And I just skimmed Nil's message that you posted ... it seems that he wants yet a third behaviour, where counts get converted into means in some way that's appropriate for what he's doing.

This is the mess: everyone wants to store 2 or 3 or 4 numbers, give them similar-but-slightly-different meanings, and have them be converted to one another using various application-specific formulas.  

Its not clear how to set this up so that everyone gets what they need.