Geometry of Pitching

jtur88 · May 27th, 2007, 07:51 PM

All pitchers (as far as I know) pitch to all batter from the same point on the rubber. But the rubber is 18 inches wide, so there is leeway there, that they can use to their advantate. Let's say Bonds is up, batting Left. If the pitcher moves to his left, and pitches with his foot just touching the left edge of the rubber, he will cut down the angle between the pitch trajectdory and the foul line by, say, 9 inches. If the foul pole is 300 feet, and the pitching distance 60 feet, the pitcher would in effect be moving the foul pole 45 inches in toward center field. This means every ball Bonds hits that goes into the stands less than 45 inches inside the foul pole, would be converted to a foul ball, just by the pitcher moving his foot to the edge of the rubber. The question now become this---how many MLB home runs pass the foul pole less than 45 inches fair? It would work for doubles, too --- how many doubles fall fair by less than about 30 inches, or grouinders that go over the bag? A pitcher that moved back and forth, placing his foot on the edge of the rubber according to the pull hitters advantage, could narros the width of the outfield by a total of 90 inches, almost eight feet, which is surelay not insignificant. To magnify the effect, for illustration, if the pitcher could pitch from 60-feet down the first base line, pure pull hitters would not get ANY hits.

nanwynnfan · May 28th, 2007, 08:54 AM

Doing a little plain geometry, here, if I remember those lessons at all:

1. since the rubber is on a diagonal, the moving of the pitcher's focal point to the left and right of center of the rubber extends a leg of a triangle up the corresponding base line [1B, 3B] by 4.5," reduced by the diagonal bias, divided by 60'6" or 1.625%. [generous]

2. The problem, as presented, assumes the pitch trajectory will be a straight line to a corresponding part of the strike zone, in which case it might well be crushed. However, any movement of the pitched ball on its way to the plate would be a departure from the model presented.

3.The problem assumes no defensive reaction by the batter to "hit the ball where it's pitched." Nonetheless, the pure geometry, given all theassumptions, would be a matter of very few inches.

Prime real-life example: Ewell Blackwell, whose sidearm whiplash from the extreme right of the rubber was daunting to right-handed hitters, was more a matter of psychology of perception than the actual physics of his motion.

***The 9" slant, left or right of center of the rubber, because of the diagonal bias, does not extend a straight line drawn to the baseline by the full 9" further diluting overall impact of extended trajectories. Extreme examples that extend the point of delivery far from actual rubber proportions is moot. In actual play, no such advantage is had by the pitcher.

Apology for early calculation errors, where 9" segments were halved..

jtur88 · May 28th, 2007, 12:30 PM

I dont understand your geometry, or what you mean by 'focal point', and I don't think you grasped my point. The length of the leg of a triangle is not material. What is relevant is the angle between the pitcher and the foul line. Throwing from the center of the rubber, that angle is 45-degrees. The closer the pitcher stands to the foul line, the more acute the angle becomes, and hence the pull hitter needs to keep the ball in a more constricted fair territory. If the pitcher moved the full extent allowable, that angle would narrow by 9 inches in an arc 60 feet from the plate, 13.5 inches 90-feet out (first base), and 45 inches at a 300-foot foul pole.

This presumes that a LH batter hits the ball to the right of the pitch trajectory (which as I understand, is the definition of a pull hitter). Do you mean to say that if the pitcher was standing on the first-base line, Thome and Bonds would hit every ball to the left of the pitcher?

BTW, I just noticed that Johann Santana pitches with his left toe barely touching the edge of the rubber---but from the same angle for both RH and LH hitters---thus cutting down on the fair territory to RH batters, but yielding the extra 45 inches to lefties.

nanwynnfan · May 29th, 2007, 12:29 PM

"If the pitcher moved the full extent allowable, that angle would narrow by 9 inches in an arc 60 feet from the plate, 13.5 inches 90-feet out (first base), and 45 inches at a 300-foot foul pole."

