You lost me after "In general.."In general the range of angles we experience perceptually and conceptually is usually through 90°. Only 30° are experienced, when seen down the center ball line, on the ball’s surface, from center ball to the edge. To experience the other 60° of angles the ghost ball center line needs to move off the ball’s surface. This fact creates two problems when looked at from the standpoint of throw and aiming.
The first is that the angles perceptually look very much alike in relation to one another but as the graph shown earlier reveals, the throw differences are not proportionate. On shots from straight in to ¾ ball the throw goes from zero to 2°. The second is that perceptually each angle is little different from the next, over the 14° of angles in the quarter and as you shift slightly to increase the cut, the throw increases lessening the actual cut. We feel the cue line shift and think the cut adjustment is enough, yet it isn’t. In the small change between ~10° and 14°, the amount of throw increases a full degree. On a shot of spot shot distance that is a over half inch or a quarter ball’s width at the pocket.
Cueing systems have emerged because of the two facts. When the center cue line moves off the surface the benefit of a physical landmark is lost. Center to edge aiming systems use the perceptual landmarking to set up reference lines then pivot to center. That allows physical locations to be used, not imaginary ones.
Going back to the graph, the 20-30° angle, with a center ball soft stun, increases throw from 3° to over 5½°. That is similar in change to the 4° shift from 10-14°. Roughly the area between about ⅔ and ½ ball contact. The point is that perceptually the difference between the two aim lines makes it easy to end up with a fat hit.
This is not an aiming thread, it’s mostly about using spin to negate throw. Regardless of aiming system to get to the gb line, the throw issue remains. By using a center ball to ghost ball reference, the throw dynamic is the same regardless of how you get to that location.
The inside convergent side application does several things.
The rotating ball decreases throw.
The inside convergent line adds cut to the contact.
And, almost more importantly the perceptual shift is felt as a difference, a definite feeling of cutting the ball is felt so the angles don’t feel like they are so close together in proximity.
By using the midpoint between the balls as the constant convergent point, it’s self adjusting. Where various pivot systems need adjustments to offsets, variable bridge lengths and further adjustments based on distances between balls, those are part of a system. Those gyrations are the process to get to a center ball aiming system that still is looking throw in the face.
Simplicity is the key. I use parallel or contact point to contact point aiming, aimed at the undercut side of the pocket. The system to get to the cb to gb line is unimportant. Once there, locate the midpoint of the distance between the two lines. That becomes the target the tip points at. Now shift the butt only, to the inside, keeping the tip pointed at that midpoint target. Once the new cue line is sensed as going to just pass the inside of the dead center of the ball, that is the cueing line. While it takes a fair bit of time to explain, it is quickly pure simplicity at the table.
Oddly once the midpoint target is set, it’s better to just focus there as that is on the straight stroke line. The perceptual effect and body sense now feels like the shot is half its original distance. Once that sense is felt the stroke through the ball can be more like simply stroking at a straight in shot..
It’s surprising how quickly your body can learn to feel like the line is right. Initially the perspective will be completely foreign feeling. The temptation is to look at the object ball. Trust that the cueing line is right and that all it needs is a straight stroke, avoiding spin. You may have to close your eyes just to get rid of subconscious cue adjustment related to visually holding onto the ob as the target, instead of the shot line midpoint. The line the cue is pointing should be the only concern. In a short time a connectedness is felt between the shot line and the ball going into the pocket. Perception calibrates and the sub/unconscious adjustments no longer occur.