''Would have been'' is used to re-imagine the past. In reality, you're saying this did not happen at all. (Or at the very least, you're not sure.)
''I was in the school basketball team.'' This is a past event, and a fact.
''I would have been in the school basketball team (if I hadn't broken my leg that year).'' You're just imagining it; it never happened. You'll see this pattern used in Third Conditional.