I would think it is not symmetrical because of the friction induced spin from hitting the rail, the rail forces against the ball after it hits rail, the slide of the ball after it hits the rail and forward arch on the cue ball as the forward roll after it hits the rail wears off, x's that by 3 as it hits each rail.
Place a ball on the table against the rail. If you roll the ball to the end rail on a 9 ft table how far did it roll? It rolled 97 3/4 inches and not 100 inches. You can get this distant by measuring from the front edge of the ball to the edge of the opposite rail. Or you can measure the wear grove that shows where the base (tangent line of the center) of the ball always is from the edge of the rail.
When you do the same on the short side a ball will roll 47 3/4 " it does not roll 50 inches.
Think of a car that has its back bumper against a pole and the space between that pole and another is 30 ft. If the front bumper hits the other pole the car did not travel 30 ft. It traveled 30 feet minus the length of the car. So when the CB rolls around the table it is not traveling on a surface that is 2 times its width.