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@gbj_tester
No, width has nothing to do with it. It just happens that a pair of sprockets connected by a chain will have their axial separation distance changed by ¼ of a chain pitch for each extra tooth added to the total. This is because the circumference of the sprocket increases by a whole chain pitch, but only ½ the sprocket is taking up chain, and the extra chain taken up is divided ½ and ½ between the upper and lower straight runs. It's not exactly that unless both sprockets are the same size, as other arrangements have more than 180° of chain wrap on the larger sprocket (and less on the smaller) and the straight chain runs are not parallel with the line connecting the two sprocket axes, but for the normal range of bicycle gearing and chainstay length, it's close enough. If your change makes the difference between chainring and sprocket smaller, the hub axle movement will be slightly back from the approximation, and vice versa, e.g. going from 48/18 to 48/19 will move the hub axle forward a bit less than ⅛", whereas going from 48/18 to 49/18 will move the hub axle forward a bit more than ⅛". The error in these cases is of the order of 0.02". This is irrelevant for clearance purposes, but handy for dialling in magic gears.