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Margin of Error at the Pocket vs Aiming Error
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Margin of Error at the Pocket vs Aiming Error - 07-12-2019, 10:44 AM

Duckie brought up a good point about the margin of error being different depending on the shot angle. But we were talking about two different margins of error. I was only thinking of the margin of error at the pocket, which is the maximum tolerance in degrees the ob could be off from center pocket and still drop into the hole. This is typically what most people refer to when talking about margin of error. The cb location does not change this, as the margin of error is only derived from pocket width, ob distance from pocket, and ob approach angle to the pocket.

However, any margin of error measured at the ghostball or aimpoint end of the shot line, or even right at the cb itself, is related directly to aiming, and this is where the relationship between cb and ob comes into the mix.

At larger cut angles, primarily greater than 30°, the allowable margin for aiming error decreases quite a bit. Example: Using ghostball aiming on a straight in shot where the ob has a margin or error of +/- 2° at the pocket.... This allows you only 0.078" (a little more than 1/16 of an inch) left or right of the perfect ghostball location. If your idea of where the cb needs to be (ghostball location) is off by anymore than this then you're likely to miss the shot.

For a 30° shot angle on this same ob the allowable aiming error would be about 87% of what it is for the straight in shot. This means you'd have +/- 0.068" (closer to 1/16 of an inch). With a 48° degree shot on the ob the allowable room for aiming error would be about 66% of what it was for straight in, which would make it +/- 0.052 (less than 1/16 of an inch). And for a 60° shot angle the room for aiming error would only be +/- 0.039" (about 1/32 of an inch).


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07-12-2019, 11:08 AM

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Originally Posted by BC21 View Post
Duckie brought up a good point about the margin of error being different depending on the shot angle. But we were talking about two different margins of error. I was only thinking of the margin of error at the pocket, which is the maximum tolerance in degrees the ob could be off from center pocket and still drop into the hole. This is typically what most people refer to when talking about margin of error. The cb location does not change this, as the margin of error is only derived from pocket width, ob distance from pocket, and ob approach angle to the pocket.

However, any margin of error measured at the ghostball or aimpoint end of the shot line, or even right at the cb itself, is related directly to aiming, and this is where the relationship between cb and ob comes into the mix.

At larger cut angles, primarily greater than 30°, the allowable margin for aiming error decreases quite a bit. Example: Using ghostball aiming on a straight in shot where the ob has a margin or error of +/- 2° at the pocket.... This allows you only 0.078" (a little more than 1/16 of an inch) left or right of the perfect ghostball location. If your idea of where the cb needs to be (ghostball location) is off by anymore than this then you're likely to miss the shot.

For a 30° shot angle on this same ob the allowable aiming error would be about 87% of what it is for the straight in shot. This means you'd have +/- 0.068" (closer to 1/16 of an inch). With a 48° degree shot on the ob the allowable room for aiming error would be about 66% of what it was for straight in, which would make it +/- 0.052 (less than 1/16 of an inch). And for a 60° shot angle the room for aiming error would only be +/- 0.039" (about 1/32 of an inch).
Interesting, Brian.

Multiply this by the fact that there's also stroking error to consider, which magnifies quickly with greater CB/OB distance. Probably why nobody ever makes a shot at pool (well, nobody I know).

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07-12-2019, 11:36 AM

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Interesting, Brian.

Multiply this by the fact that there's also stroking error to consider, which magnifies quickly with greater CB/OB distance. Probably why nobody ever makes a shot at pool (well, nobody I know).

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Copied that! Lol. It's probably also the eason why so many aspiring pool players look toward out-of-the-box aiming systems to help speed up their shot making consistency, rather than investing years of traditional old-school trial and error methods.


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07-12-2019, 02:13 PM

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Originally Posted by BC21 View Post

For a 30° shot angle on this same ob the allowable aiming error would be about 87% of what it is for the straight in shot. This means you'd have +/- 0.068" (closer to 1/16 of an inch). With a 48° degree shot on the ob the allowable room for aiming error would be about 66% of what it was for straight in, which would make it +/- 0.052 (less than 1/16 of an inch). And for a 60° shot angle the room for aiming error would only be +/- 0.039" (about 1/32 of an inch).
Presumably the allowable error as you approach 90 degrees would approach zero. If you plotted degrees (0 being straight in, 90 being maximum cut) on the x axis against allowable error on the y axis you'd get a curve with 0.078 as a max value that would approach 0. It doesn't sound like a straight line relationship. If I were better at geometry and math maybe I could say for sure.
  
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07-13-2019, 06:52 AM

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Presumably the allowable error as you approach 90 degrees would approach zero. If you plotted degrees (0 being straight in, 90 being maximum cut) on the x axis against allowable error on the y axis you'd get a curve with 0.078 as a max value that would approach 0. It doesn't sound like a straight line relationship. If I were better at geometry and math maybe I could say for sure.
You are exactly right. The margin of error for aiming purposes gets smaller and smaller as the shot approaches 90°. At 90° there is no margin.

The math is..... (allowable aiming error) = (margin of error) X sin(90 - shot angle)

So, on the example straight in shot where the margin of error (measured at the ghostball) is +/- 0.078", the allowable margin of error for aiming at the ghostball center would be:

a = (0.078")(sin(10°))
= 0.014"

You'd have to visualize the exact ghostball location within +/- 0.014" (about 1/70 of an inch).


