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View Full Version : Shot difficulty as a function of distance

dr_dave
01-01-2005, 11:03 AM
This question was originally posted at:
original question thread (http://www.billiardsdigest.com/ccboard/showthreaded.php?Cat=&amp;Board=ccb&amp;Number=172110&amp;page =0&amp;view=collapsed&amp;sb=5&amp;o=&amp;vc=1). I am answering it here so others can see it and comment on it more easily.

<blockquote><font class="small">Quote dave9ball:</font><hr> I think the articles and web site are outstanding. My engineering is a little rusty, but I think the principles are great!
Your recent article discussed difficulty related to distance. I have used the following estimation for years. I am curious if it is close to valid. I take an object ball 1 diamond from the pocket and the cue ball 1 diamond from the OB to be a difficulty of 1. I multiply the Cue to OB distance by the OB to pocket distance to get a relative number. A shot with OB 2 diamonds from pocket and cue 3 diamonds from OB is difficulty 6 ( 6 times more difficult than a 1). It can be useful in shot selection as well as speed. I consider angle difficulty to be a function of the cosine of the shot angle. I think I got this from an old Bob Jewett article. <hr /></blockquote>

My November '04 through Fanuary '05 articles posted online (http://www.engr.colostate.edu/~dga/pool/bd_articles/index.html) show the results of all of my analyses, so you might be able to compare your method or any other method to my results by looking at the plots in the articles. Shot difficulty, assuming a center ball hit, is a complex function of distance from the OB to the pocket, angle of the OB to the pocket, distance between the CB and OB, cut angle, and shot speed. I take all of these factors into consideration in my articles and analyses (TP 3.4 through 3.8) (http://www.engr.colostate.edu/~dga/pool/technical_proofs/index.html). For a non center ball hit, the effects of English (deflection/squirt, curve/swerve, and throw) would also need to be considered in a thorough analysis.

As I explain in my articles, I don't think a totally analytical approach is very practical at the table. I think knowing and having an intuitive feel for the principles derived from the analysis results is what is important. I summarize all of the useful principles in my articles.

Concerning your cosine of the angle approach, straight-on shots are the least diffcult, and 90 degree cut angle shots are near impossible, and the difficulty does incease significantly as the cut angle increases (faster than a cosine function), but if the cosine understanding helps you in your game, that's all that matters.

Scott Lee
01-01-2005, 07:58 PM
<blockquote><font class="small">Quote dr_dave Concerning your cosine of the angle approach, straight-on shots are the least diffcult, and 90 degree cut angle shots are near impossible, and the difficulty does incease significantly as the cut angle increases (faster than a cosine function), but if the cosine understanding helps you in your game, that's all that matters. [/quote:</font><hr>

dr. dave...Just to clarify something. Straight-in shots are easy, as long as you have a straight stroke, and a good solid pre-shot routine. However, the slightest imperfections in either, can result in small margins of error, creating a miss...especially when speed and distance (between the OB &amp; CB) are added to the equation. Distance to the pocket doesn't matter. This is why good instructors concentrate on what happens "behind" the CB, before moving on to what happens in front of the CB. If you have a poor quality stroke, all the extraneous knowledge is of little benefit, as you'll have difficulty stroking the CB accurately and consistently.

Scott Lee

Popcorn
01-01-2005, 08:38 PM
quote
"Concerning your cosine of the angle approach, straight-on shots are the least diffcult, and 90 degree cut angle shots are near impossible, and the difficulty does incease significantly as the cut angle increases "

A straight in shot is not the easiest shot. To a non player and theoretically it may seem so, but it is not. When the rule use to be you shot from behind the line on a scratch. You never set up straight in even if you were shooting the last 9 ball, you almost always created a little angle. I think it may have to do with the way the mind perceives the shot. With a slight angle your minds eye quickly see where to hit the ball and you make the shot. Straight in you don't have a specific target other then to hit the ball squarely straight on and that is very difficult to do and the farther away you get the harder it gets. I also don't believe that the difficulty increases significantly as the cut angle increases. It will stay somewhat the same through most of the angle but at a point will increase quickly for a very small range of the angle. Distance always is the primary factor on a pool table. An easy shot can become a difficult shot with just a little added distance.

There are other factors as well. Backwards cuts are much more difficult then say cutting a ball where a rail is in the line of sight even though the angle is the same. The minds eye uses the rail as a device to make the shot although not necessarily on a conscious level. There are many factors that go into playing that that require practical experience to understand. They may actually defy logic to the non player.

dr_dave
01-02-2005, 07:38 AM
<blockquote><font class="small">Quote Scott Lee:</font><hr>dr. dave...Just to clarify something. Straight-in shots are easy, as long as you have a straight stroke, and a good solid pre-shot routine. However, the slightest imperfections in either, can result in small margins of error, creating a miss...especially when speed and distance (between the OB &amp; CB) are added to the equation. Distance to the pocket doesn't matter. This is why good instructors concentrate on what happens "behind" the CB, before moving on to what happens in front of the CB. If you have a poor quality stroke, all the extraneous knowledge is of little benefit, as you'll have difficulty stroking the CB accurately and consistently.
Scott Lee<hr /></blockquote>
Scott, I absolutely agree with you that the fundamentals are critically important and should be stressed by instructors. If one does not have a repeatable stroke, no amount of understanding of principles can really help that much. However, regardless of how accurate one's stroke is, all of the conclusions from my analysis results are still valid (in a relative sense). For example, for good and bad player alike, a straight-in shot is still easier than a thin (large angle) cut shot, and a shot with the OB close to the pocket and the CB close to the OB is still easier than a shot with large separations between the balls and target pocket (assuming the same cut angle). Distance to the pocket does matter. But you are right that if one's stroke is poor, nothing else really matters that much.

dr_dave
01-02-2005, 08:25 AM
<blockquote><font class="small">Quote Popcorn:</font><hr>
A straight in shot is not the easiest shot. To a non player and theoretically it may seem so, but it is not.
...
With a slight angle your minds eye quickly see where to hit the ball and you make the shot.<hr /></blockquote>
You make a good point that my analysis does not take psychological factors into consideration. Some people just prefer a shot with a small angle (although it is theoretically more difficult). Also, if a person believes a straight-in shot is more difficult, it will be more difficult, regardless of what geometry and physics says.