Putting the geometry solely on your own terms:

1. extending the pitches' alleged angle edge to allow for edge of rubber stance and sidearm delivery, we can extend the effective lateral "rubber width" to something a bit over 4' [after which point an exaggerated sidearmer would probably fall down;

2. the tendenccy for an opposite-handed pitcher is to throw from away to in, thus straight-lining into the hitters' wheelhouse;

3. vice versa, same handed, the crossfire, while intimidating NOW has option [as does the above] ride in on the hitter, curve or slide away ... one is the jammer or the wheelhouse; the curve is away ... so,

my point is that the angle advantage is not a big as it looks, and the motion on the pitched ball is much more important in determining batted ball field distribution than the pitching angle [much diluted over the 60'6" span].

jtur88 · May 30th, 2007, 04:03 PM

I understand, but Im talking about a pitcher using his optimum motion that he would normally use against any given batter, he can push the batter's pull toward the foul line.

I wonder---if the rules allowed the pitcher to pitch from any point on a 60-foot arc measured from the plate, foul line to foul line, I wonder how a pitcher would oiptimize his position. Obviously, pitching to every batter, RH or LH, from exactly the same spot would seem like a strategy that could be improved upon. My questins relates not to such a long arc, but the 18-inch leeway that is allowed---which, surprisingly, no pitcher tries to gain the advantage of. As I said before, I would gain considerable advantage by pitching to Barry Bonds from right on the first-base foul line, and force him to hit the ball to the left field side of the pitch trajectory. The rules do not give us that foul-line to foul-line leeway, but they do give 18 inches of it.

nanwynnfan · May 30th, 2007, 10:04 PM

"As I said before, I would gain considerable advantage by pitching to Barry Bonds from right on the first-base foul line, and force him to hit the ball to the left field side of the pitch trajectory. The rules do not give us that foul-line to foul-line leeway, but they do give 18 inches of it."

I understand the concept you are proposing. However, a lefty facing Bonds and moving to the extreme 1B end of the rubber, gains possible maximum advantage only if the following apply:

-he's a sidearmer, with a wicked fastball crossfire approach, mixed with hard-breaking sliders and mixed speed curve change-ups that appear to start behind Bonds' head and ALWAYS break away; [an all-of-the-above pitcher might well cut down on Bonds' ability to pull, but "hangers," or those that are delivered a split-second early in the release would be in the wheelhouse ... and dead meat;

-the 18" movement, from batter to batter, would eventually screw up a pitcher's natural stance, motion and basic rhythm; and I'd guess act against consistent effectiveness, rather than enhancing it;

-again, translation of the 18" of STARTing point gets much diluted as an angle of impact, viewed over the 60'6" span, IMO

jtur88 · May 31st, 2007, 04:52 AM

Perhaps I am operating under a faulty premise, but I am assuming that the batter hits the ball according to where the pitch is coming from, irrespective of any lines that may be chalked onto the field. There are a few place hitters that have the ability to hit the ball to a pre-designated spot on a laid out field, but the huge majority simply address the challenge of trying to make the ball land within a 90-degree quadrant. This is precisely why there are so many foul balls, and why even 'hitting behind the runner' is not that easily accomplished. So the batter's goal is to not only hit the ball and do it more or less squarely, but also to time the swing so that the ball is hit back 'up the middle', within a 90-degree leeway---45-degrees to either side of the pitch trajectory, more or less according to the pitcher's natural arm angle. Anything the pitcher can do to reduce that angle to less than 45-degrees on the batters dominant side places an extra burden on the batter. If the pitcher could adapt his delivery so that he pitches sidearm to some batters and not to others, that would be a plus, but few pitchers would be capable of doing that without giving up the benefit of 'natural motion'. But, I think, what they can do, is create the effect of a sidearm release point by just standing in a different place. Again, though, my whole premisi is based on the belief that just hitting the pitch is difficult enough, and few if any batters can, at the same time, take into account a subtle change in the position of lines on the field relative to compass direction of the pitch.