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07-13-2019, 10:49 AM

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Originally Posted by BC21 View Post
You are exactly right. The margin of error for aiming purposes gets smaller and smaller as the shot approaches 90°. At 90° there is no margin.

The math is..... (allowable aiming error) = (margin of error) X sin(90 - shot angle)

So, on the example straight in shot where the margin of error (measured at the ghostball) is +/- 0.078", the allowable margin of error for aiming at the ghostball center would be:

a = (0.078")(sin(10°))
= 0.014"

You'd have to visualize the exact ghostball location within +/- 0.014" (about 1/70 of an inch).
Here's what it looks like. Unfortunately the degrees on the x axis are in radians, but it starts at 0 degrees and ends at 90 degrees. Divide by 3.14 and multiply by 180 to convert the x axis to degrees. These online plotting graphics aren't very user friendly, handy as they may be.

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07-13-2019, 04:55 PM

Here's a visualization trick that helps me "see" how big the margin of error (contact patch) is on the OB's surface:

I imagine the OB's equator is expanded outward from the OB's center until it reaches the pocket, and however big the pocket margin of error is on that expanded equator I visualize the "same" size contact patch scaled down onto the real OB's equator.

This does nothing useful for me in aiming except to demonstrate visually that it's inherently impossible and I should take up golf.

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07-16-2019, 02:51 AM

In my pool world, which is the only one that matters to me just as another’s pool world is the only one that needs to matter to them, a sighting error results in a over or under cut of where I want to put the OB.

If I want to put it center pocket but hit to one side of center pocket, that could be a sighting error or execution error. That’s for me to figure out.

If the ball goes in the pocket but not center pocket, the reason it went is because of the area on the OB that when the CB contacts inside that area will result in the OB going in the pocket, just not where intended.

In my pool world, I call that area the impact zone, not margin of error.

The pocket opening is just that......the pocket opening. It is a area where I can place the CB anywhere I need to.

You can increase that opening temporarily by compressing the corners of the pocket by the OB to make certain shots. That’s not a margin of error but a pocketing technique.

But again, this is in my pool world, yours can be whatever you want it to be.
  
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07-16-2019, 06:24 AM

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Originally Posted by duckie View Post
In my pool world, which is the only one that matters to me just as another’s pool world is the only one that needs to matter to them, a sighting error results in a over or under cut of where I want to put the OB.

If I want to put it center pocket but hit to one side of center pocket, that could be a sighting error or execution error. That’s for me to figure out.

If the ball goes in the pocket but not center pocket, the reason it went is because of the area on the OB that when the CB contacts inside that area will result in the OB going in the pocket, just not where intended.

In my pool world, I call that area the impact zone, not margin of error.

The pocket opening is just that......the pocket opening. It is a area where I can place the CB anywhere I need to.

You can increase that opening temporarily by compressing the corners of the pocket by the OB to make certain shots. That’s not a margin of error but a pocketing technique.

But again, this is in my pool world, yours can be whatever you want it to be.
I like this. I never, I mean never, think about or consider or imagine any margin of error or available pocket opening or whatever. I just put the cb where it needs to be to send the ob to where it needs to be.


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07-16-2019, 07:30 AM

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07-16-2019, 06:08 PM

Quote:
Originally Posted by BC21 View Post
Duckie brought up a good point about the margin of error being different depending on the shot angle. But we were talking about two different margins of error. I was only thinking of the margin of error at the pocket, which is the maximum tolerance in degrees the ob could be off from center pocket and still drop into the hole. This is typically what most people refer to when talking about margin of error. The cb location does not change this, as the margin of error is only derived from pocket width, ob distance from pocket, and ob approach angle to the pocket.

However, any margin of error measured at the ghostball or aimpoint end of the shot line, or even right at the cb itself, is related directly to aiming, and this is where the relationship between cb and ob comes into the mix.

At larger cut angles, primarily greater than 30°, the allowable margin for aiming error decreases quite a bit. Example: Using ghostball aiming on a straight in shot where the ob has a margin or error of +/- 2° at the pocket.... This allows you only 0.078" (a little more than 1/16 of an inch) left or right of the perfect ghostball location. If your idea of where the cb needs to be (ghostball location) is off by anymore than this then you're likely to miss the shot.

For a 30° shot angle on this same ob the allowable aiming error would be about 87% of what it is for the straight in shot. This means you'd have +/- 0.068" (closer to 1/16 of an inch). With a 48° degree shot on the ob the allowable room for aiming error would be about 66% of what it was for straight in, which would make it +/- 0.052 (less than 1/16 of an inch). And for a 60° shot angle the room for aiming error would only be +/- 0.039" (about 1/32 of an inch).

I often wondered how most defined ghost ball aiming and how to memorize the ghost ball contact point.

When trying to master a difficult shot, I'll freeze another cue ball up with the object ball as the ghost ball, then go back to the actual cue ball location where shooting from and study the fraction of the hit. It shortens the learning curve up, but obviously you can't do this in a match.
  
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07-16-2019, 09:37 PM

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I often wondered how most defined ghost ball aiming and how to memorize the ghost ball contact point.

When trying to master a difficult shot, I'll freeze another cue ball up with the object ball as the ghost ball, then go back to the actual cue ball location where shooting from and study the fraction of the hit. It shortens the learning curve up, but obviously you can't do this in a match.
Exactly! Most players can relate to visualizing the cb to ob overlap/fraction/relationship, whatever....even when looking where the ghostball should be (because it's not really there, so you have to imagine it), and by looking at the ob you can visualize the aim line.


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