# Using Physics to Understand the “Power” in Power Alleys

Ever since I discovered (for myself, at least) that horizontal direction matters when modeling batted-ball distance, I’ve been fascinated by the concept of ideal spray angle. Every discovery I’ve made along the way has only led to more questions.

For example, it looks like a batter’s ability to pull fly balls ages better than his ability to hit opposite-field fly balls. But that finding is complicated by the fact that the distance of pulled fly balls ages worse than the distance on opposite-field fly balls. Screwed if you pull, screwed if you push: thanks, Father Time.

Now, with the help of Andrew Perpetua, we have a few more graphs to help us better examine the traits of pulled and pushed fly balls. It should provide some answers. And definitely more questions, too.

First, I asked Perpetua to show me the average distance, by horizontal angle, on what I’ll call “ideal power fly balls” — that is, batted balls with a home-run launch angle (in this case, between 21 and 36 degrees) that traveled at 96 mph or more. Batted balls that meet those requirements were homers 55% of the time over the last two years. I was surprised by the outcome.

This is corrected for handedness, meaning that the negative angles are opposite-field hits and the positive ones are pull hits — regardless of whether the batter in question is a lefty or righty. My bias towards pull power is exposed as folly for good, it looks like: the ball goes furthest to the opposite-field center-field power alley! These are Statcast distances, too, so they’re likely free of human scoring bias on home runs down the line that are classified with shorter distances because of the interaction between stadium construction and the flight of the ball.

The fact that players actually should be aiming for the power alleys like hitting coaches have been saying forever probably isn’t so surprising. But we’re not ending there. Let me introduce another graph that complicates things.

This is about the time I start throwing crap around the office. After learning above that hitters record more distance on batted balls to the opposite-field power alley, we find there that they record a greater average exit velocity on batted balls down the lines. What?

Meredith Willis, a baseball data scientist with a degree in astrophysics, points out to me that it makes sense: hitters impart greater velocity on a ball pulled down the line because the bat and the ball are in contact longer; they’re imparting force on the ball for longer.

If a batter hits the ball harder down the lines, why does it go further in the power alleys? Alex Chamberlain wanted to make sure that this wasn’t our fault for having too wide a band in outcomes. So we narrowed the scope to batted balls that featured an exit velocity between just 98 and 100 mph and a launch angle of 26-27 degrees. These batted balls were converted to home runs 29% of the time. So it’s not ideal, but it is more tightly controlled.

Now, in this graph, it looks like the pull power alley is the best for distance, even if straight down the line still isn’t great. If a batter aimed for left or right center, he’d be optimizing hit spray angle — according to this graph, at least.

The problem with the ball down the line may have something to do with slices. Physicist David Kagan wrote a piece for The Hardball Times about the screaming foul ball down the line that featured this illustration.

More slice down the line means that more of the ball’s exit velocity is converted into energy that’s directed perpendicular to the playing field. In other words, a batter is striking the ball sideways and robbing it of batted-ball distance.

Kagan expounded in an email, as follows:

I suspect that the largest effect causing the inequality of barrels is indeed the spin imparted to the ball. There are two components of the spin on the ball that matter – the backspin and the sidespin. The greater the backspin the more carry on the ball. So, two equal barrels will travel different distances if they have different backspins. Sidespin will tend to reduce the carry because the balls trajectory goes somewhat sideways as opposed to straight. The more sidespin, the less the carry.

So one question is, “What determines the spin on the batted ball?”

Let’s start by assuming the bat is parallel with the ground when it hits the ball. Further, let’s imagine the bat is parallel with the line that joins first and third when it strikes the ball. That is, the ball will be heading out to centerfield. In this case, the backspin on the ball determined as you say in the article by the millimeters between the height of the center of the bat and the center of the ball. There are some usable models (from Alan Nathan of course) for finding the spin as a function of this height difference.

Complication number one: If the bat is not parallel with the ground, some of this backspin becomes sidespin. Take the extreme example where the barrel is so much below the hands that the bat is almost vertical when it strikes the ball. In this case almost all of the spin becomes sidespin. Since this contribution to the spin is not always backspin, I usually call it the “misalignment spin” because it is caused by the misalignment of the center of the bat and the center of the ball.

The misalignment spin causes the ball to move toward right field for right handed batters and left field for left handed batters when the barrel is below the hands. This spin will always cause the ball to slice.

Complication number 2: There is another source of spin when the ball collides with the bat and the bat that is parallel with the ground but not parallel to the line between first and third. That is, when the ball will be pulled or go to the opposite field. The result is a sidespin that will cause the ball to move toward the foul lines regardless of whether it is pulled or hit away. Let’s call this the lateral spin. Note this can be a hook or a slice.