<blockquote><font class="small">Quote Popcorn:</font><hr>Straight in you don't have a specific target other then to hit the ball squarely straight on and that is very difficult to do and the farther away you get the harder it gets.<hr /></blockquote>
I disagree. I think the target could not be more clear for a straight-in shot. It is a full-ball hit ... aim at the dead center ... hit the entire ball ... no need to visualize a ghost ball center at an angle ... no thinking or visualizing is required at all. But again, if somebody thinks:
"I hate straight-in shots and cut shots are easier"
none of this matters. The mind is a powerful thing.

<blockquote><font class="small">Quote Popcorn:</font><hr>I also don't believe that the difficulty increases significantly as the cut angle increases. It will stay somewhat the same through most of the angle but at a point will increase quickly for a very small range of the angle.<hr /></blockquote>
You are correct. The difficulty increases very slowly as the cut angle increases from 0 degrees and doesn't "increase significantly" until the cut angle starts getting large. Soon, I will add a plot and more discussion to my TP 3.4 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/TP_3-4.pdf) to show this more clearly. I will post an update message to this thread when it is available.

<blockquote><font class="small">Quote Popcorn:</font><hr>Distance always is the primary factor on a pool table. An easy shot can become a difficult shot with just a little added distance.<hr /></blockquote>
I agree completely. I already have a plot in TP 3.4 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/TP_3-4.pdf) that shows this. I don't think anybody would disagree with you on this one.

Scott Lee
01-02-2005, 12:12 PM
dr. dave...It is only natural that we would agree on this. I never said your conclusions weren't valid, just of less benefit to someone who doesn't have a good repeatable stroke! Again...we agree! Hope to see you if I get booked at CSU (haven't been back there since the flood took out the poolroom...and now the only table is in the student pub)!

Scott Lee

BCgirl
01-02-2005, 04:37 PM
I think that, for most people, the trouble with straight shots is indeed visualising the aiming point. Although it has been said that a full ball hit is the easist to visualise, I for one have never found that to be the case.

Clearly, technique is also a major factor, since any off-centre hit on the CB will cause greatest throw on the OB for a straight shot.

Also, many people will hit straight shots harder, and even with the same hit, the OB will travel faster on a straight shot (simple physics) than a cut shot. Therefore, the permissible pocket opening may be smaller than anticipated.

To separate stroke problems from aiming problems, it is useful to use an extended aimng point. If the shot is truly straight, aim the CB at the pocket, not the OB. If this improves your accuracy, then you are not finding the right aiming point on the OB.

Another factor is knowing where the pocket centre is. Some people find a straight-in shot from a narrow angle to be more difficult than a cut shot from the same angle. This may be because, being unable to see the OB path so clearly when hitting the cut shot, the compensation for the optimum pocket target is unconscious, whereas, for the straight-in shot, you aim more explicitly at a precise target, so clearly, you have to know where it is. When practising a particular cut angle, it may be useful to place a chalk cube at a point that defines the centre of the pocket target, and aim for that.

Each of the elements of stroke, consistency, aim, and compensation for angle, speed, and english, are factors, and the degree to which they affect shots will vary from individual to individual. It is how you go about separating the effects, and refining each skill that's important in improving your game, and it's what sets apart the true greats and the best teachers of the game from the rest.

I would note that a considerable amount of detailed analysis of permissible error on various shots is presented in "The Science of Pocket Billiards".

BCgirl

dr_dave
01-02-2005, 05:44 PM
<blockquote><font class="small">Quote Scott Lee:</font><hr> dr. dave...It is only natural that we would agree on this. I never said your conclusions weren't valid, just of less benefit to someone who doesn't have a good repeatable stroke! Again...we agree!<hr /></blockquote>
Scott, I'm sorry if I misinterpreted what you wrote. I'm glad we agree.

<blockquote><font class="small">Quote Scott Lee:</font><hr>Hope to see you if I get booked at CSU (haven't been back there since the flood took out the poolroom...and now the only table is in the student pub)!
<hr /></blockquote>
Please look me up if you visit Colorado. I hope others out there on the CCB forum would also look me up if they visit our great state.

Scott, I think I actually saw one of your exhibitions on campus about 12 years ago. I enjoyed it very much and would love to see you perform again. I didn't remember your name after all of these years, so I'm glad you jogged my memory. Regards, Dave.