May 27th, 2007, 07:51 PM	#1 (permalink)
jtur88 Hall of Famer Join Date: Nov 2006 Location: South Texas Posts: 7,857	Geometry of Pitching All pitchers (as far as I know) pitch to all batter from the same point on the rubber. But the rubber is 18 inches wide, so there is leeway there, that they can use to their advantate. Let's say Bonds is up, batting Left. If the pitcher moves to his left, and pitches with his foot just touching the left edge of the rubber, he will cut down the angle between the pitch trajectdory and the foul line by, say, 9 inches. If the foul pole is 300 feet, and the pitching distance 60 feet, the pitcher would in effect be moving the foul pole 45 inches in toward center field. This means every ball Bonds hits that goes into the stands less than 45 inches inside the foul pole, would be converted to a foul ball, just by the pitcher moving his foot to the edge of the rubber. The question now become this---how many MLB home runs pass the foul pole less than 45 inches fair? It would work for doubles, too --- how many doubles fall fair by less than about 30 inches, or grouinders that go over the bag? A pitcher that moved back and forth, placing his foot on the edge of the rubber according to the pull hitters advantage, could narros the width of the outfield by a total of 90 inches, almost eight feet, which is surelay not insignificant. To magnify the effect, for illustration, if the pitcher could pitch from 60-feet down the first base line, pure pull hitters would not get ANY hits.

May 28th, 2007, 08:54 AM	#2 (permalink)
nanwynnfan Senior Member Join Date: Nov 2006 Posts: 2,579	Doing a little plain geometry, here, if I remember those lessons at all: 1. since the rubber is on a diagonal, the moving of the pitcher's focal point to the left and right of center of the rubber extends a leg of a triangle up the corresponding base line [1B, 3B] by 4.5," reduced by the diagonal bias, divided by 60'6" or 1.625%. [generous] 2. The problem, as presented, assumes the pitch trajectory will be a straight line to a corresponding part of the strike zone, in which case it might well be crushed. However, any movement of the pitched ball on its way to the plate would be a departure from the model presented. 3.The problem assumes no defensive reaction by the batter to "hit the ball where it's pitched." Nonetheless, the pure geometry, given all theassumptions, would be a matter of very few inches. Prime real-life example: Ewell Blackwell, whose sidearm whiplash from the extreme right of the rubber was daunting to right-handed hitters, was more a matter of psychology of perception than the actual physics of his motion. **The 9" slant, left or right of center of the rubber, because of the diagonal bias, does not extend a straight line drawn to the baseline by the full 9" further diluting overall impact of extended trajectories. Extreme examples that extend the point of delivery far from actual rubber proportions is moot. In actual play, no such advantage is had by the pitcher. Apology for early calculation errors, where 9" segments were halved.. Last edited by nanwynnfan; May 28th, 2007 at 11:42 AM.*

May 28th, 2007, 12:30 PM	#3 (permalink)
jtur88 Hall of Famer Join Date: Nov 2006 Location: South Texas Posts: 7,857	I dont understand your geometry, or what you mean by 'focal point', and I don't think you grasped my point. The length of the leg of a triangle is not material. What is relevant is the angle between the pitcher and the foul line. Throwing from the center of the rubber, that angle is 45-degrees. The closer the pitcher stands to the foul line, the more acute the angle becomes, and hence the pull hitter needs to keep the ball in a more constricted fair territory. If the pitcher moved the full extent allowable, that angle would narrow by 9 inches in an arc 60 feet from the plate, 13.5 inches 90-feet out (first base), and 45 inches at a 300-foot foul pole. This presumes that a LH batter hits the ball to the right of the pitch trajectory (which as I understand, is the definition of a pull hitter). Do you mean to say that if the pitcher was standing on the first-base line, Thome and Bonds would hit every ball to the left of the pitcher? BTW, I just noticed that Johann Santana pitches with his left toe barely touching the edge of the rubber---but from the same angle for both RH and LH hitters---thus cutting down on the fair territory to RH batters, but yielding the extra 45 inches to lefties. Last edited by jtur88; May 28th, 2007 at 12:34 PM.

