Explaining this could get a little messy. I don't actually think about this anymore if I ever really did. But here we go. If you line up a long cut shot for a center cue ball hit & then shift your whole cue stick laterally so it is parellel to the center hit cut shot & you shoot it, the cue ball will 'deflect' out opposite the side of the lateral stick shift. If the cue ball does not curve back in time or curves back too much, you will miss the shot. Even if it does contact the center hit aim point you may still miss the shot because the spin will 'throw' the object ball in the opposite direction of the lateral shift.
You can not get rid of or minimize the lateral deflection unless you're using one of the low deflection shafts So, in an attempt to compensate for the cue ball squirt, instead of doing a lateral shift you can do 1 of 3 things:
1. move the back hand, pivoting on your bridge hand to move the tip to the side
2. move, slide, shift or lean your bridge (front) hand to the side to move the tip
3. or... this is what I'm pretty sure I subconsiously do, which is to move both a little, kind of pivot the stick, back hand moves in one direction & the bridge hand 'moves' in the other direction.
What happens is the cue ball squirts off 'target' or 'aim' line & curves back. To be successful you have to marry the amount of english with the speed of the shot.
I think I did a fair job of explaining it. Keep in mind I'm only talking about small amounts of stick movement. If you were watching & did not have the cue ball as a reference point, you would probably not even notice. But it is noticable because the tip relocates on the cue ball. I don't even actually do it the way I describe it. I set up on it many times with the pivot already done.
Now as for aiming. When you have decided to shoot a shot like that with some amount of side english, you have to plan for the spin to 'throw' the ball some & make the allowance for that.
It sounds complicated, but so would riding a bike if all of the diffferent components were explained with physics & biomechanics lingo.
It takes some time to get it. But when you see it done and the balls keep going in like I did when I watched the old man from whom I stole my pool, You feel like you just have to learn how to do it. Watching him do the things he did with English was like watching magic.
You do not have to use english to play some VERY, VERY good pool. But to me, that would be like painting a portrait on a normal canvas with a 4" house brush instead of a pin point artist's brush. I hope I gave the info. If you have any questions, you can private message me & I will try to answer them if I can. Sorry for being so long winded.