Popcorn
01-02-2005, 07:40 PM
I am constantly impressed by some of the stuff people write on here.

bigbro6060
01-03-2005, 12:19 AM
Straight in shots , even full length are easier if you have a good straight cue action .

dr_dave
01-03-2005, 07:48 AM
<blockquote><font class="small">Quote bigbro6060:</font><hr> Straight in shots , even full length are easier if you have a good straight cue action.<hr /></blockquote>
I agree with you completely. See my previous reply (http://www.billiardsdigest.com/ccboard/showthreaded.php?Cat=&amp;Board=ccb&amp;Number=172180&amp;page =&amp;view=&amp;sb=&amp;o=&amp;vc=1). Also, I've been thinking some more about why some people might think straight-in shots are more difficult. When you miss a straight-in shot, the tendancy might be to think (even if only subconsciously): "How could I miss that shot ... it was straight-in?" Even people that don't think straight-in shots are easier still might know it subconsciously. Therefore, one might think it looks bad to miss a straight-in shot. I don't think anybody minds a short, straight-in shot; but for longer shots, some people might prefer a cut angle. Maybe subconsciously, one might think that if they miss it, he or she has an excuse: "The shot was long and there was a cut angle angle, so I didn't expect to make it." The tendancy might be to not "cut" oneself any slack when the shot is straight-in, thinking it should not be missed. But we all know that long shots are just tough, whether they are straight-in or not. A long, straight-in shot is still easier than a long cut shot (especially for larger cut angles), but it is still difficult and requires a consistent, straight stroke.

Qtec
01-03-2005, 10:00 AM
<blockquote><font class="small">Quote bigbro6060:</font><hr> Straight in shots , even full length are easier if you have a good straight cue action .

<hr /></blockquote>

Isnt any shot? /ccboard/images/graemlins/smirk.gif

Qtec

Bob_Jewett
01-04-2005, 04:53 PM
<blockquote><font class="small">Quote dr_dave:</font><hr>... Concerning your cosine of the angle approach, straight-on shots are the least diffcult, and 90 degree cut angle shots are near impossible, and the difficulty does incease significantly as the cut angle increases (faster than a cosine function)... <hr /></blockquote>
The shot difficulty goes up as the inverse of the cosine or the secant of the cut angle (to first order). There is a simple method of calculating this visually on the table, which lets you get the basic difficulty of the shot (product of distances) fairly easily, and is illustrated in the April 1994 issue of BD.

For teaching purposes, the shot difficulty number (product of distances in diamonds as dave9ball said) is useful to point out how much error is allowed in the physical alignment. For example, if you have ball in hand in balk, and the object ball is three diamonds from the corner pocket, the difficulty is 3*3 or 9. If all of the error in your shot is in where your back-hand is at impact, then it must be in a window that is 1/9 of an inch wide (for typical pocket widths, etc.). Alternatively, you could give this as roughly +- 1/9th of a centimeter, or pretty much within a millimeter of the correct location.

As for the comment made by someone that a full shot makes the object ball move faster than a cut shot, that's true, but if you come over two balls off straight-in for the shot I described above, the speed of the object ball will go down by less than 1% because of the cut angle (speed of the object ball goes as the cosine of the cut angle).

Ron Shepard has pointed out a major problem with straight-in shots if you play them as stop shots. If you get any unintended side spin at all on the cue ball, and the cue ball arrives at the object ball with no follow or draw, the side spin will have maximum effect. What this means practically is that if you have problems with unintended english, you should play straight-ins as slight follow or draw shots instead of perfect stop shots. But you should also try to perfect your stroke so that you don't have the problem.

The simple theoretical treatment of shot difficulty doesn't treat the various problems you might have with off-center hits, crooked tables, crooked sticks, bogus pockets, broken balls, .... It does give you an idea of how much accuracy is required to make various shots. Among other things, it tells you how difficult bank shots are apart from whatever surprises you get when the ball hits the cushion.

dr_dave
01-05-2005, 11:08 AM
<blockquote><font class="small">Quote Bob_Jewett:</font><hr>The shot difficulty goes up as the inverse of the cosine or the secant of the cut angle (to first order). There is a simple method of calculating this visually on the table, which lets you get the basic difficulty of the shot (product of distances) fairly easily, and is illustrated in the April 1994 issue of BD.<hr /></blockquote>
I apologize if I misrepresented your method. Unfortunately, I have not been a BD subscriber for that long; and honestly, if I were I probably wouldn't have kept the old magazines around that long. Maybe we should try to convince BD to post all our past artilces on their website so our writings can be more easily accessed as references.
<blockquote><font class="small">Quote Bob_Jewett:</font><hr>Ron Shepard has pointed out a major problem with straight-in shots if you play them as stop shots. If you get any unintended side spin at all on the cue ball, and the cue ball arrives at the object ball with no follow or draw, the side spin will have maximum effect. What this means practically is that if you have problems with unintended english, you should play straight-ins as slight follow or draw shots instead of perfect stop shots. But you should also try to perfect your stroke so that you don't have the problem.<hr /></blockquote>
That's a great point ... interesting principle. As I'm sure you would probably agree, as with many principles in pool, it is probably wiser for someone to try to improve their stroke, and be able to hit the center of the ball more reliably, before trying to understand and apply principles that may be above their level of play.

<blockquote><font class="small">Quote Bob_Jewett:</font><hr>The simple theoretical treatment of shot difficulty doesn't treat the various problems you might have with off-center hits, crooked tables, crooked sticks, bogus pockets, broken balls, ....<hr /></blockquote>Great point. It also does not include psychological factors (e.g., see my other response (http://www.billiardsdigest.com/ccboard/showthreaded.php?Cat=&amp;Board=ccb&amp;Number=172184&amp;page =&amp;view=&amp;sb=&amp;o=&amp;vc=1)) which can be huge. I'm sure Freud would have a lot to say about pool, with the cue stick being so long and stiff (even with a Predator shaft).

