That is a great question on the O.D. No one has really asked that before.
I’ve found that different O.D.’s have “sweet spots” for ring sizes.
1.2″ O.D. (half dollar 1.7 mm thick) is great for men’s sizes from 9 – 14. You can go bigger or smaller but the pattern can become distorted if you do. Also, the ring will become much thinner when stretched more and thicker when reduced more. .96″ O.D. (quarters 1.36 mm thick) work well for woman rings size 4-8 or so. Same issue when stretched or reduced past these sizes. 1.5 ” O.D(silver dollars 2.62 mm thick) work well for size 11 plus. Up to 25 or even a woman’s small cuff bracelet.
I guess the O.D. is designating the general “mass” of the ring in conjunction with the I.D. and thickness. Thickness is also a consideration. I’m thinking 9 gauge for men’s because a man typically wants a good hefty ring. This may be on the thicker side but I am assuming a thinning of the metal when you roll the pattern. If you etch it on, I’m wondering how that may feel. The cut side or hole side of the ring will be about 1/3 thinner due to stretching, leaving 2 mm of metal. Before you order the silver, you may want to experiment on some copper to see what you like in regards to thickness? Can you roll the sheet yourself to a thinner gauge if need be? I would say your safe with a minimum of 1.4 mm for woman and minimum 1.6 mm for men.
So, small O.D.’s cant be big rings without massive distortion, thinning and narrowing of the band. Large O.D’s cant be smaller rings without distortion, thickening and widening of the bands. There is a sweet spot for O.D’s, band width, and thickness in regards to ring sizes and patterned metal.