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.
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.”
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.
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.
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.