tl;dr Series: Spin Doctors
by elcroata on Aug 2, 2010 5:48 AM PDT
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Despite your self-deprecating comments about the graphics
this is a very good explanation, and the graphics are very, very helpful.
One thing I’ve always wondered (and now I know that it has to do with the Magnus force): unless there’s a sudden gust of wind, the drag on the ball is going to be constant from the time it leaves the pitcher’s hand to the time it arrives. Technically, I suppose, that isn’t true: drag relates to the square of the velocity of the ball, so if the ball leaves the pitcher’s hand at 100 mph, falling to 88 when it crosses the plate, the drag itself will be decreasing as the ball moves towards the plate. That is, 55 feet from the plate, drag is based on a velocity of 100 mph; 30 feet from the plate, drag is based on a velocity of 94 mph or something, etc. But as you said, the speeds at which pitches are thrown are “scientifically similar,” so close enough.
But the Magnus force is based on how quickly the ball spins, and what I don’t know is to what extent that rate of RPM changes between the pitcher’s hand and the plate. When I throw a ball straight up in the air, it slows down, eventually stops, and falls back down to me where I catch it as a pop up. In that instance, there’s actually a moment where the velocity of the ball is zero. But the ball never stops spinning. So the spin and the horizontal/vertical velocities can change independent of one another.
And it seems to me that that could be one explanation for how a breaking ball really does break in the air. A fixed RPM at 100 mph won’t move the ball as much as the same RPM at 88 mph, will it? Gravity is constant, but Magnus could change at one rate while drag changes at another, and thus there’s a different combination of forces affecting the ball’s flight when the ball gets to the plate.
"And Julio Franco is batting right-handed!" -- Wayne Hagin, A's radio play-by-play, mid-80s
That's correct
The spin factor (S) is the ratio between the rotational speed and translational speed, or the spin and the speed. The same amount of spin will have more effect on an object with lower velocity; conversely more spin on a same velocity will have the similar effect.
And as for the graphics – thanks for the flowers, as the Germans would say :)
"Be more concerned with your character than your reputation, because your character is what you really are, while your reputation is merely what others think you are."
– John Wooden
One more factor is angle of the pitch
That is, gravity is pulling the ball down — if the ball is thrown exactly parallel to the ground, that effect will be at 90 degrees to the ball’s trajectory. But no pitcher does this. Some pitchers are really tall and throw the ball from very high; some are short and throw the ball at a flatter trajectory; a very few, like Ziggy, actually throw the ball with an upwards trajectory (at least, I think it’s upwards — if he throws a pitch that ends up at a batter’s shoulders, the ball arrives at the plate farther off the ground than it was when he threw it).
Every one of those angles changes the actual effect of gravity on the ball’s flight. Obviously, if you could throw a ball from directly above the plate, gravity really would make the ball accelerate as it approached the hitter! But a very tall pitcher, like Chris Young, could as least conceivably throw a ball from well over 7 feet off the ground that crosses the plate 1 foot off the ground — that’s a ratio of 1 foot of drop for every 8-9 feet or so of horizontal distance (since his stride brings him closer to the plate than 60 feet). That angle won’t affect drag or the Magnus force, but gravity would be working with Young’s fastball, not against it, at least more so than it would with Braden’s fastball, let’s say, which is thrown maybe 5 feet off the ground. So that might well mess with the batter’s learned expectation of how the ball should decelerate on the way to the plate. And as we know, 1/16 of an inch on the bat (or less!) can be the difference between a HR and a fly ball.
"And Julio Franco is batting right-handed!" -- Wayne Hagin, A's radio play-by-play, mid-80s
I assume you are talking about fastball,
when you say that the balls are always thrown on a down plane . Most curveballs are actually thrown on an angle slightly above the one parallel to the ground – otherwise they would never reach the plate.
And as for gravitational effects on velocity – there are none. Well, at least not on the horizontal component of it, which is what determines how fast the ball will reach the plate. The vertical component of the velocity (the only one that gravitation effects by the nature of it being parallel with the imaginary plane in front of the home plate), will not change when the ball reaches the plate – it will change the where and in case you are mentioning (steeper angle from a taller pitcher) it will change the amount of torque the ball has, making such a fastball a “heavy” one.
"Be more concerned with your character than your reputation, because your character is what you really are, while your reputation is merely what others think you are."
– John Wooden
Okay, that makes sense
Still, gravity would change the amount of time it takes for a horizontally-thrown ball to reach the batter by lengthening its route to the plate, wouldn’t it? Which might seem like a “slower pitch” to the hitter. Whereas it wouldn’t to that to a ball thrown (or dropped) from straight above.
