Once you start figuring out the elastic collisions with the rails, there's even more to consider. Rails are positioned such that the balls strike them on their northern hemispheres. Because the rails are a wedge, the ball will get pinched between the rail and the table. To understand this collision, you need to take into consideration the rotational momentum of the ball. This is easier to solve when it is a completely orthogonal collision with no lateral rotations.

If the ball strikes the rail on an angle, the rails twist to absorb the impact and will recoil with a force that isn't just a simple reflection, but that also has a force vector tangent to the ball and back towards the origin. This directly affects the spin of the ball when it leaves the rail.

Combined, a bounce off the rail is a very complicated collision. The net result of which has balls that strike the rail at lower velocities closely matching a reflection, but if struck with a higher velocity, the reflection straightens out into a bounce more perpendicular to the rail.

In short, the rails are highly dependent upon the velocities at impact, and perhaps more so than at break, are affected by rotational momentum.

That's why I always open pool games with a full-strength shot. Now there's SCIENCE to prove it.