The reason some Oxford colleges admit a higher proportion of state-school students than others is that a higher proportion of their applicants come from state schools. This often reflects the mistaken belief on the part of applicants that a state-school applicant must have a better chance of admission at a college that already has a high proportion of state-school students. Simple arithmetic shows the error.
I have always argued for post-qualification admissions, no interviews, and raw A-level scores; I have got nowhere and do not expect that to change.
Warden, New College, Oxford