SPetty
01-05-2005, 12:06 PM
<blockquote><font class="small">Quote dr_dave:</font><hr> Maybe we should try to convince BD to post all our past artilces on their website so our writings can be more easily accessed as references.<hr /></blockquote>Yes, please. Let us know what we can do, if anything, to help make this happen.

dr_dave
01-05-2005, 12:13 PM
<blockquote><font class="small">Quote SPetty:</font><hr> <blockquote><font class="small">Quote dr_dave:</font><hr> Maybe we should try to convince BD to post all our past artilces on their website so our writings can be more easily accessed as references.<hr /></blockquote>Yes, please. Let us know what we can do, if anything, to help make this happen.<hr /></blockquote>
Maybe if enough readers send a letter to the editor at
email@billiardsdigest.com
they will think it is important and dedicate resources to have it done. It might be expensive, but it would also be extremely valuable.

dr_dave
01-05-2005, 02:05 PM
<blockquote><font class="small">Quote BCgirl:</font><hr>I would note that a considerable amount of detailed analysis of permissible error on various shots is presented in "The Science of Pocket Billiards".<hr /></blockquote>
I have studied Koeher's Chapter 4, and it is not clear to me how thorough his analysis was, because he does not describe how he got his numbers, and he does not provide plots that can be compared to mine. My impression is that he did not include all of the factors that I did in my analysis. One thing that makes me question his results is a statement he makes on page 46:

"The unique thing about corner pockets is that the effective pocket size remains the same regardless of approach angle."

(the italics and bold are his)

This is completely wrong! /ccboard/images/graemlins/frown.gif
To know why, see my Nov'04-Jan'05 articles posted online (http://www.engr.colostate.edu/~dga/pool/bd_articles/index.html) or see pages 60-78 in "The Illustrated Principles of Pool and Billiards."

Bob_Jewett
01-06-2005, 10:08 AM
<blockquote><font class="small">Quote dr_dave:</font><hr> (pocket size same regardless of approach angle)

This is completely wrong! /ccboard/images/graemlins/frown.gif
<hr /></blockquote>
I agree that pocket size changes with angle for the corner pockets, but the variation shown in your analysis is very puzzling for slow-speed shots. (Note that one diagram is incorrectly labeled as "slow" when it should be "fast.")

Did you verify the shapes by measurements?

A related question: is there a single point (or nearly) that represents the center of the target from all angles?

dr_dave
01-06-2005, 10:42 AM
<blockquote><font class="small">Quote Bob_Jewett:</font><hr> <blockquote><font class="small">Quote dr_dave:</font><hr> (pocket size same regardless of approach angle)
This is completely wrong! /ccboard/images/graemlins/frown.gif<hr /></blockquote>
I agree that pocket size changes with angle for the corner pockets, but the variation shown in your analysis is very puzzling for slow-speed shots.:(<hr /></blockquote>
I was also a little surprised by the results. But the shapes make sense intuitively based on the arguments and principles I present in my Nov'04 - Jan'05 articles (http://www.engr.colostate.edu/~dga/pool/bd_articles/index.html). Also, video demonstrations NV 3.12-3.15 (http://www.engr.colostate.edu/~dga/pool/normal_videos/index.html) explain the effects fairly well (see the articles for more detail).
<blockquote><font class="small">Quote Bob_Jewett:</font><hr>(Note that one diagram is incorrectly labeled as "slow" when it should be "fast.")<hr /></blockquote>
Where did you see this error? I just checked on pages 69-71 of my book and everything seems to be labeled properly there.
<blockquote><font class="small">Quote Bob_Jewett:</font><hr>Did you verify the shapes by measurements?<hr /></blockquote>
Not in detail, just anecdotally with the video demonstrations. I also checked my analysis calculations (TP 3.4-3.12 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/index.html)) very carefully ... several times. Also, the important thing to me is the overall shape of the curves, not the exact numerical values. Experiments might show variances from the curve shapes, but I would expect the trends to be very close. I am confident with the analyses I performed. I am also confident with the conclusions I made from the results (see the articles). ; although, a detailed experimental verification study would make me even more confident. Are you offering to do this study? /ccboard/images/graemlins/laugh.gif
<blockquote><font class="small">Quote Bob_Jewett:</font><hr>A related question: is there a single point (or nearly) that represents the center of the target from all angles?<hr /></blockquote>
No. The effective target center varies with entry angle. I did not present these results in my book or articles because I thought they were too much information, but I have plots in my technical analyses if you want to look at them. The graphs plot "offset" (distance from the geometric center of the pocket to the center of the effective target size) vs. angle to the pocket.

Jude_Rosenstock
01-06-2005, 10:54 AM
Okay, I just have to say that if you think straight-in is not the easiest angle, you should try another hobby. Ball-in-hand with the game winning ball in the center of the table, if you do not set yourself up with a straight shot, throw your cue out and take up something else. This game simply is not for you.

Jude M. Rosenstock

Qtec
01-06-2005, 12:41 PM
[ QUOTE ]
Quote Bob_Jewett:
--------------------------------------------------------------------------------
A related question: is there a single point (or nearly) that represents the center of the target from all angles?
--------------------------------------------------------------------------------

No. The effective target center varies with entry angle. <hr /></blockquote>

Dave, you need to learn to read! [ We are all guilty of this offence sometimes. /ccboard/images/graemlins/wink.gif]
IMO, Bob is messing with you. /ccboard/images/graemlins/laugh.gif
I,m pretty sure it was a trick question.! He/Bob [ I think] is talking about the Ghost Ball method of sighting, when you are ALWAYS aiming for the same point.[ assuming you are hitting thru the middle of the Qb of course]

Your website is full of good info, but I think a lot of your videos are staged to prove an assumption, rather than to record an event.
Your cut v,s carom example was totally unfair on the cut shot. If you wanted to be fair, you should have put a ball[ over the pocket] on the right hand pocket.
The SIT shot video that went wrong?
Nobody would try and pot that ball just using SIT. You just bend the Qball a bit and you cant miss.
Any good player would bend that ball. Without a doubt.

