A couple of Game-Changing Concepts in Baseball Pitching
The physics behind the movement of a pitch has always been a subject of fascination for players, coaches, and fans alike.
With the use of new technologies and the boom in popularity of Pitching Labs we have started to understand a little bit better the physics around pitch movement but, believe it or not, we are still in diapers and there is more to go.
In recent years, the focus has been on Spin Rate and pitch Velocity as key factors in determining the pitch 2D movement. But we live in a 3D World, so: what’s happening with the information of the other dimension?
It is well known in the industry that messing the timing of hitters is part of the art of pitching and it is not only about “How” it moves, it is also about “When” it moves. So, changing speeds and late break has been and still are, a fascinating but poorly understood phenomena throughout the years.
But now, with all the technology available we have found a couple of groundbreaking concepts that haven’t been measured or discussed enough, with the potential to shake up our understanding of pitching dynamics and deception:
Movement of the pitch in the 3rd Dimension.
Flight Time and Distance.
Speed Differential.
Spin Rate Differential.
Spin Axis Angle Variation.
Spin Axis Stabilization.
Cross-sectional area of the ball.
Late Break
Some of these concepts have not been measured nor discussed yet (except by Speed Differential and Flight Time measured by Hawk-Eye System), but we will delve deep into the world of Baseball physics to explore the intricacies of the timing and movement of the pitch in 3 Dimensions.
Get ready to embark on a journey of cutting-edge science and unparalleled insights into the art and science of pitching in baseball. Let's dive in!
What 3rd Dimension and what do I mean by Movement in this Dimension?
I'm talking about Depth and how the ball behaves differently than it's supposed to in that plane of motion..
We already know that every pitch slows down during its flight, due to air resistance, creating a 9.5-10.5 MPH speed differential between the speed of the pitch right out of the hand and at the moment of it crossing the home plate. But how about when a pitch slows down at a higher or lower rate than the normal range?
Even so, why have we been taking that differential so lightly?
Let me try to explain it as simply as possible: any fastball that leaves the hand at 90 MPH arrives at the catcher's mitt at ~80 MPH due to two factors: environmental conditions (air resistance) and ball flight conditions.
So, any variation in the ball flight conditions or environment could lead to a larger or smaller speed variation during the flight which translates into a Depth position variation when compared to where the ball was supposed to be considering the same pitch average values. It is to say that if the pitch slows down at a higher rate than usual, its position would be closer to the pitcher when compared to the position of the same pitch type.
That position variation is what I call “movement” in the 3rd Dimension.
After this basic explanation, we can dig deeper into the physics details to understand how this “movement” is possible and how to calculate it.
First, let’s start talking about those two conditions that interact between each other to create more, or less, air resistance: Ball Flight Conditions and Environmental Conditions.
Ball Flight Conditions are established by velocity, Spin Rate, Spin Axis Angle and how & when the seams align while the ball is spinning during the flight. On the other side, environmental conditions are determined by air density, humidity, temperature and altitude.
We already know a lot about Environmental Conditions but we have undervalued them for years. It is true that these can’t change a lot between pitches but can be very different from one city to the other, for example: as we know, it is not the same thing to pitch in Miami or San Diego than to pitch in Colorado. A fastball may have more “Gain” (a pitch that loses less speed than average) in Colorado than in Los Angeles and a Changeup may have more “Loss” (a pitch that loses more speed than average) in San Diego than pitching in Colorado.
Finally, the “movement” on the 3rd Dimension has not been studied enough due to some indifference and lack of technology, in the past, to measure it.
The issue has been that we are talking about variations in speed and time that appear to be too small to be considered, but the truth is that a variation of 0.007 sec in the flight of a 95 MPH fastball is equivalent to 1 Ft of distance.
Let’s dig deeper into Flight time and Distance
Flight Time and Distance
In sports, time is short but distances are long.
We already know that 0.40 sec is a very small amount of time to recognize a pitch, project it, swing it and make contact.
The thing is that this sequence is not made one task at the time. It is made simultaneously. At the time the batter is trying to recognize the pitch type and its location he has done the loading movement and is already moving forward to meet with the ball.
So, everybody in baseball knows that Timing is a key element of a batter's success and messing with Batters Timing is one of the key elements of a Pitcher’s success.
To mess the Batter timing, pitchers need to change the flight time of the pitch in a couple of milliseconds. The flight time for a 95 mph fastball is 0.40 sec (avg) and a 85 mph changeup has a 0.45 sec flight time, that is to say, 0.05 seconds apart, which seems to be a negligible difference. But distance wise those two balls are around 7 feet apart.
This means that if a batter completely mistakes a changeup for a fastball and doesn’t make any adjustment on the go, he would be putting the sweet spot of the bat over home plate at the time the ball is still 6.5 feet (approx) from home plate.
