This is the cause of jumping balls when shooting draw shots for me. I found a while ago that I had developed a "clutch", tightening up my grip and yanking up my elbow at the very last minute before contacting the cue ball. Up until I hit the cue ball everything looks fine and my grip is medium-loose, but at the moment of contact it all changed dramatically.
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This is the most common problem that I've seen from teaching. Although I'm not teaching any longer I believe it still is the most common fault. Once that grip tightens up it sets off a chain reaction which include moving up your upper arm and shoulder. It's easy to see.
For some it varies to a degree including a rushed backswing and fast forward progression. Nothing can help once it's set in motion. Rush back and you will start forward to fast. This alone makes the grip want to tighten just to hold on to the cue. Remember slow back and slow forward, it varies from player to player but it simply means slow down.
I think the key is the player just isn't sure or positive what they want to do. Or they do know but it may be to much for their current playing level. If any doubt creeps in then we do what is common, react. That reaction is not going to be a nice fluid stroke "through" the c/b. It will be more similar to what I call "A Clean and Jerk". LOL
So you start back from square one, set up short draw shots (ball to ball) and increase the distance you draw each time. When you mess up the distance go back to where you have control. Its nothing new, there a variety of drills to build on. Then increase the ball distance etc. Once your fairly sure of what you can handle use that as a measure during competition. If you try something over your head you'll be sure to end up back or near where you started.

When you play within yourself it sure makes the game more fun. Use that and the drills to build your confidence. Then you'll start seeing improvement because your hitting the c/b exactly where you intended. I don't think taking a diviot out of the table is in anyone's wildest imagination of being even remotely close to where you started at address.
Rod