Actually ring and pinion ratio is all about diameter -- although not the outer diameter of the gears themselves but the contact area. The teeth is only a consequence of how to mesh the ring and pinion gears w/o having them slip past each other once torque is applied. The two gears could even be conic sections (that is imagine if they had no teeth) and it would still work but would probably slip due to torque. When we set up ring and pinion gears, we aim for a sweet spot between the "toe" and the "heel". The center of the contact pattern (which is dependant on the pinion depth) becomes the effective diameter of the ring gear, the rest of the ring gear towards the "toe" and the "heel", is dead weight. Counting the teeth and dividing is just an easy way to determine the approximate gear ratio, but you can very easily change the gear ratio slightly by changing the pinion depth -- which is why the difference between 4.11 and 4.10 is negligible after you factor in other fudge factors such as tire diameter due to wear, age (ring and pinion settings will change with use), tire pressure, weight distribution (which affects tire diameter), and so on. "Backlash" is then the margin of error between the teeth count and the effective diameters that the gears are using, allowing us to run a gear set that has been labeled 4.10 as really 4.097, 4.103, and so on.