Lots and lots of fail in here. One tooth usually moves the axle by less than 1/8". Going from 14t to 17t will move you further than going from 18t to 21t. Because the relative change in size of the smaller cogs is bigger than the larger cogs.

On my kilo with the stock chain length & sprocket (48), I've run from 15 to 19 (with 23c tires) - and could easily still fit with a 14t cog, but that'd be way to many gear inches. Barely any clearance with the 19t and the tire / seatpost, but it looks sweet. btw - after all those sizes, I now run 48/17t (whatever GI that is....) and not for the skid patches, honestly.