I don't think there is any 1 floor that has a higher percentage than others. My guess would be floors 3 and 4. If a large balcony is important, request it. And while there may be specific room numbers that have been reported with large balconies (can't think of a specific one off the top of my head), it may be the wrong room size you are looking for anyway.
I wouldn't request a room number, the chances of that happening are slim to nil. If someone checked in 2 days before you and was assigned the room with the large balcony but doesn't check out before you do, there's no way for you to get it.
Long story short; if large balcony is of interest, request it. But keep in mind, that it's just that...a request.