The Snidely Whiplash Inverse Proportionality Theorem of "Family Plans"

I wish this blog were not anonymous because I would dearly love to have this medical theorem named after me. I'll do the next best thing therefore and name it for my favorite arch-villain, Snidely Whiplash (click above to learn about him).

I don't know why it irks me so much, but when a nurse comes to tell me that there is a "family plan in room 12" my heart sinks in my chest and I think of stabbing myself through the eye with a pen to lessen the pain I already feel.

A family plan means that there is more than one patient from the same family in the room. The 'reasoning' seems to be something like this, "Junior has the sniffles, we can go the the ER for free and we don't have a regular doctor, let's get the whole clan checked out 'just in case we might be getting sick', plus we can get a work note."

So without further ado, may I present the Snidely Whiplash Inverse Proportionality Theorem of Family Plans (the result of a placebo-controlled double-blind study spanning eight institutions, with approval of their respective institutional review boards, and with and n of over 10000 and p value way less than .05):

The chance of any one patient in a room actually being sick enough to require a prescription is inversely proportional to the number of patients in the room. First corollary, the chance of any patient in the room being sick enough to be admitted to the hospital is proportional to the inverse cube of the number of patients in the room. Second corollary, the chance of me ever seeing a dime for the bill generated from the "family plan" approaches the asymptote of zero if the number of patients in the room is greater than two.