Some physics help

I’m hoping to find a math or physics genius to help with this.

I know a pitcher doesn’t release the ball at exactly 60’6” from the back of the plate. I also know that a pitch released at some velocity will not maintain that velocity until it reaches the back of the strike zone. But for our purposes, its ok to compute a velocity in ft per seconds for the 60’6”. At 80mph it would take .5114 seconds to go the 60’6”. Or 117.33 feet per second.

Again, assuming everything’s all nice in a perfect world, we know a baseball is going to drop some distance in that amount of time. What I’d like to know is, how much would it drop in 30’, 45’ and 60’? Please bear with me because there is a question coming. :wink:

Some of the assumptions you are making don’t warrant the number of significant figures you are using.

Let’s stick with your assumptions, neglect air resistance, and use the following numbers:

The pitch is released at a velocity of 80 mph and does not decelerate due to air drag…thus it travels at a constant velocity of 80 mph for 60 ft.

Let’s assume for the moment that the ball’s spin, and the angle of the spin axis with respect to the direction of flight, can be neglected (in general, like air drag, the spin properties of pitched balls are actually very important to an accurate solution of your question).

Okay, so we’re going to simplify things and say that it takes 0.5 sec for the ball to go 60 feet, and no other force is acting on the ball except the gravitational force that accelerates the ball downward, toward the earth, at a rate of 32 ft/sec*2.

The distance that the ball has dropped, at any interval between 0 sec (the pitcher’s release point) and 0.5 sec (home plate) is:

d = 1/2 at2 ; where d = distance, a = acceleration (32 ft/sec2), and t = time of flight.

So, after 0.5 sec of flight, the ball drops:

d = (1/2) x (32 ft/sec2) x (0.5 sec2) = 4 ft

At 80 mph, the ball will take 0.25 sec to go half the distance (30 ft) to home plate, so to calc the drop from gravitational force:

d = (1/2) x (32 ft/sec2) x (0.25 sec2) = 1 ft

At 45 feet of flight distance, the ball will have dropped 2.25 feet due to gravity alone.

What’s the question that’s coming next?

[quote=“laflippin”]60’ - d = (1/2) x (32 ft/sec2) x (0.5 sec2) = 4 ft

30’ - d = (1/2) x (32 ft/sec2) x (0.25 sec2) = 1 ft

At 45 feet of flight distance, the ball will have dropped 2.25 feet due to gravity alone. [/quote]

Thank you! You wouldn’t believe how many times I’ve tried to get those numbers through the years. :wink:

As for the factors that act on pitched balls, for the most part people simply ignore getting down to the minute facts like air friction or spin, and just deal with the numbers the same way the announcers at the LLWS deal with a 77MPH pitch being the equivalent of a 100MPH pitch in the ML. They use straight up numbers and don’t sweat the small stuff, even though it is important in reality. This way we can talk to each other in English rather than formulae, that many wouldn’t understand.

As for the question, you know me, I’ve always got some wild hair up there, and lookin’ for some way to either explain something or a simple way to help someone. Hold on now cause this is gonna get a bit strange. And if you see my math in error, please don’t hesitate to correct me.

Just to try to give a visual picture, imagine a generic strike zone for a HS player to be the 17” wide and 18” high, starting at 18” off the plate up to 36”. Also, you have to imaging that the strike zone is that same goofy 2 dimensional thing we all see on TV rather than a heptahedron, which is what it really is. The reason I’m trying to give the visual, is so its easy to imagine a drawing on a wall 60’ away, like we used to do when we were kids.

If it were 30’ away rather than 60, in order to keep the perspectives the same, it would only be 8.5” wide and 9” in height. But, assuming a pitch at 60’ and 80MPH had to be released at 6’ off the ground in order to hit the bottom of the strike zone, to release it at the same place and have it hit the bottom of the strike zone at 30’, the bottom of the strike zone, would have to be 4’3” off the ground.

Remember, I’m looking to make the strike zone not just look exactly the same because its half the distance, in order to use the same timing and velocities, it would need to be significantly higher as well. Or at least I’m thinking that’s true. :wink:

Now if we do the same thing at 45’, the zone would only be 12.74” wide, 13.5” high, and the bottom of the zone would have to be in a place that would account for the 2.25’ drop.

If you understand my description, am I understanding how it works correctly? Now’s your chance. Go ahead and do your worst. :wink:

It seems to me like you’re mixing apples with oranges and maybe throwing in a few bananas to slip on, too.