May 29th, 2007, 12:29 PM	#4 (permalink)
nanwynnfan Senior Member Join Date: Nov 2006 Posts: 2,579	"If the pitcher moved the full extent allowable, that angle would narrow by 9 inches in an arc 60 feet from the plate, 13.5 inches 90-feet out (first base), and 45 inches at a 300-foot foul pole." Putting the geometry solely on your own terms: 1. extending the pitches' alleged angle edge to allow for edge of rubber stance and sidearm delivery, we can extend the effective lateral "rubber width" to something a bit over 4' [after which point an exaggerated sidearmer would probably fall down; 2. the tendenccy for an opposite-handed pitcher is to throw from away to in, thus straight-lining into the hitters' wheelhouse; 3. vice versa, same handed, the crossfire, while intimidating NOW has option [as does the above] ride in on the hitter, curve or slide away ... one is the jammer or the wheelhouse; the curve is away ... so, my point is that the angle advantage is not a big as it looks, and the motion on the pitched ball is much more important in determining batted ball field distribution than the pitching angle [much diluted over the 60'6" span]. Last edited by nanwynnfan; May 29th, 2007 at 09:32 PM.

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May 30th, 2007, 04:03 PM	#5 (permalink)
jtur88 Hall of Famer Join Date: Nov 2006 Location: South Texas Posts: 7,857	I understand, but Im talking about a pitcher using his optimum motion that he would normally use against any given batter, he can push the batter's pull toward the foul line. I wonder---if the rules allowed the pitcher to pitch from any point on a 60-foot arc measured from the plate, foul line to foul line, I wonder how a pitcher would oiptimize his position. Obviously, pitching to every batter, RH or LH, from exactly the same spot would seem like a strategy that could be improved upon. My questins relates not to such a long arc, but the 18-inch leeway that is allowed---which, surprisingly, no pitcher tries to gain the advantage of. As I said before, I would gain considerable advantage by pitching to Barry Bonds from right on the first-base foul line, and force him to hit the ball to the left field side of the pitch trajectory. The rules do not give us that foul-line to foul-line leeway, but they do give 18 inches of it.

May 30th, 2007, 10:04 PM	#6 (permalink)
nanwynnfan Senior Member Join Date: Nov 2006 Posts: 2,579	"As I said before, I would gain considerable advantage by pitching to Barry Bonds from right on the first-base foul line, and force him to hit the ball to the left field side of the pitch trajectory. The rules do not give us that foul-line to foul-line leeway, but they do give 18 inches of it." I understand the concept you are proposing. However, a lefty facing Bonds and moving to the extreme 1B end of the rubber, gains possible maximum advantage only if the following apply: -he's a sidearmer, with a wicked fastball crossfire approach, mixed with hard-breaking sliders and mixed speed curve change-ups that appear to start behind Bonds' head and ALWAYS break away; [an all-of-the-above pitcher might well cut down on Bonds' ability to pull, but "hangers," or those that are delivered a split-second early in the release would be in the wheelhouse ... and dead meat; -the 18" movement, from batter to batter, would eventually screw up a pitcher's natural stance, motion and basic rhythm; and I'd guess act against consistent effectiveness, rather than enhancing it; -again, translation of the 18" of STARTing point gets much diluted as an angle of impact, viewed over the 60'6" span, IMO

May 31st, 2007, 04:52 AM	#7 (permalink)
jtur88 Hall of Famer Join Date: Nov 2006 Location: South Texas Posts: 7,857	Perhaps I am operating under a faulty premise, but I am assuming that the batter hits the ball according to where the pitch is coming from, irrespective of any lines that may be chalked onto the field. There are a few place hitters that have the ability to hit the ball to a pre-designated spot on a laid out field, but the huge majority simply address the challenge of trying to make the ball land within a 90-degree quadrant. This is precisely why there are so many foul balls, and why even 'hitting behind the runner' is not that easily accomplished. So the batter's goal is to not only hit the ball and do it more or less squarely, but also to time the swing so that the ball is hit back 'up the middle', within a 90-degree leeway---45-degrees to either side of the pitch trajectory, more or less according to the pitcher's natural arm angle. Anything the pitcher can do to reduce that angle to less than 45-degrees on the batters dominant side places an extra burden on the batter. If the pitcher could adapt his delivery so that he pitches sidearm to some batters and not to others, that would be a plus, but few pitchers would be capable of doing that without giving up the benefit of 'natural motion'. But, I think, what they can do, is create the effect of a sidearm release point by just standing in a different place. Again, though, my whole premisi is based on the belief that just hitting the pitch is difficult enough, and few if any batters can, at the same time, take into account a subtle change in the position of lines on the field relative to compass direction of the pitch.