With IIRC the ring that Verlat can give you in Verdistis (if you heal him in Aleroth), I got a really good ring the first or second try, saved, reloaded a couple times noting the average was worse than what I had, so reloaded the save with the 'identified' ring, only to find that the stats were different. I had to reload quite a bit to get another ring comparable to the first.