I would agree with lefty1 in that if you want to lease an apartment for the following year that you need to begin this process in September as most of the preferred locations fill up fast. Most students do this in groups of students as many of the larger apartment complexes have apartments that house 4-5 students (some smaller number apartments are available but are usually more costly). So you really need to have a group of students who are willing to commit to live together or be willing to pay the monthly rent for the apartment with fewer students.
It appears that for upper class on-campus housing a student can apply as an individual or as a group of up to 4 students. It was not clear if the group of students would only be only eligible for one lottery pick or if each student in the group would be eligible for a lottery pick. I guess this needs to be clarified. If each student in a group would be eligible then, at least statistically, one’s chances would be better applying as a group. .