Which shot allows for the greater margin of error?

[jsp]

Umm...I'm glad that where you play doesn't have friction but everywhere I've played does.

Haha...true.

But if you think about it, except for the case where the OB and CB are frozen together, friction and throw can only increase your margin of error in both cases (for a straight in shot). For the 9ball case, it will increase your margin of error more than the 8ball case.

JSP, I commend you. You always show a willingness to do the calculations that I think I could probably do, but it would take way more time and mental effort than I'm willing to invest. Are you by any chance a math teacher? I ask because I know very few people willing to derive geometry equations for fun

-Andrew

No, i'm not a math teacher, just someone that has too much time at work. Correction, someone that wastes too much time here at work.

 

[Colin Colenso]

That's what I thought.

But actually the 9ball (the ball closer to the CB) has signifcantly more margin of error than than the 8ball (the ball closer to the pocket). Here are the numbers I used...

CB distance to pocket opening = 10 feet (120'')
pocket size = 4.5''
9ball distance to front edge of pocket opening = 2.25'' (to the front edge of the 9ball)
8ball distance to CB = 2.25" (ball edge to ball edge)

Results...
8ball margin of error = +/- 0.356 degrees
9ball margin of error = +/- 0.558 degrees

So the 9ball has about 57% MORE margin of error than the 8ball. Those numbers don't sound very big. However, compare it to the worst case margin of error with the OB (as you would expect) being right at the midpoint between the pocket and CB. The margin of error in this case is a miniscule +/- 0.042 degrees.

I always thought that margin of error would be pretty much symmetric around the midpoint between the CB and pocket. After graphing the solution, it more or less does look symmetric until the OB gets a couple of ball's widths distance away from the CB and pocket. At this closer proximity, the margin of error on the CB side goes up much faster than the pocket side.

If you're not convinced, just think of the extreme case of the 8ball hanging right on the edge of the pocket compared to the 9ball being virtually frozen on the CB. For the 9ball, you can pretty much aim in any foward direction (again, neglect throw and friction effects) and the 9ball should head towards the pocket. Your margin of error is huge...pretty much the full 180 degrees. However, to pocket the 8ball, you still need to have the CB contact the 8ball, so your margin of error is still very limited.

So going back to the original example, you should be able to pocket the 9ball about 50% more times than the 8ball...in theory. It's funny how the practical world doesn't exactly agree with the theory.

Neat, huh? If anyone is interested, I'll post my derivations and calculations...NOT!

That is neat jsp!
I figured the math would come out something like that. But you have to take into account throw induced from a slight off center hit on the CB which will be much more significant on the close ball than the distant ball. eg. Hit the CB 1/8th tip off center will throw the close ball off a pocket width, but will have much less influence on the long shot, presuming the bridge is close to the pivot point.

Also, when the angle is slightly off straight, you have contact induced throw, that varies considerably with stun or follow or touches of side english etc.

Colin

 

[Andrew Manning]

But if you think about it, except for the case where the OB and CB are frozen together, friction and throw can only increase your margin of error in both cases (for a straight in shot). For the 9ball case, it will increase your margin of error more than the 8ball case.

Well yes, in the case of a center-ball hit, friction would only decrease the negative effects of a directional error. Unintentional side-spin, however, comes into play significantly in the case where the CB and OB are quite close together. A good player knows how to use side-spin to throw a ball into the pocket when the CB and OB are close together and not quite lined up with the hole. The same concept could easily throw a ball out of the pocket when they are lined up with the hole.

-Andrew

 

[cuetable]

Since these are shots on the table, by a human, I think we should take the stroke, power and follow through into consideration also.

When shooting the 9 ball, one can only use a dabbing short stroke with a follow through of less than 2.25". However, when shooting the 8 ball, he can use a long and smooth stroke with a follow through of 20" or longer. The cueball will advance quite a distance before it leaves the cue tip. Therefore, the cue ball travelling distance are not the same.

Cheers
Wei

 

[chuchu1604]

It's the 9-ball in my opinion

 

[Mark Avlon]

The results to this poll are quite interesting. It seems that 80% of the respondents should read page twelve of this file...

http://www.sfbilliards.com/cols1992-2000_txt.pdf

 

[Double-Dave]

Hi jsp,

I'm not entirely sober, so forgive me if I'm wrong, but didn't you confuse the balls? You write a distance from 8-ball to cb of 2.25 inches, but shouldn't that be the 9-ball? Also in my view the distance from the 8 to the pocket in the example edge to edge is about 3.25 inches, I think that makes a big difference here. Again I hope this makes sense when I read it back tomorrow. Sorry for dragging out old cows, but I voted and now I would like to know for sure if at all possible.

Bob's article (page 12+13) didn't work for me I must say, he ignores the tightening of the pocket for on the rail shots for example.

gr. Dave

 

[Double-Dave]

Hi jsp,

I still feel the same, guess I wasn't that far gone. Did you get the balls mixed up?

gr. Dave

 

[jsp]

I'm not entirely sober, so forgive me if I'm wrong, but didn't you confuse the balls? You write a distance from 8-ball to cb of 2.25 inches, but shouldn't that be the 9-ball?

Dave, thanks for the correction. I did get the balls mixed up when I stated the distances. I will edit my previous post.

Also in my view the distance from the 8 to the pocket in the example edge to edge is about 3.25 inches, I think that makes a big difference here.

In my initial post, I said that the 8ball is a ball's width away from the pocket opening. So by definition, that implies the distance from pocket opening to the edge of the 9ball is 2.25''. However, it is 3.375'' from the pocket to the center of the 8ball...and 3.375 is the actual number I used in the formula I derived to calculate the OB margin of error (my equation deals with distances from the pocket opening to the center of the OB, not ball edge). So Dave, I did use 3.375'' instead of 2.25'' when calculating the error, but the distance is between pocket to ball edge is still 2.25''.

(Actually, at first I did use 2.25 in my equation, and the error for this distance turned out to be more than double the error for the 9ball. However, I then realized that using 2.25 in my formula didn't exactly gel with what I initially said in my first post, so I inputted 3.375 instead).

Thanks for the comments Dave. It's nice to know that there are people that actually pay attention to my posts.

 

[Double-Dave]

Hi jsp,

I only looked at the cuetable, that´s why I thought it was 3.25 inches. I hate to nitpick, but I also feel that pocket size / tolerance for the shot should be more like 2.5-3 inches but that won´t affect the outcome. It would be nice if you could post again, what you calculated to be the shot with the greater margin of error, to avoid any confusion

gr. Dave

 

[jsp]

It would be nice if you could post again, what you calculated to be the shot with the greater margin of error, to avoid any confusion

The 9ball (the ball closer to the CB) still has the greater margin of error.