I think you can figure overlapping contact from the speed of the cue ball and the contact time. After first contact, the direction of the cue ball and its speed will be changing to the new path, so it's a little complicated, but you can take an average to determine how much it will move towards the other ball during contact. The time will be about 0.1 millisecond. If the cue ball is moving towards the other ball at 1 m/sec on average during the contact time, it will move about 0.1 millimeter, so any shot within +-0.1 mm of the exact center will result in overlapping contact. That's for a medium speed shot. A slower shot has to be more centered because the contact time will be about the same but the average speed sideways will be smaller (and directly proportional to the incoming speed).