Qtec

dr_dave
01-06-2005, 01:09 PM
<blockquote><font class="small">Quote Qtec:</font><hr>Quote Bob_Jewett:
--------------------------------------------------------------------------------
A related question: is there a single point (or nearly) that represents the center of the target from all angles?
--------------------------------------------------------------------------------

No. The effective target center varies with entry angle.

Dave, you need to learn to read! [ We are all guilty of this offence sometimes. /ccboard/images/graemlins/wink.gif]
IMO, Bob is messing with you. /ccboard/images/graemlins/laugh.gif
I,m pretty sure it was a trick question.! He/Bob [ I think] is talking about the Ghost Ball method of sighting, when you are ALWAYS aiming for the same point.[ assuming you are hitting thru the middle of the Qb of course]<hr /></blockquote>
I disagree. I think Bob had a valid and intelligent question, and I gave him an answer. If Bob was toying with me, he can let us all know, but I don't think he would do that.

The "target" we are talking about here refers to the object ball entering the pocket (i.e., what is the effective size of the pocket). You are thinking about the aim point, AKA ghost ball center. This is different.

dr_dave
01-06-2005, 01:34 PM
<blockquote><font class="small">Quote dr_dave:</font><hr> <blockquote><font class="small">Quote BCgirl:</font><hr>I would note that a considerable amount of detailed analysis of permissible error on various shots is presented in "The Science of Pocket Billiards".<hr /></blockquote>
I have studied Koeher's Chapter 4, and it is not clear to me how thorough his analysis was, because he does not describe how he got his numbers, and he does not provide plots that can be compared to mine. My impression is that he did not include all of the factors that I did in my analysis. One thing that makes me question his results is a statement he makes on page 46:

"The unique thing about corner pockets is that the effective pocket size remains the same regardless of approach angle."

(the italics and bold are his)

This is completely wrong! /ccboard/images/graemlins/frown.gif
To know why, see my Nov'04-Jan'05 articles posted online (http://www.engr.colostate.edu/~dga/pool/bd_articles/index.html) or see pages 60-78 in "The Illustrated Principles of Pool and Billiards."<hr /></blockquote>
I just want to be clear to everybody that I meant no disrespect whatsoever in my message. I think Jack Koehler's book "The Science of Pocket Billiards" is great, and it even served as inspiration for me when I was contemplating writing my book. Having written a book, I know how difficult it is to keep it error-free. I've already found a couple of small errors in my book, and I thought (after reading it several times myself and having many others read my final draft) that it was as error-free as possible. I guess we're all just human after all.

Qtec
01-06-2005, 01:38 PM
[ QUOTE ]
The "target" we are talking about here refer,s to the object ball entering the pocket (i.e., what is f the effective size of the pocket). You are thinking about the aim point, AKA ghost ball center. This is different.
<hr /></blockquote>

Tell me Dave, how can the target be something we cant see. If I am cutting into a bind pocket, how can I aim for something that is out of site. By definition, this must be impossible!

The TARGET is what we aim for.
The ball going in the pocket is a CONSEQUENCE of hitting the TARGET.
Dont you you think?

Q

silverbullet
01-06-2005, 01:59 PM
<blockquote><font class="small">Quote Popcorn:</font><hr>
A straight in shot is not the easiest shot. To a non player and theoretically it may seem so, but it is not. When the rule use to be you shot from behind the line on a scratch. You never set up straight in even if you were shooting the last 9 ball, you almost always created a little angle. I think it may have to do with the way the mind perceives the shot. With a slight angle your minds eye quickly see where to hit the ball and you make the shot. Straight in you don't have a specific target other then to hit the ball squarely straight on and that is very difficult to do and the farther away you get the harder it gets.
<hr /></blockquote>

I would qualify as a non-player, because on a long shot that looks like a straight in, my eye cannot see if it is a degree off(a degree or so cut). On long shots, which look straight, I use an aiming system, for that reason. And also, if the exact center of the cb is not struck on the long straight, even if it is perfectly straight, can also result in a miss.While, it is true that such a mistake can be made due to improper stroke and thus imparting unintentional 'backhand english' on the ball, it can also occur if what the player sees as exact center is say 1/4 tip side: a perceptual thing. So you can have A + B = miss

A- The shot is not really a perfect straight
B- Compounded by not striking the perfect center of the CB

Laura

daviddjmp
01-06-2005, 02:15 PM
I also think a full table straight in shot where the CB is far enough from the rail to put your bridge hand on the table and the OB is about two feet from the pocket is the hardest shot. When I warm up, I hit a rack or two of these with absolutely middle ball (at least I try). Making these shots really does force your stroke to be absolutely straight. Very hard, for me at least, but it is good practice nonetheless-

Jude_Rosenstock
01-06-2005, 02:26 PM
<blockquote><font class="small">Quote daviddjmp:</font><hr> I also think a full table straight in shot where the CB is far enough from the rail to put your bridge hand on the table and the OB is about two feet from the pocket is the hardest shot. When I warm up, I hit a rack or two of these with absolutely middle ball (at least I try). Making these shots really does force your stroke to be absolutely straight. Very hard, for me at least, but it is good practice nonetheless- <hr /></blockquote>

What makes this shot difficult is the distance, not the angle. Trust me, if you're having problems hitting a straight-in shot from five feet out, setting it up as a cut from the same distance isn't going to make it any easier. There is a plain and simple truth here and that is the straight-in shot has the greatest margin of error. It's simply the largest target you'll ever have. There are plenty of reasons why people still miss them and I include myself on that list but the fact remains, it's still the easiest shot in pool. When you're positioning for the game-winning shot, your goal is short &amp; straight. Never in the fifteen years I've been playing pool have I seen a player take ball-in-hand on the nine and set up an angled shot.