I mean, it is pretty clear that, all other factors being held exactly constant from pitch-to-pitch, the trajectory of a ball thrown from the pitcher’s hand to several different distances is going to place the ball at several different heights. Trajectories of objects in gravitational fields are always non-linear (curved), but they obey Newton’s laws of motion, so…yes, one could compute how the bottom (or the top) of the strike zone would need to change in order to accomodate different pitching distances when all of the other pitch conditions were held constant. Side-to-side changes in the zone are irrelevant since the force of gravity doesn’t act from the side on earth. But more to the point, what is the relevance of this entire idea? The top and bottom of the strike zone are not defined by the sides of an single-sized rectangle (or a 3D rhombus)…the vertical dimension of the zone is defined by the height of the batter’s knees and the length of his torso, as far as I understand it, so the vertical dimension of the strike zone at any pitching distance is related to the size of the batter-of-the-moment.

[quote=“laflippin”]It seems to me like you’re mixing apples with oranges and maybe throwing in a few bananas to slip on, too.

I mean, it is pretty clear that, all other factors being held exactly constant from pitch-to-pitch, the trajectory of a ball thrown from the pitcher’s hand to several different distances is going to place the ball at several different heights. Trajectories of objects in gravitational fields are always non-linear (curved), but they obey Newton’s laws of motion, so…yes, one could compute how the bottom (or the top) of the strike zone would need to change in order to accomodate different pitching distances when all of the other pitch conditions were held constant. Side-to-side changes in the zone are irrelevant since the force of gravity doesn’t act from the side on earth. [/quote]

Well, you see apples, oranges, and bananas, and I see fruit salad. :wink:

I didn’t mention side to side changes. I decreased the size of the strike zone relative to the distance.

The relevance of the idea, is that it’s a concept not everyone takes the time to conceptualize.

What’s a 3D rhombus got to do with anything? The strike zone is a heptahedron, and always has been.

And yes, the vertical zone is dependent on his knees, but the length of his torso doesn’t really have as much to do with it as his stance as he’s preparing to hit a pitched ball. But that’s really neither here nor there either.

Where do pitchers throw more pitches, in games or in practice? Do the pitches in practice get judged by whether they’re strikes or balls, or how they’re delivered? Heck, most of the time I see pitchers throwing a simulated inning or at bat, there isn’t even a batter there. More often than not, the catcher is calling balls and strikes on some generic batter in his mind. So how is it that the vertical strike zone is so important, but is so seldom worried about in actual practice?

How do you teach pitchers to throw strikes? At the HS level and below, that’s got to be the greatest problem for pitchers. Its not that they can’t throw the ball hard because that isn’t now, nor has it ever been a requirement for pitching success, and neither is the number of different pitch types a pitcher throws. But, throwing strikes is a prerequisite for even minimal success.

So how do you do that, and to what degree does it work? Do your pitchers display a higher degree of accuracy than other pitchers?

Go to http://www.infosports.com/scorekeeper/images/pitching10.pdf and take a look at page 60 and 61. Those are the numbers from our 2010 season. Then take a look here http://www.infosports.com/scorekeeper/images/cpitching.pdf at pages 95 and 96. That’s from our last 4 years. Go here http://www.infosports.com/scorekeeper/images/fpitching.pdf to see our just completed fall ball numbers.

When you look at things that way, its pretty easy to see which pitchers aren’t getting the job done as far as throwing strikes, and its pretty easy to see how our pitcher stack up against our opponents in head to head games. So how do your pitchers fare? If they generally do better than your opponents, whatever you’re doing is working, but if they don’t, perhaps you might consider changing something.:wink:

Sorry, I don’t know where the rhombus notion came from…just a brain cramp, I guess.

Interesting tangent into ideas about a practice zone vs real-life game zones; however, I’m still not sure where this discussion is going.

There is some research out of at least one academic biomechanics lab to suggest that pitchers should practice pitching at the exact distance that they must use under game conditions at their current level. That may seem like a firm grasp of the obvious, but I believe that the concept of “distance-specific accuracy training” is backed up by some quantitative numbers using real pitchers.

Given that pitchers should generally practice at their game distance, a second question I thought I understood from your discussion is: What does one use as the target in practices?

For me, that’s simple…I won’t catch my son anymore, so I stick a catcher’s mitt on a tee and put that behind home plate…he throws to that target. I don’t call balls and strikes in practice, he simply throws all of his pitches to the glove. What height? The center of the glove is about 2 feet plus maybe a couple of inches off the ground. My practice job is to feed the kid balls from the bucket and reset the target whenever he hits it.

