I think that's because it's not pure lottery. First, everyone is ranked by seniority and then grades in descending order (i.e. people with 12 averages get top pick and then 11.9, 11.8...etc.), and then I guess there is some sort of lottery between people of the same average maybe? And that's why people with higher averages are more likely to get into Keyes, which is a popular pick.
Citation:
"
I'm a returning resident and didn't get the room I asked for. Why not?
The room was probably assigned to a student who was higher on the priority list for room assignments. Student staff and IRC Reps are assigned rooms first, then student on the Dean's Honour's List
according to year and academic average, and then students by lottery number
."
http://housing.mcmaster.ca/Residence..._FAQ.html#16_1
Keyes & Bates are very popular amongst upper years, so I would also say you are less likely to get in, and much more likely to get a single room.