There probably is an element of luck….and bad luck in your case.
They are probably looking to meet self-set quotas of offers from different types of school, with different A Level predictions, international,home, contextual etc. And even with an excellent PS there could be too many of your type of application.
The only thing re PS that people sometimes suggest, is that you need to state what you’ve learned from your wider reading etc, or where there is debate, which argument you think is stronger and why, and what further reading the earlier reading has led you onto. So you need to comment on the wider engagement and not just list it. At be you did all that or maybe you didn’t.
But ultimately you didn’t do anything wrong. You clearly have a strong application. You’ve got as St A offer and got to the interview stage at Oxford. Your PS can’t be too weak can it!
Was Durham your favourite behind Oxford? It’s hard if that’s the case. Will you go to St A if the others don’t come through?
As you know, Econ is more competitive than any5i g else at the moment. You are an excellent candidate and there are just too many like you. Some get lucky and get the offer and some don’t.
And I do think there’s a numbers game to offers too. They will give some offers to those with just one A star or 2 A stars and reject some with all A stars. I do think they have to consider how likely someone is to accept and firm their offer…and those with the very top profiles and Oxbridge applications might choose somewhere else, whereas those with maybe 1 A star or 2 might have less options and firm Durham. There’s a lot of complicated number crunching and probability rating of applicants …it isn’t simply that the very best X number get an offer. And that’s hard to take if you know people with lower grade profiles who got offers when you didn’t. And it won’t be the case they all had superior PS. Sorry this happened. Hope LSE comes through.