"And Julio Franco is batting right-handed!" -- Wayne Hagin, A's radio play-by-play, mid-80s
It wouldn't affect the time
The overall route would be longer, but the overall speed would be higher, too, due to the gravitational addition.
The significant component (in this case the one perpendicular to the plane in front of the home plate) of the route and the significant speed would remain unaffected.
Imagine standing on a third deck, right above the plate and watching a pitch. You can’t tell if the gravitation is strong or weak, you can’t even tell if there is one. You can only recognize the horizontal component of the movement. You can’t tell if the pitch is thrown on a plane somewhat more slowly or with an angle somewhat faster, as long as the horizontal speed is the same.
Perhaps a quick graph will make clearer what I am trying to say:
Speed changes, distance changes, time remains the same, speed over ground remains the same.
"Be more concerned with your character than your reputation, because your character is what you really are, while your reputation is merely what others think you are."
– John Wooden
Interesting
So speed increases in a way that’s related to the Pythagorean theorem, right? That is, if we call the horizontal black line A, the vertical black line B, and the red line C, then A^2 + B^2 = C^2. So if the ball travels line A in the same time as line C, then the velocity has to increase (due to gravity) in a degree exactly proportional to the ratios in that formula, right?
I took physics for non-science majors in college, but that was over 20 years ago, and off the top of my head I can’t remember the formula for acceleration due to gravity.
"And Julio Franco is batting right-handed!" -- Wayne Hagin, A's radio play-by-play, mid-80s
It does in this case
Because the two components (gravity and initial velocity) are at the right angle to each other. This is more of vector addition, which is a very simple thing – you just draw the two forces in the direction they act, and then move the starting point of one to the ending point of the other one, without changing its angle (like the penultimate graphic in the article). The resulting combination (addition) is the vector that goes from the beginning of the vector you didn’t move to the end of the one you did.
I suck at explaining when I’m hungry, and I haven’t eaten in 6 hours, sorry.
The gravitational acceleration is 9.81 m/s2, meaning that the vertical speed (towards the ground) will increase 9.81 m/s for every second of the free fall.
"Be more concerned with your character than your reputation, because your character is what you really are, while your reputation is merely what others think you are."
– John Wooden
Actually, early in the season
a lot Wuertz’ sliders never reached the plate.
I like Cindi. A. She never pretends to know more than she does. B. She has unbridled enthusiasm for her "Hotties," and isn't afraid to show it. -IM4Oakgal
drag forces
will also slow down the spin of a ball. In fact, in the approximation that a drag force is just proportional to velocity, the linear velocity and angular velocity of the ball should decay away at the same rate.
To throw some math out there, either velocity would obey the following differential equation (pardon the LaTeX):
\dot{v} = -b * v
with the solution:
v(t) = v_0 * exp(-b * t)
So after a time \tau, both the linear and angular velocity would have decayed away by a factor exp(-b * \tau).
but, despite all the equations,
I’m really not sure that the original hypothesis (that both drag forces for linear and angular motion are proportional to the respective velocities) is true. I could imagine some turbulence effects that allow the ball to retain its spin even as linear velocity slows down.
Would the irregular surface of a baseball signifantly affect the way that angular velocity decays?
"And Julio Franco is batting right-handed!" -- Wayne Hagin, A's radio play-by-play, mid-80s
Wait, I see that you anticipated my question and answered it below! Thanks!
"And Julio Franco is batting right-handed!" -- Wayne Hagin, A's radio play-by-play, mid-80s
Thank you again, elcroata,
for your enlightening and fascinating contributions.
"Not in your wildest alcoholic nightmare would you ever imagine such events unfolding!" Bill King
Two quick ones
Before I head home and hit the traffic jam:
1) Rising fastballs
As Dan always points out and as I mentioned in this article, when we say “rising fastball”, we actually mean “less-so falling baseball”. However, a baseball that rises on the merit of the spin alone is physically possible – it would probably take a labor of love between Joel Zumaya and Randy Johnson, baby-fed HGH from day one to throw it, though.
If a fastball with about 110 mph would be thrown on a horizontal plane and had more-less double the spin a normal one has it would truly rise.
2) The same effect applies to the batted ball, as well.
Hitting the ball with the back spin will make it travel further than the one without one or the one with the top spin. There are always debates in the scientific community, whether the batted ball will travel further if hit on a fastball or on a curveball. If, hit on a fastball it will have a higher initial velocity, if hit on a curveball it will have more back spin (top spin of a curveball translates to back spin of a batted ball). The last I heard is that the curve ball is actually a better pitch for longest possible distance.