Here is some really shocking trigonometry that no pitcher should ever consciously think about: The approximate height of a strike zone (let’s say 2 1/2 feet from top to bottom, just for discussion) and the distance that a pitch must travel from release to HP (let’s say 55 feet, for discussion) defines a triangle whose angle arising from the pitcher’s hand is just 2.6 degrees. So, for two otherwise identical pitches, the difference between the original trajectories of the ball at release point, in order to hit the top or the bottom of the strike zone, 55 feet away, is just 2.6 degrees.

Since the radius of the ball is about 1.5", a 2.6 degree difference in orientation at the surface of the ball means that the two different trajectories (to hit the top versus the bottom of the 2 1/2 high zone that is 55 feet away) only differ by about 1/16 of an inch at the pitcher’s release point.

This type of control, during the stress of a typical pitch delivery, is way beyond brain surgery…there is just no obvious way that an athlete could exert that type of control consciously. It pretty much has to be something that becomes unconsciously ingrained with repeated practice, practice, practice.

And, the conclusion of this leads nicely to the well-known advice to pitchers from catchers: “Don’t try to think out there, Meat, it only hurts the team”.

No biggee! Heck, when I found out what it was really called a few years back, I felt as though I had cracked some secret code! :wink: As an aside, how many people do you think really understand that the S-zone isn’t a rectangle such as they see on ESPN during a game?

Thinking is always good because it generally leads to thinking about things other than the original thought. Wouldn’t it be funny if someone tried it in some form and it actually helped?

I’d like to see it because I’d like to see how they made that determination.

Assuming your understanding about game distances is valid, you’re on at least the correct general track about targets. One things for sure, its rare that there’s an umpire in the bullpen. :wink:

Why did you quit catching him? But I do like the mitt on a stick. Do you keep track of his accuracy with his different pitches and the windup and stretch? I like that idea much more than the net with the batter and strike zone painted on it. Its much more precise.

[quote]Here is some really shocking trigonometry that no pitcher should ever consciously think about: The approximate height of a strike zone (let’s say 2 1/2 feet from top to bottom, just for discussion) and the distance that a pitch must travel from release to HP (let’s say 55 feet, for discussion) defines a triangle whose angle arising from the pitcher’s hand is just 2.6 degrees. So, for two otherwise identical pitches, the difference between the original trajectories of the ball at release point, in order to hit the top or the bottom of the strike zone, 55 feet away, is just 2.6 degrees.

Since the radius of the ball is about 1.5", a 2.6 degree difference in orientation at the surface of the ball means that the two different trajectories (to hit the top versus the bottom of the 2 1/2 high zone that is 55 feet away) only differ by about 1/16 of an inch at the pitcher’s release point.

This type of control, during the stress of a typical pitch delivery, is way beyond brain surgery…there is just no obvious way that an athlete could exert that type of control consciously. It pretty much has to be something that becomes unconsciously ingrained with repeated practice, practice, practice.

And, the conclusion of this leads nicely to the well-known advice to pitchers from catchers: “Don’t try to think out there, Meat, it only hurts the team”.[/quote]

Actually, that’s exactly the basis of my lifelong argument that pitchers aren’t and can’t be nearly as accurate as people make them out to be. Too many very minor things can have a massive effect on the outcome of a pitch. Its also why I get so snarky about mounds and how they’re set up and cared for. Way too many people blow off any discussion of such minutia because they feel its no big deal for a P to just make some kind of magic adjustment and take care of it.

Here is the reference:

Res Q Exerc Sport. 2009 Sep;80(3):469-79.

Challenges to cognitive bases for an especial motor skill at the regulation baseball pitching distance.

Simons JP, Wilson JM, Wilson GJ, Theall S.

Department of Kinesiology and Physical Education, California State University-East Bay, Hayward, CA 94542, USA. jeff.simons@csueastbay.edu

We tested expert baseball pitchers for evidence of especial skills at the regulation pitching distance. Seven college pitchers threw indoors to a target placed at 60.5 feet (18.44 m) and four closer and four further distances away. Accuracy at the regulation distance was significantly better than predicted by regression on the nonregulation distances (p < .02), indicating an especial skill effect emerged despite the absence of normal contextual cues. Self-efficacy data failed to support confidence as a mediating factor in especial skill effect. We concluded that cognitive theories fail to fully account for the patterns of observed data, and therefore theoretical explanations of the especial skills must address noncognitive aspects of motor learning and control.