Jude M. Rosenstock

Jude M. Rosenstock

dr_dave
01-06-2005, 02:26 PM
<blockquote><font class="small">Quote Qtec:</font><hr><blockquote><font class="small">Quote dr_dave:</font><hr>The "target" we are talking about here refers to the object ball entering the pocket (i.e., what is the effective size of the pocket). You are thinking about the aim point, AKA ghost ball center. This is different.<hr /></blockquote>
Tell me Dave, how can the target be something we cant see. If I am cutting into a bind pocket, how can I aim for something that is out of site. By definition, this must be impossible!
The TARGET is what we aim for.
The ball going in the pocket is a CONSEQUENCE of hitting the TARGET.
Dont you you think?<hr /></blockquote>
I apologize for the confusing terminology. Instead of using the phrase "target size" I should have just stuck to "effective pocket size." The effective pocket size has nothing to do with the cue ball (directly). The effective size of the pocket (and the effective "center" of the pocket) does vary dramatically with angle to the pocket. I hope that is clearer.

Qtec
01-06-2005, 02:46 PM
Dave, when a player shoots, his TARGET is NEVER a POINT in the POCKET, it is ALWAYS a POINT on or near the OB. eg the center of the GB.
Q

Jude_Rosenstock
01-06-2005, 02:54 PM
<blockquote><font class="small">Quote Qtec:</font><hr> Dave, when a player shoots, his TARGET is NEVER a POINT in the POCKET, it is ALWAYS a POINT on or near the OB. eg the center of the GB.
Q <hr /></blockquote>

Why? Do you like shooting balls into rails? Of course the target is the pocket! Let's not get too technical here! Yes, the shooter is looking at the object ball but prior to that, he's determining a target on the object ball in relation to a pocket target.

Jude M. Rosenstock

dr_dave
01-06-2005, 03:05 PM
<blockquote><font class="small">Quote Qtec:</font><hr> Dave, when a player shoots, his TARGET is NEVER a POINT in the POCKET, it is ALWAYS a POINT on or near the OB. eg the center of the GB.<hr /></blockquote>
I agree completely!

A player's target is the center of the imaginary ghost ball necessary to create the desired impact line. This will determine (along with throw effects (http://www.billiardsdigest.com/ccboard/showthreaded.php?Cat=&amp;Board=ccb&amp;Number=168241&amp;page =&amp;view=&amp;sb=&amp;o=)), where the object ball will go. You want to "target" the object ball so it is aimed at the center of the "effective size" of the pocket. This effective size varies based on the angle of the object ball to the pocket. Also, as Bob asked about previously, the "center" of the "effective size" of the pocket is not always the geometric center of the pocket, except when the object ball angle to the pocket is zero.

The diagrams in my Nov'04 instructional article (http://www.engr.colostate.edu/~dga/pool/bd_articles/nov04.pdf) illustrate all of this stuff (angle to the pocket, effective pocket size, effective object ball "target center", etc.) fairly clearly. Please check it out.

dr_dave
01-06-2005, 03:12 PM
<blockquote><font class="small">Quote Jude_Rosenstock:</font><hr>What makes this shot difficult is the distance, not the angle. Trust me, if you're having problems hitting a straight-in shot from five feet out, setting it up as a cut from the same distance isn't going to make it any easier. There is a plain and simple truth here and that is the straight-in shot has the greatest margin of error. It's simply the largest target you'll ever have. There are plenty of reasons why people still miss them and I include myself on that list but the fact remains, it's still the easiest shot in pool. When you're positioning for the game-winning shot, your goal is short &amp; straight. Never in the fifteen years I've been playing pool have I seen a player take ball-in-hand on the nine and set up an angled shot.<hr /></blockquote>
Jude,
Very well stated!

daviddjmp
01-06-2005, 03:12 PM
Yes, they set up a very short straight shot, not a very long one-

dr_dave
01-06-2005, 03:17 PM
<blockquote><font class="small">Quote Jude_Rosenstock:</font><hr> <blockquote><font class="small">Quote Qtec:</font><hr> Dave, when a player shoots, his TARGET is NEVER a POINT in the POCKET, it is ALWAYS a POINT on or near the OB. eg the center of the GB.
Q <hr /></blockquote>

Why? Do you like shooting balls into rails? Of course the target is the pocket! Let's not get too technical here! Yes, the shooter is looking at the object ball but prior to that, he's determining a target on the object ball in relation to a pocket target.<hr /></blockquote>
Thank you, Jude. Very well stated!

Jude_Rosenstock
01-06-2005, 03:21 PM
<blockquote><font class="small">Quote daviddjmp:</font><hr> Yes, they set up a very short straight shot, not a very long one- <hr /></blockquote>

Jude M. Rosenstock

daviddjmp
01-06-2005, 03:26 PM
That shot difficulty increases with more distance-

daviddjmp
01-06-2005, 03:27 PM
At least for me-

Jude_Rosenstock
01-06-2005, 03:42 PM
<blockquote><font class="small">Quote daviddjmp:</font><hr> At least for me- <hr /></blockquote>

That's a complete waste of bandwidth. I can't even believe I wasted the time to scroll down.

