With the new profile pages, I can now see my own and other users' rare accomplishments in the rarest badges section.
This led me to be curious about exactly how rare these rare badges are.
Would it be a lot of work to display the percentage of users on the site (perhaps only calculating with users who have 200+ reputation) that have that badge next to each rare badge? Or as part of the pop-up info that appears when you hover the cursor over the badge? I have a feeling some of my gold badges aren't actually as rare as some of the silver ones.
No, I don't have any pressing need for this feature. No, it isn't solving anything that I couldn't tediously calculate on my own for every time I look at someone's profile summary. I just think it would be nice.
EDIT: To highlight the significance of this information, according to the query in the answer below I have eleven badges that are rarer than my rarest gold badge on Mi Yodeya. My rarest badges are actually my bronze badges.