MYSQL Query - Unexpected result in text messaging database
Your SELECT clauses may not be optimal. I suspect that Count(Messages.SenderID = People.ID) equals the total number of rows in the result set: for each row, Messages.SenderID = People.ID equals either 1 or 0, and MySQL simply counts all the 1s and 0s, and it ends up with a total number of 54 (6 times 9). Try using SUM(Messages.SenderID = People.ID) instead.

By the same logic, I would replace SUM(Case When Recipients.RecipientID = People.ID THEN 1 ELSE NULL END) with SUM(Recipients.RecipientID = People.ID).