PMID: 19791633

Somewhere or other I think I have the full article in .pdf form, but couldn’t lay my hands on it. In any case, I can’t send .pdf’s via post or PM so…if you are really burning to read the complete article, PM me your regular e-mail address and I’ll see if I can find it.

post script: I found the .pdf file of the full article referred to above…

…it’s pretty interesting support for distance-specific training of pitchers.

The article also references some other research work that was done with skilled basketball players on an unmarked gym floor. That study found that an “especial” skill also emerged for shooting free-throws from the set position at exactly the regulation free-throw distance–which is something that players practice all the time. However, jumpshots made from the free-throw distance didn’t correlate to an “especial” skill. Jumpshots are practiced from many different distances so…no especial distance-skill relationship emerged for that.

The baseball pitcher study was in agreement with the earlier basketball free-throw study: In order for an “especial skill” to emerge you need to spend lots and lots and lots of time practicing your specific target-based skill at the exact distance that is correct for whatever target you are interested in…

Again, folks who want to read the full text article can send me their e-mail address by PM.

From just the little you quoted, I’m making a couple of guesses.

1st of all, describing college pitchers as “expert” is at best a reach, but even so as soon as they started bouncing the distances around, they inadvertently caused “issues”, at least for me. I’ll wait until I see the entire article to comment further on that.

What they demonstrated is something I used to do with my son all the time, and a few other kids on occasion. I’d allow him to get positioned, then blindfold him and have him pitch. It didn’t take very long for him to be able to get the ball near or in the strike zone. It worked or didn’t work with other kids pretty much along the lines of how well they could throw the ball where they wanted.

I always just assumed it was because pitchers who worked hard on execution and timing and throwing within themselves rather than worrying about velocity and throwing at 100%, would logically just be able to perform a repetitive movement over and over again with some degree of ease.

I’ll be really interested to find out if when they moved the distances, they allowed for the difference in gravity’s effect, or whether they either had a catcher and used his mitt as the target, or did what you did and pt a target on something stationary. Whether or not people realize it, their brain makes adjustments based on computations they’re used to. Until the brain gets fully used to the new distance, I can’t see any way it could produce the desired accuracy.

I’m really looking forward to reading the study. 99% is gonna shoot right over my head, but I’m guessing I’ll be able to understand their methodology.

“1st of all, describing college pitchers as “expert” is at best a reach,”

-----------They are talking about a group of athletes who, by the time they are pitching in college, have all performed the same skill from the same distance for thousands of hours. That qualifies as “expert” relative to untrained or marginally trained pitchers.

“What they demonstrated is something I used to do with my son all the time”

-----------Not really. They are talking about the specificity effect of thousands of hours of practice of pitching at one specific distance.

"Whether or not people realize it, their brain makes adjustments based on computations they’re used to. Until the brain gets fully used to the new distance, I can’t see any way it could produce the desired accuracy. "

-----------Fully agree with that, and believe that it is the major theme of the article…i.e., thousands of hours of pitching at 60’6" can make you especially skilled at 60’6", but your skill may not translate to longer or even to shorter throws.

At further issue here, is the balance between time spent in practice doing long-toss, presumably for strengthening purposes, versus time spent practicing pitching at exactly the regulation distance, and from a mound vs flat ground…because the sloped mound is certainly an important part of the skill-specificity question for pitchers, one would think.

Categorizing 7 pitchers from what appears to be the same college team are certainly “expert” in comparison to some group of pitchers. But, I have yet to see any team, even the best ML team, with 7 of its pitchers being “top tier” in relation to all other pitchers at their level. I suppose its really only a matter of semantics though, and if they’d have simply said college pitchers and left off the descriptive “expert”, I wouldn’t have minded nearly so much. But when they slap the tag “expert” onto the control group, I believe it gives a false sense of what is being witnessed.

And so am I. The only difference is in how it was expressed. They did it one way, I another, but they both showed the effect of training.

Which was basically the premise of my original question. I believe how the measurements take place make all the difference in the world. Pitching isn’t really a test of accuracy in the same sense that shooing a bow and arrow is. While the true “target” a pitcher has is the strike zone, he’s using the catcher and the plate as a means of sighting in where he wants the ball to go. That’s why I maintain that if a pitcher were blindfolded so he didn’t know where the measurement of accuracy would take place and he just used his ingrained memories, the measurement could be at 30’ 45’, 60’, or even 65’ and be predicted.

Now there’s something I’m totally behind you on for a couple reasons. The 1st is that there is no relation between pitcher success and arm strength that I know of. By that I mean, there are pitchers who throw 97MPH who are devastating, and the there are pitchers who throw 97 who the batters can’t wait to dig in for. But that’s another argument.