Jude M. Rosenstock

Bob_Jewett
01-06-2005, 03:51 PM
<blockquote><font class="small">Quote dr_dave:</font><hr>
<blockquote><font class="small">Quote Bob_Jewett:</font><hr>Did you verify the shapes by measurements?<hr /></blockquote>
Not in detail, just anecdotally with the video demonstrations.
<hr /></blockquote>
Until the shape -- which you will have to admit is very, very strange, like a Batman profile -- is verified by actual measurements, I'll put it in the "tentative result" category. I've thought about what it would take to measure it to a pocket width accuracy of 1/8 inch, and it's not simple.

[ QUOTE ]
I am confident with the analyses I performed. <hr /></blockquote>

Briefly, what causes Batman's ears? Why is the peak at 2 degrees from parallel to the cushion? What determines the relative sizes of A and B?

[ QUOTE ]

<blockquote><font class="small">Quote Bob_Jewett:</font><hr>A related question: is there a single point (or nearly) that represents the center of the target from all angles?<hr /></blockquote>
No. The effective target center varies with entry angle. <hr /></blockquote>
Well, maybe a little, but the target for the corner pocket is clearly the same for the 0-degree approach angle and the 45-degree approach angle. That is, a single point works for those three shots (along each cushion and from the head or foot spot, whichever is nearer). Also the center of the target for the side pocket is a single point for both the straight-in and for the two shots that can barely be made. How far does the center wander from that point?

Qtec
01-06-2005, 03:53 PM
[ QUOTE ]
a target on the object ball <hr /></blockquote> So you agree that the TARGET is the OB and not the pocket? You can only shoot at one thing.

Q

Bob_Jewett
01-06-2005, 04:00 PM
<blockquote><font class="small">Quote Qtec:</font><hr> So you agree that the TARGET is the OB and not the pocket? You can only shoot at one thing. <hr /></blockquote>
Well, in the conversation I was having, the target is the pocket (or somewhere in the pocket). The particular question I was posing is: where is the center of the pocket? I've seen lots of players shoot for the back of the pocket liner (which tends not to work well from some angles). I think it's useful to know where the center of the pocket is -- even more useful than knowing how large the pocket is.

dr_dave
01-06-2005, 04:29 PM
<blockquote><font class="small">Quote Bob_Jewett:</font><hr><blockquote><font class="small">Quote dr_dave:</font><hr>
I am confident with the analyses I performed.<hr /></blockquote>
Briefly, what causes Batman's ears?
Why is the peak at 2 degrees from parallel to the cushion?<hr /></blockquote>
The diagrams and examples in my Nov'04 - Jan'05 articles (http://www.engr.colostate.edu/~dga/pool/bd_articles/index.html) explain the reasons much better; but in simle terms, at shallow angles to the rail (about 2 degrees from the rail is optimal), because the object ball can glance off the rail well in front of the pocket and still go in makes the effective "size" of the pocket much larger.

<blockquote><font class="small">Quote Bob_Jewett:</font><hr>A related question: is there a single point (or nearly) that represents the center of the target from all angles?
<blockquote><font class="small">Quote dr_dave:</font><hr>No. The effective target center varies with entry angle.<hr /></blockquote>
Well, maybe a little, but the target for the corner pocket is clearly the same for the 0-degree approach angle and the 45-degree approach angle. That is, a single point works for those three shots (along each cushion and from the head or foot spot, whichever is nearer). Also the center of the target for the side pocket is a single point for both the straight-in and for the two shots that can barely be made. How far does the center wander from that point?<hr /></blockquote>
As shown in Diagram 3 in my Nov'04 article (http://www.engr.colostate.edu/~dga/pool/bd_articles/nov04.pdf), I measure the "offsets" relative to the geometric center of the pocket at the leading rail edge of the pocket jaws. The offset vs. entry angle plots near the ends of TP 3.5 and 3.6 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/index.html) show how the "target center" varies with entry angle. For a slow shot, the point varies by as much as about 0.6 inches for a corner pocket and about 0.3 inches for a side pocket. I hope that helps.

dr_dave
01-07-2005, 10:13 AM
<blockquote><font class="small">Quote Bob_Jewett:</font><hr> <blockquote><font class="small">Quote Qtec:</font><hr> So you agree that the TARGET is the OB and not the pocket? You can only shoot at one thing. <hr /></blockquote>
Well, in the conversation I was having, the target is the pocket (or somewhere in the pocket). The particular question I was posing is: where is the center of the pocket? I've seen lots of players shoot for the back of the pocket liner (which tends not to work well from some angles). I think it's useful to know where the center of the pocket is -- even more useful than knowing how large the pocket is. <hr /></blockquote>
Bob,
Thank you very much for clarifying this. I'm glad you weren't just trying to pull my chain as was suggested.

In my previous post (http://www.billiardsdigest.com/ccboard/showthreaded.php?Cat=&amp;Board=ccb&amp;Number=173184&amp;page =0&amp;view=collapsed&amp;sb=5&amp;o=&amp;vc=1) I explained how I define the center of the pocket for different angles to the pocket. I know the TPs are very difficult to follow, because I don't include much explanation, but the diagrams in my articles and the plots at the end of the TPs help illustrate the terminology, results, and principles.

In the next few months, I hope to write-up my analyses in greater detail, with more illustrations and explanations, so they might be more understandable. I'll post an update message if and when those are available.

BCgirl
01-07-2005, 10:20 PM
<blockquote><font class="small">Quote dr_dave:</font><hr>
I have studied Koeher's Chapter 4, and it is not clear to me how thorough his analysis was, ...

One thing that makes me question his results is a statement he makes on page 46:

"The unique thing about corner pockets is that the effective pocket size remains the same regardless of approach angle."

This is completely wrong! /ccboard/images/graemlins/frown.gif
<hr /></blockquote>

I think that as a scientist, you should understand that this comment is a fairly reasonable first approximation, but the rotating pocket concept is certainly not the most complete analysis. It is, however, a very useful concept for visualising the ideal target point.

