@mondaytosunday and @FebuarySmith - in answer to your questions, I had a DS who applied (successfully) to Cambridge post A-levels for a humanities / social science subject with 3 A stars and an A star EPQ. I think I read somewhere that for most humanities courses, having three A stars achieved will guarantee an interview. However, whether this is actually the case or not, they do interview about 75/80% of applicants anyway, so maybe not a huge deal.
This is just my suspicion and I have no special insights at all, but I wouid think they are probably looking for something a bit 'more' from post A-level candidates. They will definitely want to know what they are doing in the gap year.
I can't remember the exact stats, but I think it's something like 60% of humanities students actually at Cambridge achieved 'at least 3 A stars' at A level. So having those grades means they can place applicants within the 'top 60%' of the actual cohort, I would think. But also, the actual subjects are probably relevant - eg. If applying for Classics, they might not be too bothered that they got an A in Chemistry, rather than an A star. Hope that makes sense?
I agree with the poster above who says luck has a lot to do with it and all this talk about 'they know what they are looking for' is just hype.
I think all the DC can do is be realistic about the numbers of applicants per place. Recognise it's a very imperfect admissions process as all colleges interview differently (certainly at Cambridge). Anyone with a few A stars and As could easily cope (academically) at Cambridge - it's not that different to any other uni, just nice buildings, etc. Yes they have to write an essay a week, but it's not as if they have anything else to do! And these essays are just ti trigger discussion in tutorials, they are not graded. Also, they are catered for and don't have all the stress of finding accommodation for the second and third years and all that drama they have at other unis. Also, Cambridge is fairly compact and even the colleges a bit outside the centre are really not far when you think about how accommodation is at other unis.
If there is an admissions test, this will be important. Also look at HOW they interview at different colleges (eg. is there reading material the day before, the week before, none)? This can make a big difference. Also, what are the specialisms of the DoS and what di they teach? HSPS is a broad subject, so if they are more interested / informed in the Sociology modules (for instance) maybe don't go for a DoS who teaches the IR modules. Also, find out if it's two subject interviews, or a general interview and a subject interview. A general interview will be taken by a senior admissions tutor who does not teach that course, so will be much more about the PS, supra-curricular and what they are doing in the gap year to boost their application. Subject interviews tend to just dive straight into a text or some other material, as if it were a real tutorial.
Hope this is a bit helpful going forwards. As I say, this is stuff I suspect in retrospect having gone through the process, but I'm no expert!