How about if I just say that IMHO a pitcher would be better off if he’d spend an additional hour a week pitching from a mound than throwing long toss. :wink:

A 10 minute rest interval after 54 throws? WOWSERS! I’m gonna make sure I pose the question to the folks over at ASMI as to what they think of that as a scientific method for measuring pitching accuracy. Their answer could be revealing if viewed from the perspective of fatigue.

Probably the greatest “concern” I have about it, is from everything I “understand”, throwing that many pitches in such a short period of time should have had some bearing on the final result. How much, I don’t know. But, if it doesn’t, there’s a whole lot of people out there in baseball land who are dreadfully in error about how they judge fatigue in pitchers.

All in all, I found the paper very interesting, at least the parts of it I was able to understand. :wink:

Thanx for the article LA!

"I have yet to see any team, even the best ML team, with 7 of its pitchers being “top tier” in relation to all other pitchers at their level. I suppose its really only a matter of semantics though, and if they’d have simply said college pitchers and left off the descriptive “expert”, I wouldn’t have minded nearly so much. But when they slap the tag “expert” onto the control group, I believe it gives a false sense of what is being witnessed. "

----------With due respect, I think it is off the point to get stuck on the issue that there undoubtedly are other pitchers who are “more expert” than the group they chose.

The authors gave their definition of “expert” within the context of their research and they showed that the 7 people they defined as “experts” all showed evidence of distance-specific “especial skill” for pitching to a defined strike zone.

Actually, these experienced pitchers are not a control group…a proper control group would have been age/size matched individuals with no pitching experience. One would expect to see from such a control group that there is no emergent “especial skill” at any distance.

I can think of several interesting extensions of this study, and wrote to one of the authors about it when the article first appeared in 2009…it would be really important to know whether the “especial skill” of experienced pitchers at 60’6’’ tends to vanish when this identical set of experiments is conducted without a mound. My gut feeling is that it would…after all, “expert” pitchers do not spend countless hours throwing from exactly 60’6" on flat-ground. This “especial skill” relationship is probably also associated specifically with the use of a 10" mound.

Another interesting extension that just came to mind from your concern about the level of expertise represented in the Simons paper: It would be conceptually easy to perform this exact experiment with pitchers who are stratified by their level of “expertise”… HS, college, MILB, MLB for example. One might reasonably expect to see stronger and stronger correlations to the distance-specific “especial skill” at 60’6" (from a mound!) as the experience level goes up. Unfortunately, in reality it might be very, very difficult to round up these disparate groups to conduct the study…especially at the elite end of the spectrum.

No offense taken. All I was doing was point out that those folks very likely didn’t have much of an idea about the relative skills of pitchers, and that quite possibly could have a huge effect on the outcome of the study. For my money, I’d rather they had picked pitchers who were as close to “average” as possible, or as widely varied as possible.

Yes they did, but only as they defined it, which is ok as far as it went.

I agree, which is why I had problems with it right out of the box. But, its still a valid study that gives lots of room for thought.

Did he respond? If so, what did he say?

You’re correct. But then again, “expert” pitcher don’t practice their pitching skills from flat ground very often at any distance, so it makes logical sense to me that they’d do poorly from flat ground.

I wonder if the 10” mound is really that much of a factor. My GUESS is, college mounds tend to be much more likely to be set to the proper height and slope than HS mounds.

You really would have a difficult time proving much of anything with HS pitchers. As I said, the simple fact that very few of them actually pitch on an exact 10”, 1” per foot slope. That brings something else to mind. I hadn’t thought about it before, but by using an artificial mound, something got introduced into the experiment that I doubt anyone took into account.

As REAL a mound is used, it degrades to a certain extent. Depending on the composition, it might stay reasonably intact for a full game, but its extremely unlikely, and it I haven’t seen anyone go out and reset the slope in the middle of a game since I did it regularly about 5 years ago. With a portable mound, two things happen. #1 its unlikely the pitchers will throw in spikes, and #2, the slope and condition of the mound will be almost exactly the same on the last pitch as the 1st.

I’ve lost the data after many years, but I distinctly remember my boy’s travel team pitcher’s did noticeably better as far as strike percentage and 1st pitch strikes when they had to use a portable mound. Jeez, I hadn’t thought about that in at least 9 or 10 years.

Bottom line on that study is, there are a lot of obvious follow-on studies that should have taken place. Do you know of any others?