While I think that your geometry approach is valid, it does not take into account the effects of non-ideal cushion reflection, or of english transferred to the CB from cushion contact. It also creates an ideal model of the pocket, from which every pocket will vary to some extent. Small variations in the cut of the pocket may have significant effects on the results.

In the majority of experiments in the Science of Pocket Billiards, as I recall, most of the information is derived from repeatable experiments, using a machine set-up to ensure that human-induced errors are eliminated. From what I understand from previous threads, this is something that you have not done in your own work.

My intention is not to pick apart your own theory, or book, which I have not read. But I do think that when you use a purely mathematical analysis to criticise someone else's analysis, your argument would be very much stronger if your theoretical plots were backed up by accurate and repeatable experimentation in a controlled environment.

After all, anyone who has ever used a diamond system, kicking system, or aiming system knows that it's a first approximation, and that every system and theory is only as good as the extent to which it holds up under experimentation, and across a wide range of table conditions.

BCgirl

dr_dave
01-09-2005, 10:26 AM
<blockquote><font class="small">Quote BCgirl:</font><hr>While I think that your geometry approach is valid, it does not take into account the effects of non-ideal cushion reflection, or of english transferred to the CB from cushion contact. It also creates an ideal model of the pocket, from which every pocket will vary to some extent. Small variations in the cut of the pocket may have significant effects on the results.<hr /></blockquote>
You are absolutely correct. Rail-induced spin and rail throwback &amp; inefficiency were not accounted for directly. Furthermore, these effects can vary significantly from table to table and with shot speed. However, these effects are much smaller at slower speeds (see NV 3.13 and 3.15 (http://www.engr.colostate.edu/~dga/pool/normal_videos/index.html) and HSV 3.8 (http://www.engr.colostate.edu/~dga/pool/high_speed_videos/index.html)). I do account for the effects indirectly with the different assumptions I make for fast vs. slow shots, but you are correct that my assumptions are idealized somewhat.

Concerning pocket geometry, I have assumed that it matches the BCA specifications exactly. You are correct that pocket geometry can vary significantly from one manufacturer (and table model) to the next and based on whether or not the pockets are shimmed. It would take a lifetime to analyze and experimentally determine the exact "shapes" for all possible conditions.

<blockquote><font class="small">Quote BCgirl:</font><hr>In the majority of experiments in the Science of Pocket Billiards, as I recall, most of the information is derived from repeatable experiments, using a machine set-up to ensure that human-induced errors are eliminated. From what I understand from previous threads, this is something that you have not done in your own work.<hr /></blockquote>
Again, you are correct. I have not experimentally verified all of my analyses. I do have online video demonstrations and high-speed video footage that provide some support, but I have not performed scientifically rigorous experimental verifications. The purpose for most of my analyses is to help explain effects and principles that are observable. For example, I suspected from experience that the margin of error is larger for slow corner pocket shots at shallow angles to the rail. My analyses just help explain this theoretically. But you are correct, the only way to know the exact "shape" for a given table would be to perform an experimental study on that table. Furthermore, the shape would be different at every speed. A thorough experimental study would be a daunting task.

Having said all of this, I still think the principles presented and conclusions made in my Nov'04 - Jan'05 articles (http://www.engr.colostate.edu/~dga/pool/bd_articles/index.html) are valid and useful to know, and I think many inexperienced players (and some experienced players) can benefit from the knowledge.

dr_dave
01-31-2005, 11:44 AM
<blockquote><font class="small">Quote dr_dave:</font><hr><blockquote><font class="small">Quote Popcorn:</font><hr>I also don't believe that the difficulty increases significantly as the cut angle increases. It will stay somewhat the same through most of the angle but at a point will increase quickly for a very small range of the angle.<hr /></blockquote>
You are correct. The difficulty increases very slowly as the cut angle increases from 0 degrees and doesn't "increase significantly" until the cut angle starts getting large. Soon, I will add a plot and more discussion to my TP 3.4 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/TP_3-4.pdf) to show this more clearly. I will post an update message to this thread when it is available.<hr /></blockquote>
I just added some analysis and a plot to the end of TP A.4 (http://www.engr.colostate.edu/~dga/pool/technical_proofs/TP_3-4.pdf). The new plot shows how the required cue ball accuracy varies with shot cut angle (for a given distance shot). Also included, below the plot, are some example numbers that show:
<ul type="square"> a straight-in shot is 1.15X (15%) easier than a 30 degree cut angle shot
a straight-in shot is 1.97X (97%) easier than a 60 degree cut angle shot.[/list]
I think most players intuitively know that cut angle reduces your margin of error dramatically. Now, it is clear by how much.

Qtec
01-31-2005, 11:48 AM
So basically, a straight in shot is the easiest?

Qtec

dr_dave
01-31-2005, 11:52 AM
<blockquote><font class="small">Quote Qtec:</font><hr> So basically, a straight in shot is the easiest?<hr /></blockquote>

Qtec
01-31-2005, 11:56 AM
It makes sense to me .

Some might not agree tho. /ccboard/images/graemlins/laugh.gif

Qtec

dr_dave
01-31-2005, 12:07 PM
<blockquote><font class="small">Quote Qtec:</font><hr> It makes sense to me.

Some might not agree tho. /ccboard/images/graemlins/laugh.gif
<hr /></blockquote>
People have a right to disagree; but if they do, I hope they can back up their arguments with experimental and/or theoretical evidence.

HALHOULE
01-28-2007, 10:16 PM
AND IF IT IS NOT QUITE STRAIGHT ???