Originally Posted by Russ Roth

And both of you would be wrong. The chain doesn't "digitize" anything. Toss on 4 different 16t cogs from different brands and see what the results are, high end brands will give you more consistent results, cheaper brands less consistent. For a deeper dive look into bmx fractional gearing which over emphasizes the differences, but when you have kids who are trying to get that 1/2" longer gear inch a 16 1/4 cog can do the job. There's no 1/4 tooth, they've just cut the valleys shallower to add the difference. Example, https://identifybmx.com/products/5-bolt-fractional-gear BMXers get deeper into it than any other sport and the chain isn't digitizing anything. The same issue exists accidentally when trying to keep a kid's bike within an allowed limit. When they say 19' 10 1/4" they really mean it. Absolutely, tires make a difference, but so does the rest of the parts, it might not even be a quality difference but simply that different manufacturers have different standards on where the valley sits, but that's what really determines the real diameter of the cog.