The Physics of Barreled Balls

Yankees' rookie Gary Sanchez was among the leaders in Barrels in 2016. (via Arturo Pardavila III)

Yankees’ rookie Gary Sanchez was among the leaders in Barrels in 2016. (via Arturo Pardavila III)

I guess I wasn’t paying attention because back in September 2016 Mike Petriello wrote that Statcast debuted a new metric called “Barreled Balls.” According to MLB’s Statcast Glossary, the barreled ball designation is assigned to balls with specific exit velocities and launch angles that have “historically led to a minimum .500 batting average and 1.500 slugging percentage.”

These are hard hit balls with speeds off the bat of 98 mph and higher with launch angles that range from line drives to fly balls. As you might guess, barreled balls are the drives that result in a high fraction of doubles and home runs.

Recently, Eno Sarris of FanGraphs wrote about some quirks in the barreled ball designation. In his article he concluded that there may be more than just statistics at play when it comes to defining a well hit ball. He is correct, there is physics going on behind the scenes.

The barreled ball designation statistically treats the exit velocity and the launch angle as independent quantities – just numerical entries in the Statcast database. At the 2016 SaberSeminar, my presentation described the physics behind the correlation between the exit velocity and launch angle. I won’t drag you through all of it here – just the main points.

kagan-1

Above is a plot of the launch angle versus exit velocity for all balls hit at greater than 100 mph in 2015. The ones in red resulted in homers while the ones in blue were not. The green lines denote the barreled ball range. The physics is indicated by the black curve which bounds the grand majority of the data indicating a correlation between launch angle and exit velocity.

The plot shows that to hit the ball at a high speed you have to hit it at a low angle. This physics is most easily understood in the collision of two pool balls. In what follows, think of the cue ball as the bat and the eight ball as the baseball (in this case on a tee instead of being pitched).

Let’s imagine you’re not playing a usual game of pool where the object is to get the ball in the pocket. Instead, suppose the goal is to have the cue ball strike the eight ball in such a way that that the eight ball heads off with the highest possible speed. A direct hit is the way to go. That is, you want the cue ball to move along the line that goes from the center of the cue ball to the center of the eight ball.

Now let’s change the goal. Suppose you have to still hit the cue ball just as hard, but you want the eight ball to head off at a low speed. You know the answer is to shoot the cue so it barely touches the eight ball. The result of this oblique collision is the eight ball heads off at a large angle with respect to the initial direction of the cue ball and the eight ball moves rather slowly.

So instead of being independent quantities, there is a relationship between the launch angle (the direction of the eight ball) and the exit speed. If you want to see an approximate set of equations to describe the correlations look here.

In his article, Sarris was motivated to use a linear regression model to see if other Statcast variables showed correlation with batted ball distance. He found that air density, horizontal direction (spray angle), and spin showed significance as well as the exit speed and launch angle.

Again, physics is behind these correlations. The air density correlation relates to the drag force that I have written about many times. The basic physics is, the thicker the air the more the ball slows as it flies resulting in shorter distances. Enough about the weather, otherwise we would also have to take into account the wind.

Spin also has a strong effect on the flight of the ball. The essence of getting a pitch to move or break is to put spin on the ball. This movement will also occur on a batted ball with spin. Spin has two relevant components – backspin and sidespin. Unfortunately, Statcast and the data collection system it relies upon doesn’t distinguish between backspin and sidespin. It just records the total spin. Alan Nathan tried to deal with this issue here.

Let’s look at the backspin first. Using Alan Nathan’s Trajectory Calculator, here’s a graph showing the effect of backspin on a moderately well hit ball. The greater the backspin the more carry on the ball. As I have said before, “The backspin can change ‘a can of corn’ to a pretty serious blast.”

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However once again, backspin is not an independent variable. Just as the launch velocity will tend to be higher and the angle lower when the bat makes a direct hit on the ball as opposed to an oblique collision, the backspin on the ball will be smaller when there is a direct hit as opposed to an oblique collision.

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To wrap our heads around the cause of backspin on a 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 base at that instant. That is, the ball will be heading out to center field.

In this case, the backspin on the ball is determined by the vertical distance between the height of the center of the bat and the center of the ball. If the center of the ball and the center of the bat are perfectly aligned, there will be no backspin at all. The higher the ball hits above the center of the bat, the more backspin there will be.

So, a liner to center will generally have less backspin than a fly ball. There are some usable models (from Alan Nathan, of course) for finding the spin as a function of the height difference between the centers of the bat and the ball.

Now let’s look at sidespin. Sidespin is the devil that causes the hooks and slices in your golf game. Both hooks and slices shorten the distance of your drives. The same is true for shots off the bat. The graph below shows the effect of sidespin on the distance traveled by a ball that would go 423ft without any sidespin.