"Be more concerned with your character than your reputation, because your character is what you really are, while your reputation is merely what others think you are."
– John Wooden
I'm a little unclear on what's wrong with calling it a "rising fastball"
instead of a “less falling” one? I mean technically, a fastball isn’t going 90MPH; it’s going closer to 30 kilometers/second along with the rest of the earth.
I like Cindi. A. She never pretends to know more than she does. B. She has unbridled enthusiasm for her "Hotties," and isn't afraid to show it. -IM4Oakgal
Your "technically" is misleading semantics here
As the “technical” velocity of the baseball changes with your frame of reference. If you’re the laces on the baseball, you “technically” only have angular velocity… And I think the most commonly agreed upon frame of reference for a baseball blog would be that of the pitcher/observer – which means 90MPH and less rising fastballs.
Maybe I'm having a different conversation based on misunderstanding.
What I’m talking about has nothing to do with velocity. As a ball approaches the plate does it, on a vertical plane, have upward movement, “less downward movement than it had a few feet before,” no movement, or downward movement?
I guess if it’s the second one, you technically shouldn’t call it “upward movement” any more than you should call a slightly less steep hill a flat surface. Though if it walks like a duck, acts like a duck, and appears to be a duck, then I’ve probably eaten it in a Chinese restaurant.
I like Cindi. A. She never pretends to know more than she does. B. She has unbridled enthusiasm for her "Hotties," and isn't afraid to show it. -IM4Oakgal
It has less downward movement
than the ball would have if it had no spin. Not necessarily less downward movement than it had a few feet before.
"Be more concerned with your character than your reputation, because your character is what you really are, while your reputation is merely what others think you are."
– John Wooden
So then my question is --
independent of spin/no spin, as the ball travels does it only ever move laterally or downward, or can it, at some moment, be higher (vertically) than it was at some moment before?
I like Cindi. A. She never pretends to know more than she does. B. She has unbridled enthusiasm for her "Hotties," and isn't afraid to show it. -IM4Oakgal
No, it can not
Unless it was thrown upwards (first few milliseconds of a curveball) or, as I posted somewhere else in this thread, thrown at 110mph with around 4k rpm spin.
"Be more concerned with your character than your reputation, because your character is what you really are, while your reputation is merely what others think you are."
– John Wooden
OK, that's my understanding too
My question, then, is, what is it that makes it appear to rise such that a hitter is likely to swing under it?
I like Cindi. A. She never pretends to know more than she does. B. She has unbridled enthusiasm for her "Hotties," and isn't afraid to show it. -IM4Oakgal
It is the _relative_ rise
Basically for our eyes it is irrelevant whether the ball really rises or just sinks less. And the ball with a lot of backspin will sink less than expected, thus appearing to us as rising.
This is an interesting graph (not mine) showing the difference between the trajectory of the ball with spin and without.
We are expecting the ball closer to the black line, whereas it will come more along the red trajectory. We normally start our swing about the half way in, and if you see the 30ft mark, the two are very similar at that point.
"Be more concerned with your character than your reputation, because your character is what you really are, while your reputation is merely what others think you are."
– John Wooden
That's awesome, thanks
Wouldn’t it be prudent for big league hitters to expect the red line when facing a Breslow?
“Bres…low…You don’t have to put on a red line. Bres….low!”
I like Cindi. A. She never pretends to know more than she does. B. She has unbridled enthusiasm for her "Hotties," and isn't afraid to show it. -IM4Oakgal
Sure, but some of his pitches do that and others don't.
Also, if they’re not familiar with him they might not have been coached about what to expect from his pitches.
There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy.
To backup what you're saying and put another way
The Rising Fastball — For years batters swore that some pitchers could throw a rising fastball that would “jump” a half foot as it crossed the plate, making it hop over the bat. But this isn’t possible, Bahill says. Even the greatest pitchers can’t violate the laws of physics. Once a ball is thrown, it follows a smooth trajectory. Physics simply doesn’t allow abrupt jumps in that trajectory.
So what’s happening? “The batter is using the wrong mental model,” Bahill says.
Batters divide a pitch into thirds. The first third is sensory gathering, the second is computing, and the third is swinging. So a pitcher throws several 90-mph fastballs and the batter develops a mental model and reaction to this speed, Bahill says.
