it easier to swing. So there’s a bit of a trade-off, here, in terms of the speed.

Sounds complicated. Told you so.

Anyway, that’s one effect of moving the center of mass— the bat is somewhat easier to swing. This also shifts the location of the most effective impact position for the bat.

Oh, the “sweet spot!” Sigh. Yes and no.

The problem here is that there are several different things people can mean by “sweet spot.” The two main ones are “the place where the ball leaves the bat at the highest speed,” and “the place where hitting the ball ‘feels’ best to the batter.”

Are those not the same? Sadly, no. As I said, it’s complicated.

The “feels best” point involves two different effects, one of which is the vibration of the bat in the hands. If you’ve ever played baseball or softball, you’ve probably had the experience of hitting a ball and having it really sting your hands— part of that is the way the bat responds to the impact. The ball striking the bat starts the bat vibrating in response, with the amount of vibration depending on exactly where it’s struck, and that vibration is communicated to the hands of the batter, which tends to be kind of painful. If the ball hits at just the right point (a “node” in the pattern of vibration), the impact will produce very little vibration, and thus the batter won’t feel that in their hands.

So that’s the sweet spot. Well, it’s a sweet spot. There’s another thing people talk about in this context, which is the “center of percussion.” That’s the point on the bat where the impact produces the minimum force on the rotation point.

If a ball strikes the bat at a point that isn’t the center of mass— let’s say toward the far end of the bat from there— the effect of the impact is to make the bat rotate about the center of mass. Which would cause the end of the bat to go in the direction the ball was headed, and the handle to move back toward the pitcher. But it also tries to make the bat as a whole move in the direction the ball was headed. At some point, those two effects exactly cancel each other out, and the resulting force on the handle of the bat is zero.

That also probably feels better on the hands, right? Exactly. Which is why you’ll hear baseball players who just hit a ball a really long way say that it didn’t feel like anything at all— they’ve hit the ball at the center of percussion, which produces the minimum reaction force on their hands. Which can also be seen as a “sweet spot.”

And those aren’t the same point? Sadly, no. The location of the nodes of vibration depends on the details of the shape of the bat, and the center of percussion depends on the shape and also the grip. They tend to be near each other, but not exactly the same. What batters mean by “sweet spot” is probably some combination of the two.

So which of those is the best spot to make the ball go really far? Sadly, neither. The exact point where the ball comes off the bat the fastest is generally near those other two points, but not exactly the same as either. And will depend on fine details of the shape of the bat and the particulars of where a given player holds it, and all that kind of stuff.

That seems really complicated. Yes, well, that’s why we prefer our cows to be spheres.

And that brings us around the the really important part of these “torpedo” bats, which is that they’re specific to the player. If you look at the various photos attached to stories about the Yankees batting explosion, you’ll quickly notice that the bat Anthony Volpe is using is a different shape than the one Jazz Chisolm is using, which is a different shape than the one Austin Wells is using.

This is the result of a complicated process of analyzing each player’s swing to determine exactly where on the bat they’re most likely to strike the ball, and adjusting the mass distribution to make that point maximally “sweet.” It’s probably iterative, too— testing a standard bat, then one “torpedo” shape, then another, etc., and eventually arriving at one that’s maximally effective.

So you’re saying I can’t just order a “torpedo” bat for my 11-year-old online and watch him start launching bombs? No, definitely don’t do that. It’s almost certainly a waste of money for anyone who isn’t a professional baseball player who already has a well-tuned swing. A random youth player or beer-league adult probably isn’t hitting the ball in a consistent enough manner for it to even be possible to design a bat that matches their swing. And a random mass-produced “torpedo” shape isn’t likely to just happen to fit their swing.

Is that why this hasn’t been a Thing before now? Pretty much, yeah. Tuning the bat shape to an individual swing is a complicated process, and involves a lot of technology that’s only become practical relatively recently. And if you’re not going to do the individual tuning, the traditional shape is almost certainly simpler and cheaper to mass-produce.

Since this has become a Thing, though, I would absolutely expect to start seeing big racks of “torpedo” style bats at your local sporting goods store. I would not expect an enormous increase in the number of balls leaving Little League fields as a result, though.

And, really, the whole thing is probably overblown, as demonstrated by the way the Yankees followed up their incredible offensive outburst against Milwaukee with two relative stinkers against the Diamondbacks.

Volpe’s still hitting bombs, though… True enough; he’s the Torpedo Kid. But really, last weekend probably tells you more about the weaknesses of the Brewers pitching staff than it does about bat technology.

Still, any excuse to talk about physics is a Good Thing. Even if it does ultimately boil down to “It’s complicated…” (And that’s before getting into the psychological aspects, as noted toward the end of this NPR piece about the “torpedo” craze…)

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So, yeah, there’s some physics. Wish I’d been able to do it in a more timely manner, but better late than never. Anyway, if you want more of this, I have good news: The Pip’s baseball season is starting soon, so you’re highly likely to hear a lot more about the game if you click this button:

And if you want to correct any errors I made in the above, or introduce further complications, the comments will be open:

1. Leanhardt joins the very short list of at-least-temporarily-famous people I have played sports against, joining his Ph.D. advisor Wolfgang Ketterle (we played pick-up soccer at a Gordon Conference) and mine, Bill Phillips (we played ultimate frisbee at a Laser Cooling Group picnic one year when I was a grad student), and Senator Chris Murphy of Connecticut, who was a freshman on the rugby team when I was a senior at Williams.

2. Hey to Tom Swanson.