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The red curve was generated assuming the backspin was the same regardless of the amount of sidespin. The blue curve assumes that the total spin on the ball is constant so any increase in sidespin comes at the expense of backspin. Why would an increase in sidespin cause a decrease in backspin?

One of the two sources of sidespin can be understood if the bat is not parallel with the ground when it collides with the ball. Take the extreme example where the barrel is so much below the hands that the bat is almost vertical. In this case, all of the spin due to the misalignment of the center of the ball and the center of the bat becomes sidespin not backspin.

Typically, a batter swings the bat in such a way that the barrel is a bit below the handle when it hits the ball. Thinking it through for the ball heading for center field, the misalignment spin now causes less backspin and results in some sidespin compared to a collision with a level bat. So, for a typical ball up the middle, the barrel being below the handle does trade off backspin for sidespin.

Typically, misalignment sidespin causes a ball hit to center to move toward right field for right handed batters and left field for left handed batters. The misalignment sidespin will always cause the ball to slice if the barrel is below the hands. Center fielders know this instinctively from decades of playing the game.

To complicate things a bit more there is a second 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 base. 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 depending upon whether the ball is pulled or hit the other way.

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 the batter’s right) 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 foul line (slice toward the batter’s right) and the lateral spin will do the same thing. This explains the knowledge of corner outfielders that pulled balls are more likely to stay fair than balls hit the opposite way.

What is the point of all this? Let’s put it this way: the very high correlation between gender and pregnancy indicates that there might more than just statistics involved. The statistics of the barreled ball illustrate the same phenomena.


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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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dominik
Guest
Nice article David. I think that the 10 degree Peak is related to the “attack” angle of the bat. Now there is a lot of talk about a slight Uppercut to match the plane of the pitch (like 5-10 degrees downward or so). The average swing (of the guys who hit that hard) probably goes up about 10 degrees and if Exit and attack angle match you have got the highest energy Transfer because less energy is lost into spin. so I would not say you have to hit the ball low to hit it hard but you have to… Read more »
dominik
Guest

Of course I meant pitch PLANE not plain, sorry for the typo, I’m no native english Speaker.

BTW the average MLB Launch angle was just under 10 degrees in 2016 so that also Points to that being the average “attack angle”..

Cliff
Guest
Cliff
As a matter of curiosity, how much effect does the pitcher’s arm angle on delivery contribute to sidespin? Typically, pitchers today throw what is commonly called three-quarter-arm but some of them are closer to straight overhand while others closer to sidearm: the axis of the spin changes. Suppose you have a pitching machine that delivers a fastball at the same speed and same backspin but you can vary the “arm” angle. As the delivery angle decreases toward straight sidearm, the amount of sidespin when the ball meets the bat increases. Is there an arm angle for delivery that gives the… Read more »
channelclemente
Guest
channelclemente

First class summary and explanation. BTW, didn’t you publish those findings you acquired on ballspin, etc. at Minute Maid?

Jetsy Extrano
Guest
Jetsy Extrano

Dominik, it should be possible to create a speed/angle scatterplot for an individual hitter, like Davis — then look for the launch angle of his highest speeds, where he’s squaring the ball perfectly. If there’s enough data, that should tell you his swing plane.

(Do hitters adjust their swing plane with the approach angle of the ball? Contact-seeking hitters anyway?)

Peter Jensen
Guest
Peter Jensen
The misalignment sidespin will always cause the ball to slice if the barrel is below the hands. This statement is incorrect. If the contact point is above the centerline of the bat swing plane the ball will have a slicing spin induced movement. If the contact point is below the centerline it will hook. Think of your extreme example and what the ball would do if the ball doesn’t hit the bat squarely. In this case, the backspin on the ball is determined by the vertical distance between the height of the center of the bat and the center of… Read more »
Alan M. Nathan
Guest

For whatever it’s worth, I agree with Peter’s mainpoints. As for his last question, see Figure 4 of this: http://www.fangraphs.com/blogs/spinning-out-of-control/. The Statcast data support the idea that there is more slice on balls to opposite field than hook on pulled balls.

Regarding some of the other comments about the relationship between exit speed and launch angle and the importance of swing plane and “offset”, I suggest taking a look at my articles from a year or so ago: http://www.hardballtimes.com/optimizing-the-swing/ and http://www.hardballtimes.com/optimizing-the-swing-part-deux-paying-homage-to-teddy-ballgame/

Peter Jensen
Guest
Peter Jensen

Alan – I looked at your figure 4 again and don’t see that is evidence for any “Lateral spin” as david claims. The 10 degree offset toward left field can be explained by having more balls hit with the bat angled slightly toward left field. I asked for a citation of video showing the type of spin David is claiming because I can’t picture how the ball bat collision could produce that spin and I have never heard of other researchers claiming that it exists.

