Statistics here, which give you the realities rather than the myths:
www.ox.ac.uk/about/facts-and-figures/admissions-statistics
senua's 'bit of a lottery' is again frustrating. In my subject, we get all candidates to sit an aptitude test. We look carefully at their exam results and predictions. We look at a piece of written work they have sent in. We look at their UCAS form. When looking at the test result, the written work and the UCAS form, we pay careful attention to the contextual data we have on their school and any other contextual 'flags' (as per the Guardian article). We then rank candidates on the basis of that evidence so that we can see who to interview. We then give the top candidates at least two interviews. The interviews model the format and intensity of tutorial teaching. We use our professional experience to select those candidates who show the most potential to do well in the tutorial and collegiate system - why would we do otherwise? Accountability is provided to some degree by our subsequent exam results. My Faculty also follows candidates through the system to see how various bits of admissions data correlate with final exam performance (which again informs my decision-making as a tutor).
How might we make this more transparent or predictable, given that many many of our applicants are very able and well qualified? It may look unpredictable from the outside, to people who don't see the whole cohort of candidates, but it seems odd to think that we are conducting a lottery (we don't think that other professions do this?).
It must be so hard to go through that process, as a very very talented and high achieving applicant, and not get a place. Easier to blame the system rather than accept that you didn't make the grade (though I do accept that we make such fine-grained decisions that this is not a perfect system - how would YOU balance potential against current achievement?). I've seen it at close hand both when I was an applicant and now from the other side. It must be so hard to accept that you were great, but that others were yet more exceptional, either in terms of their achievement or their potential. This produces zero's 'critical mass', which then puts many candidates off.
If you look at the admissions statistics, the lack of state-school students is largely a result of a lack of state-school applicants. We do lots of outreach work to try to change this. What else should we do?