Conversions for unusual units of time

Once in a blue moon = once every 2.71 years, on average

Once every death of a Pope = once every 12.75 years, on average, considering only the period from 1903 to 2005, given that all previous times occurred before 1900, which is about when being seen by a doctor started becoming more likely to help you than to hurt you.

Once every resignation of a Pope (or "abdication of a Pope") = once every 247.875 years to 495.75 years, on average, not counting Pope Benedict XVI's resignation, and depending on whether it was only four other Popes that have resigned or eight that have. Alternatively, if you want to consider only Pope Benedict XVI and the previous Pope to resign (Pope Gregory XII, in 1415), then you could say "once every 698 years."