Unless the number of levers is difficulty-dependent (in which I need to man up and try for more gold badges) or else I have been godly unlucky so far, I dispute that statistic. I don't recall levers appearing at all in cave or arena layouts, and it's not uncommon to find zero on a given level of any other type.
This feels like the Aurora Medallion all over again, except as well as luck you also need to continually take risks with your serious characters. Forget that, my 20/40 medals right now are nicely even anyway. :P