0.45 seconds / 54.5 ft = 0.008 seconds per foot.
If we meet these values in the middle we have 0.0075 sec/ft.
So: 0.05 seconds divided by 0.0075 sec/ft = 6.6 ft.
It’s not a common thing to see a batter swinging a ball that is 6 ft from the home plate but this is because batters are able to do adjustments on the go, in a way that, they are able to slow down their motion or keep the bat in their power position a little longer, waiting for that pitch that fooled them. However we have seen Javi Baez swinging a pitch that is way in front of him and more recently we saw Trea Turner being fooled the same way.
In this math exercise, we have considered a Fastball and a Changeup. Pitches that have completely different speeds out of the hand, to make it easier for us to compare Flight times and in consequence to better illustrate the different positioning in the 3rd Dimension at the time the ball is over the home plate.
This is the main reason why the change up was created: to mess up the timing of the batters. They are ready to hit the ball when it hasn’t arrived yet.
Now let’s talk about pitches of the same kind and a little known secret hiding in the ball flight: Every pitch loses speed during its flight. That means that a 95 MPH fastball doesn’t arrive at the catcher’s mitt at 95 MPH.
Speed Differential
As I said, it is known that every pitch loses 9.5-10.5 MPH when comparing the Velocity at release and at the moment the ball arrives at the Catcher’s Mitt. We have called this: Speed Differential.
But why have we been taking this differential so lightly? At the beginning of this article we saw that a small variation in the flight time can become a huge difference in the position of the ball in the 3rd Dimension, let’s call it: Deepness.
The Avg Flight Time of a 4 Seam Fastball thrown at 95 MPH (with a 6ft extension) that arrives at the home plate at 85 MPH is 0.414 sec. When we compare it to another with the same Velocity at release, 95 MPH but it loses 9 MPH instead of 10, its Flight Time is 0.411 sec which represents a difference in the Deepness Position of 5 inches.
Considering that any value that modifies the projected location of the ball the batter did, would make that pitch highly deceiving, 5 inches of “movement” would be well appreciated as it could make the difference between a connection down the line or straight to the Outfielder (to mention just one example).
So, to be able to modify the flight time of the pitch we need to reduce or to create a bigger amount of Drag Force which combined with Magnus Force can also modify the path of the pitch.
Magnus Force & Spin Rate
First, let's discuss the concepts of Magnus Force & Spin Rate.
Spin rate refers to the number of revolutions per minute (RPM) of the baseball as it travels through the air. The higher the spin rate (with a perpendicular axis to the direction of the flight) the greater the Magnus force, which is the force that creates movement in the ball.
But let’s be clear, RPM’s are just a way to express the speed of the spin but, obviously, it is not the amount of rotations of the ball during the flight. It is to say that 2550 RPM equals 17 rotations of the ball. Yes, just 17.
Those 17 rotations are the ones that create the Magnus Force that moves the ball in the desired direction.
At this point I’m wondering if wouldn’t be more interesting to express the Spin Rate in RPS (Revolutions Per Second) or to create a more precise stat like “Physical Revolutions”? Referring to the amount of revolutions that actually happened.
As Magnus force is directly proportional to the Effective Spin Rate of the ball. Therefore, we can state that a higher Spin Rate will result in a greater Magnus Force and more movement on the ball. But, in order to fully understand the behavior of the ball during its flight, it is important to remember there are other factors that contribute to the Magnus Force and movement.
Considering all the other factors if we give it a try to illustrate the Magnus Force in a formula it could look something like this:
Fm = π * r3 * ρ * v2 * A * EVspin
Where:
Fm is the Magnus force
π (pi) 3.14159
ρ is the air density/resistance (Kg/m3, which could be considered a constant)
v is the velocity of the ball (MPH)
r is the radius of the baseball (cm)
A is the cross-sectional area of the ball ( cm2, size of the seam shifted wake).
EVspin is the angular velocity (RPM, Effective Spin Rate).
As we can see Magnus Force is not alone. Air density, velocity, spin axis angle and cross sectional area, which is correlated to the seam shifted wake, are contributors to the direction and amount of movement of the ball during the flight.
So, let’s see the whole picture:
If we throw a smooth sphere (without seams) into the air, Velocity (V) is the factor that creates the natural balanced resistance, created by the interaction between the flying ball and Air Density (ρ). If we add some Spin Rate, with a Spin Axis perpendicular to the Direction of the motion, it modifies the natural balanced resistance and creates Magnus Force due to the unbalanced resistance created now for the interaction of the Spin with Air Resistance.
