I was trying to figure out CTE. I met someone at the Chicago AZB Meetup (Mantis99) who showed me the pivot. I was aiming with the edge of my stick at that time. It was startling.
I noticed that if I aimed the outside edge of my cue (so cut right use left edge of cue) at the contact point through the center of the CB and then pivoted I would make the ball in the center of the hole instead of sometimes hitting the edge of the hole or even rattling the shot.
I used to just aim the center of the cue at the contact point for straight-ish shots and then the edges for cuts around a certain amount. Then I added points in-between. So instead of aiming the edge of the tip at the CP I might aim the 2 o'clock mark at the cp. Etc.
It worked well but it did require a bit of judgement to figure out. Once I added the pivot then it just became edge to CP and pivot. The pivot isn't an objective 1/2 ball though. I don't know if the perception changes it or experience dictates how far to pivot but it just works. It kind of snaps into place visually.
I've figured out that usually I end the pivot with the center of the cue aiming at the center of the CB and the center of where the ghost ball would be if I just lay my cuestick down and look at it. But the angle of my stroke would add just a little inside english. So that's what I expect to be basically the perfect place to aim.
But when I'm doing the pivot it looks like it's just pivoting on the CB. Which I think is a perception thing.
Why a little inside? Same reason pro golfers don't play a straight ball. If they are playing a fade and they hit it a little off it will either be a little less fade or a little more fade. Both of which they can allow for on the course.
If they hit a straight ball and hit it a little bit off - it could go a little right or a little left. Either one can cause problems. The worst shot a pro can hit is the old dreaded "double cross" - meaning they were trying to play a fade and hooked it instead. I think it's the worst shot for pool players too but since most players try to play "straight" they don't even really know what happened except that they missed the shot.
Pool is the same way. If you are aiming to allow for a little deflection then if you hit a little more or a little less you'll be fine. Because the deflection will still work to offset the throw on the side you choose (a little inside).
If you try to hit it straight and slightly mis-hit you can hit it either too thick or too thin. Meaning that you'll have an unpredictable result with throw + deflection. So you could miss the ball completely. On straight-ish in shots you could hit the ball on the wrong side and get the wrong position or even follow the shot in. Even if you make the shot. I think aiming straight shots by aiming center CB to center OB is the worst way statistically to shoot them. I have much more success using a pivot. Like 9-10/10 instead of 5/10 for a full table straight shot. I was playing a guy 1p the other day and he kept leaving me trap shots...straight in stuck on the end rail...and I kept drilling them in using exactly the pivot system you've described here. He got very upset with me.
On the other hand, if you're shooting a straight in shot and you play for the CB to deflect a certain way - even on a straight in shot - you are putting your errors on the same side of the shot so you are much less likely to miss the shot and much, much less likely to have the CB do something unexpected whether you make it or not.
I suspect that CTE is similar to what I'm doing but because I aim at the CP instead of the reference points it's easier for me because I never have to try and figure out what the reference point might be. I can't wait for Stan's book to add to what I've already figured out.