Thanks for all of the responses.

I agree that this discussion is somewhat academic and in the real world cog gapping comes down to rider preference. It is just simple math, but this thread did give me the light bulb moment.

In most cases an incremental increase or decrease when determined as a percentage it is an easy and straight forward calculation. If you ride at 10mph and increase by 2 mph the increase is a simple 20%. You pump up a tire to 100psi and a week later it is a 90psi, the decrease was 10%. The "from" is always a the denominator and the incremental (or "to" value) is always the numerator. Easy peasy. That works well because increase values are greater and decrease values are smaller.

But with a freewheel/cassette the smaller the cog the greater the increase in ratio, gear inches, and speed (at a consistent cadence). Going from a 14t to a 12t results in a decrease in cog teeth but an increase in ratio/gear inches. It would seem that using gear inches is the best method.

However, the result is the same to the gear inch "from" calculations if the difference in cog teeth is divided by the number of teeth in the "to" cog.

Upshifting 14t to 12t when 2 is divided by 12 (to) = 16.7% and 87.93 divided by 75.37 (from) = 1.167 (16.7%). It also works with downshifting 12t to 14t when 2 is divided by 14 (to) = 14.3% and 75.37 divided by 87.93 (from) = 0.857 (14.3%).

John