Your mind can recognize a half ball hit exactly the way it recognizes if a flight of stairs is the proper pitch you are used to seeing all over the place or if it's too steep or too shallow.
Work on this skill and you will have a pretty good reference for a ton of shots that come up.
Break the balls and look around until you see a shot on any ball into any pocket that you think is half ball. It can be right, left, back cut, corner pocket, side pocket, short, long or anywhere. Then shoot it concentrating on the half ball hit with no regard to position. Then look around from where the cue ball landed and find another one. There will be tons of them on a crowded table, there always are. If they don't look perfect but close shoot them half ball anyway. Did they go into the side of the pocket you expected? Did they miss as expected? Once you can visualize this accurately and confidently you're on your way to much better potting. Everything else is just a slight adjustment except the steepest of cuts.
Once your mind is trained to see these 30 degree cuts you will have a foundation for calculating aiming from a "home" aim point. There is no better feeling than looking at the cheese and realizing it's a perfect half ball hit to a pocket.