Alan M. Nathan
Guest
Alan M. Nathan
Peter: If you read the article with the Fig. 4, I talk about precisely the same thing as Dave does in his article. The primary focus in my article is the slicing of fly balls hit to CF. My Fig. 4 compares landing direction with initial direction. You really don’t need video; the data speak for themselves. Note that the data are for RHH. I also included data for LHH by changing the sign of both angles. The data clearly show that the deviation of trajectory from initial direction is larger for balls hit to RF (slices) than for those… Read more »
Peter Jensen
Guest
Peter Jensen
Alan – Please feel free to correct me if you think any of my following statements or reasoning are wrong, Almost all balls that are hit by MLB hitters are hit with the bat at a lower than horizontal angle. All hit balls that are hooked have a contact point that is lower than the bats centerline in the swing plane. Therefore all hooked balls will also have topspin. Conversely, all sliced balls will contact the bat above the centerline and therefore will have backspin. The Magnus force of backspin causes balls to rise where the Magnus force of topspin… Read more »
MGL
Guest
MGL
“I also read that very high backspin rates actually reduce distance at high velos because they increase lift but also air drag).” I thought this was the case as well. I thought that there is an optimal backspin rate depending on the launch angle, such that above that backspin rate the distance starts to decrease. In golf, too much backspin on a drive results in shorter drives although that might have to do with higher backspin being the result of an offset hit (lowering exist speed) or too high a launch angle, both of which decrease distance. Including some fixed… Read more »
Tangotiger
Guest
Tangotiger
David, terrific primer, a great reference to send people. *** Just a minor note here: “The barreled ball designation statistically treats the exit velocity and the launch angle as independent quantities” When you say “independent”, do you mean independent from each other, or independent (as a pair) to other variables? If it’s the former, note that they are dependent on each other. If you mean the latter, then I’d say that the pair of variables are agnostic to the remaining variables, not independent. It’s an intentional choice to create a metric with these two launch variables, while ignoring the others,… Read more »
Andy
Guest
Andy

David can speak for himself, but I thought he meant the former. Yes, they are dependent on each other, and that was his point of the pool ball analogy:

“So instead of being independent quantities, there is a relationship between the launch angle (the direction of the eight ball) and the exit speed.”

My understanding was that he wanted to make it very clear that one can’t treat launch angle and exit speed as independent quantities, which one might infer by the definition of barrelled balls as involving a range of each.

tangotiger
Guest
tangotiger

If it was a range of each independent, the result would be a rectangle. Which it is not.

tangotiger
Guest
tangotiger

From the glossary:

For example: A ball traveling 99 mph always earns ‘Barreled’ status when struck between 25-31 degrees. Add one more mph — to reach 100 — and the range grows another three degrees, to 24-33.

Keith York
Guest
Using a cue ball is a great analogy for explaining spin effects. I just don’t know if a great hitter has the capacity to impart English on the batted ball. Seems like it all falls on chance, early vs late timing of the swing and accuracy of the barrel whether squared up or oblique. The degree of swing arc is dependent on where the pitch is that the hitter is chasing. Barrel severely below hands for low inside, fattest for high and away. Not sure how my comment adds to the discussion. David and Allen are amazing theoretical minds and… Read more »
Keith York
Guest

Flattest, not fattest.

Alan M. Nathan
Guest
Alan M. Nathan
Peter: I do not agree that balls that hook necessarily have topspin. Most balls hit into the air, say at a launch angle greater than about 15 deg (perhaps even less), have backspin, with the attack angle falling below the centerline angle (see diagrams in my article). It would be easy to show this empirically if we had hang time data from Statcast. The direction (spray angle) of the fly ball is primarily determined by the angle of the bat in the horizontal plane, with small modifications due to the “non-squareness” if the barrel is tilted down. Similarly with the… Read more »
Andy
Guest
Andy
“If the center of the ball and the center of the bat are perfectly aligned, there will be no backspin at all. The higher the ball hits above the center of the bat, the more backspin there will be.” That appears to be correct if the bat is not rotating, but is that always the case? Suppose the batter’s hands move in such a way that the bat rotates in a clockwise (RHB) or counter-clockwise (LHB) direction around its long axis? Wouldn’t that impart backspin to the ball even if the center of the bat and center of the ball… Read more »
Andy
Guest
Andy

When I say clockwise or counter-clockwise, I mean from the perspective of the batter looking towards the end of the bat.

Alan M. Nathan
Guest
Alan M. Nathan

Quick answer: Yes. Longer answer: For any reasonable estimate of the bat rotational speed about he long axis (say about 1/4 turn in 100 ms), the effect on spin of batted ball is small. I did an estimate a few months the ago but don’t have the time right now to re-do it or find my previous result. However, I do remember the effect being essentially insignificant.

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