So, by adding sense to the Spin we can control the Sense of the Magnus Force Vector. As we already know, Back Spin fights against gravity, Top Spin creates downward movement and Side Spin creates a Right or Left Magnus Force Vector Sense. Up to here we are creating movement in 2 dimensions: Up/Down or Right/Left.
We also can control the magnitude of the Magnus Force by modifying the Spin Axis Angle, which is the element that is going to determine the efficiency of the Spin over the desired direction.
Time to add the seams to the sphere. Element that creates more friction between the air and the ball. When the seams align in a way that creates a smooth area it creates the Seam Shifted Wake effect.
So, can we control the way the ball decelerates during the flight the same way we can control the way it moves side to side or up and down?
The deceleration of the ball is mainly related to the environmental factors but I have no doubt that ball flight conditions like Spin Axis Angle or Seam Shifted Wake effect, in a lower scale, can also affect the way the ball decelerates during the flight.
We can only confirm this by precisely measuring Flight Time, Speed Variation and Spin Variation down to the millisecond and millimeter.
Spin Differential
Spin Differential was a hypothesis based on physics. Air Resistance and its friction are slowing down the ball during its flight, so we could infer the same thing should be happening with the Spin Rate.
This Spin Variation hadn’t been measured until now that I have tested this theory with the most accurate and reliable system in the market: Hawk-Eye Innovations System.
Now we know there can be a Spin Rate Differential between 5 and 300 RPM from release to home plate. Being the lowest amount of Spin Differential when the Spin Axis is parallel to the direction of motion and the higher when the Spin Axis is perpendicular to the direction of motion. I’m still doing some research to identify the exact range for every pitch type and/or Spin Rate range value.
Why would this 5-300 RPM difference be important to measure? Because when it combines with Spin Axis Angle Variation value, another interesting value that hasn't been measured yet, and the alignment of the seams it can lead us to understand how to create late or early breaks.
Spin Axis Angle Variation-Stabilization
Spin Axis Angle Variation refers to any change in the orientation of the Spin Axis of a baseball during its flight from the pitcher's hand to the catcher's mitt. This concept challenges the conventional notion that the spin axis is a fixed, unchanging parameter, but we also have seen that the Observed Movement can, sometimes, be different from the Measured Spin Based Movement (Expected).
This suggests that there could be subtle variations in the Spin Axis Angle that can have a profound impact on the movement and effectiveness of a pitch.
The last touch with the tip of the finger(s) on the ball determines the orientation of the Spin Axis of a pitch and any force applied, not perpendicularly to the center of the Spin Axis at the release point could contribute to create a moving Spin Axis. Also, Air Resistance could be strong or weak enough to allow or slightly modify the orientation of this Axis.
As soon as the ball leaves the hand, Velocity, Spin and Air start its interaction to create Magnus Force. But it can take some time for the Axis to stabilize after the release or to lose stability during the flight depending on the pitch type and velocity.
The time taken to the Spin Axis to stabilize or to lose stability is a consistent contributor to early or late brake.
So finally, let’s talk about
BRAKE & EVEN MORE INTERESTING: LATE BREAK
Late Break not only depends on the Spin Rate, Spin Axis Angle and its variation or stabilization. There is another phenomenon that contributes to the movement of the pitch: The Seam Shifted Wake Effect.
Seam Shifted Wake is a curious effect in which the Seams align in a way that creates a predominantly smooth area in one of the sides of the ball. This Smooth area finds more resistance on its interaction with the air and creates Magnus Force parallel to the Spin Axis.
The strength of the Magnus Force created by the Seam Shifted Wake is directly proportional to the size of the “Smooth” Area of the Ball.
We can have an idea of the size impact of this area by measuring the Cross Sectional Area (base of the Smooth Area). A Cross Sectional Area of a ball is the two-dimensional area that is obtained when a sphere is sliced perpendicular to some specified axis at a point.
The positioning of this cut gives us the direction in which the Magnus Force will be created and its size will tell us the amount of smooth surface that will create that Magnus Force. The bigger the smooth area, the stronger the Force.
The ball during its flight experiences a natural air resistance on its frontal area which, due to the Spin Rate and Spin Axis Angle, interacts with the Air creating a Magnus Force that should always be perpendicular to the Spin Axis.
So, one way to create Late Break is by making the Spin Axis to stabilize late and the other way is by producing a second Magnus Force through the creation of the Seam Shift Wake. This effect will generate a Magnus Force parallel to the Axis, and as we saw previously, a late stabilization of the Spin Axis could lead to a late creation of the Second Magnus Force and in consequence a Late Brake.
All these findings are really interesting and exciting to me. I’m wondering how much control we are going to have to create movement in all 3 dimensions in the near future.
Hope you have enjoyed this lecture as much as I did writing it.
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