Now let’s combine the misalignment spin and the lateral spin for a right handed batter pulling a ball down the left field line with the barrel of the bat below the hands when it hits the ball. The misalignment spin will cause the ball to move away from the foul line (slice toward right field) while the lateral spin will cause the ball to move toward the foul line (hook). That is, they tend to cancel each other.

Contrast this with the right hand batter hitting one down the right field line with the barrel below the hands. The misalignment spin will cause the ball to move toward the right field line (slice) and the lateral spin will do the same thing. Now we know that outfielders know that pulled balls are more likely to stay fair than balls hit the opposite way.

That’s a lot to digest. Kagan provides another way to illustrate the effects of different spins, though. He created two models for batted balls — one that features constant backspin and a varying sidespin, to reflect balls hit toward center field, and a second model for balls hit down the line where there is a trade-off of backspin for sidespin. Here’s what he ended up with:

If a batter loses backspin while gaining sidespin, the effect on distance is far more dramatic than the other way around. Backspin is good for distance (Kagan has more on the effect of spin on the flight of a baseball over at The Hardball Times today), so he wants backspin. If that’s true, it stands to reason that barreled balls hit down the lines are less effective than those hit toward the middle of the diamond.

If you want to know more about slicing and hooking and balls in play, Alan Nathan wrote a great piece here just a few weeks ago. His focus was a bit more on one play and how the outfielder might perceive the ball, but a lot of what he says is mirrored here.

The fact that the misalignment spin and lateral spin cancel each other out on pulled balls may render the batted ball to the pull-side power alley the ideal sort of contact. Most of that ball’s effective spin is backspin, which helps carry the ball. As opposed to batted balls center field, the power alleys generally feature shorter distances to the walls, too, which means that homer probability goes up closer to the corners. So batters shouldn’t only aim for home runs down the line: it might cost them distance on all fly balls. And they still want to make sure they’re swinging at the right balls if they’re tying to pull: — pulling the outside pitch leads to worse outcomes. But it looks like a pull-power-alley approach is great.

Because (a) exit velocity increases on a pulled ball, but (b) spin interferes and creates lower distances closer to the corners, there’s a sweet spot: the pull-center power alley. “Power” is in the name.

Guess batters should keep trying to hit it there.

With a phone full of pictures of pitchers' fingers, strange beers, and his two toddler sons, Eno Sarris can be found at the ballpark or a brewery most days. Read him here, writing about the A's or Giants at The Athletic, or about beer at October. Follow him on Twitter @enosarris if you can handle the sandwiches and inanity.

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Mattabattacolamember
7 years ago

Super interesting Eno. I am curious to see how much distance a batter loses by going down the line compared to how much shorter the fence is. Based on your graph of both it looks like the “down the liners” go like 360-370, whereas the power alleys around 400. So yes they hit it further in the alley but is the gain in distance worth it when you can clear the fence down the line easily at 370?

side note, whoever initially decided a baseball fence should get deeper as it gets away from the line seems pretty genius right now considering this new info

Mattabattacolamember
7 years ago

Is there any data out there tracking bat angles? Stanton comes to mind as someone who keeps and extremely flat bat (parallel to the ground) just from an eye test and he crushes the ball. Maybe he loses some contact because of this?

7 years ago

You only lose distance if you hold exit velocity constant, which as your chart shows, it isn’t. It’s easier to hit the ball harder down the lines, which is simple conservation of momentum: a head-on collision will kill more momentum than an oblique one.

You’ll probably notice that the difference in EV between balls hit to center and balls hit down the lines is greater on hard pitches and lesser on soft pitches.

Alan Nathanmember
7 years ago

I don’t agree with your “simple conservation of momentum” explanation for why balls hit down the line are hit harder. As “proof”, consider a ball thrown at an oblique angle against a wall. It loses energy in the perpendicular direction due to the coefficient of restitution. But it loses less energy in the transverse direction due to friction. So, the bounce speed is larger the more oblique the collision, since there is less perpendicular energy to lose. It’s a question of energy dissipation, not momentum conservation.

The same essential physics applies when a bat is swung, although the details are different since the motion of the bat contributes to the energy in the perpendicular direction.

For a ball hit off a tee, there is zero transverse energy and the exit speed is independent of direction for fixed bat speed.

All these qualitative features I just described are verified in my ball-bat collision model.

7 years ago

Oh so your model would also give higher exit velocities in elastic collisions at 45 degrees horizontal compared to dead on?

Alan Nathanmember
7 years ago

Yes, as long as we aren’t really talking about “elastic” collisions. There is lots of energy loss and that is crucial to the conclusion. If the collision were really purely elastic (i.e., no energy loss, COR=1, no friction), then the exit speed will be independent of angle (for the ball-on-wall situation).

7 years ago

But exit speed shouldn’t be independent of angle in perfectly elastic bat-ball collisions, though right? Because the bat isn’t massive.

Alan Nathanmember
7 years ago