Then the pitcher slips in a 95-mph fastball. During the sensory gathering segment of the pitch, the batter doesn’t see anything different. He calculates where the 90-mph fastball would go and swings at that spot. But the 95-mph fastball has a flatter trajectory. It doesn’t drop quite as much from the pitcher to plate because it’s going faster.
“When the batter starts to swing, he takes his eye off the ball to look at the predicted bat-ball collision point,” Bahill says. “When the ball comes back into his view, it is higher than his mental model predicted and he sees it ‘jump’ higher than where he calculated that it would be.”
by LowcountryJoe on Aug 3, 2010 5:15 AM PDT up reply actions
If you were standing on a huge treadmill
and decided to walk against the direction of the treadmill belt, wouldn’t you call that walking forward? It doesn’t matter if you’re walking forward very slowly or walking forward fast enough to compensate for the treadmill. You’re still walking in the forward direction.
I just got my pant leg stuck
Could you PLEASE help?
I like Cindi. A. She never pretends to know more than she does. B. She has unbridled enthusiasm for her "Hotties," and isn't afraid to show it. -IM4Oakgal
That kid is back on the escalator again!
Take your silver mod tubescreamer, your dr. z, your nocaster, put them in a pile and burn them. if god gave you a thousand years, you still couldn't touch this. you can't f***ing keep time to this.
Anyone here ever play Trac Ball?
It’s a kids’ toy that looks like a cross between a jai alai xistera and a handle-less lacrosse stick. You use it to throw a ball made of plastic (like a big wiffleball, except without any holes), or a solid ball made of hard styrofoam.
The Trac Ball basket gives you the ability to put huge amounts of spin on the ball, and you can use it throw curveballs, screwballs, and genuine rising fastballs. And the ball really does “break” towards the end of its flight if you throw it with enough spin.
So it is definitely physically possible to launch a genuine breaking pitch (i.e., a pitch that changes course during its flight) or a genuine rising fastball. The problem, as you say elcroata, is the extent to which a human propelling a baseball from his or her hand is able to do this.
"And Julio Franco is batting right-handed!" -- Wayne Hagin, A's radio play-by-play, mid-80s
perhaps the sweetest beach game of all time
you can get that thing to rise of inches off the ground to head high
by NRC on Aug 2, 2010 2:21 PM PDT up reply actions
Thanks elcroata..
great post!! It is commentators like you who make AN one of a kind on the internet.
Most of these graphics look like my brain trying to comprehend math
But I recommending it because it looks really cool!
AN: We is all growed up now.
And one more clarification
When I say that spin can make a ball faster, probably a better expression would be “less slow”. A pitched baseball will not accelerate due to the spin, much like with “rise”, it will only decelerate less.
Like Breslow himself said:
…and I don’t know exactly how to quantify that but maybe its pitches that keep their velocity…
I don’t know if Breslow puts more spin on the ball then other pitchers, I am just saying that it is physically feasible that some pitchers have fastballs that keep their velocity more than the others. Normally, I would guess that guys like Pedro Martinez would be able to put great spin on the ball, what with their long fingers, allowing for more angular velocity when snapping the ball.
"Be more concerned with your character than your reputation, because your character is what you really are, while your reputation is merely what others think you are."
– John Wooden
I think spin can help the ball preserve its velocity
The laces on the ball must create a lot of turbulence, and turbulent air creates less drag than a laminar flow. One of the classic examples of this is golf balls, where the dimples create turbulence that allows the ball to fly farther (because the drag is reduced). Supposedly people used to use smooth balls for golf, but then someone realized that old, beat-up balls would actually travel further than brand new ones.
I posted the OP to my Facebook
Then, a former co-worker posted an article to me that referenced one of his professors. Here’s a book his professor co-wrote:
Oooooh. A z-component to the Magnus force didn't even cross my mind.
Great stuff, elcroata.
The best thing about PitchFX (okay, one of them), is that we can check and confirm all of this. PitchFX tracks starting speed, ending speed, and spin. So I can just throw, for example, Henry Rodriguez’s last three appearances into a scatter chart and look for correlation (click for a bigger version):
Slight correlation in favor of spin rate leading towards less speed lost.
How does PItchFX measure spin?
"And Julio Franco is batting right-handed!" -- Wayne Hagin, A's radio play-by-play, mid-80s
Same way it measures speed and break:
High-speed cameras. I assume it watches the laces and extrapolates.
We desperately need Pitch FX for politicians.
I like Cindi. A. She never pretends to know more than she does. B. She has unbridled enthusiasm for her "Hotties," and isn't afraid to show it. -IM4Oakgal
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