Okay, let's elaborate on what Bradshaw posted.
First off, when dealing with balls being pocketed you're dealing with the forces of forward momentum. When pocketing balls, you're requiring the pocket to change the angle of a moving object, that requires a greater force needed to overcome the momentum of the moving object, being the object balls.
If you had zero down angle, or a 90 degree down angle, depending on how you want to look at it, with the forward momentum force of the object ball hitting the inside pocket angle, with no down angle at all, the forward momentum force of the object ball would in fact cause the object ball to jump straight up out of the pocket and off the table, because all that energy is going somewhere if its not contained inside the pocket.
Now, downangle is actually another word for deflection in the case of the pockets. When you add a negative down angle, meaning a tilting back angle to the pocket facing, what you're essentially doing is creating a wall that when the object ball runs into it, the ball is deflected, or driven down towards the slate. When this action occurs, the speed of the ball is greatly reduced, and that reduction translates into the balls sitting on the pocket shelf. The greater the down angle, the higher the deflection result. Diamonds use a deeper shelf on their 9fts than most other 9fts, so they use a 15 degree down angle. Brunswick uses a 12 degree down angle. The difference between the two is the Diamond down angle helps assist the object balls to deflect deeper towards the throat of the pocket, trying to help pocket the ball, but at the same time, the deeper down angle also exposes a little more slate shelf for the balls to sit on when they come to a rest.
So, if you used the Diamond 15 degree down angle on the typical GC pocket down angles, they would cause the pockets to play bigger by deflecting the balls deeper towards the throat of the pocket, but with the shorter shelfs, balls fall in much easier!
Nose heights can vary anywhere from 1 5/16" to 1 3/4" so thats why the nose height has nothing to do with how the actual pockets play, and requardless of how thick or thin the rails are, the down angle in the pockets serve to do the same thing requardless of who made the pool table.
Then the other factor that can screw up any down angles from working correctly, and that is the use of soft facings and soft cushions. The combination of those two together can make pockets play so badly you end up with the Olhausen pocket rattle!