I shouldn't comment on HN from bed after an evening out. Of course the rule of proportion is the wrong approach here. Even though the dimensional analysis seems to work out, it's still wrong. Bad case of thoroughly addled brain, this is supremely embarassing, and too late to delete now. I should be able to do this in my sleep, but I clearly wasn't. Seems there's not enough probabilities in my day-to-day, I will make a point of adding a few to fix my intuitions.