What are my chances at acceptance to Oxford PPE if I have the following:
1580 SAT
800 Math 2
800 US History
8 5’s on AP exams including (AP Euro, AP US History, and AP Microeconomics and AP Macroeconomics)?
In addition, with this profile, what TSA score would probably needed to secure admission?
There is no score, and no set of stats that will ‘secure’ admission. Applicants with TSA scores in the 86-90 range (Part A) and 81-85 range (Part.B ) have been turned down after interview (the numbers with scores higher than those are too small to be meaningful). And even applicants with TSA scores as high as 76-80 (Part A) and 81-85 (Part.B) have not been invited to interview. The break point is in the 66-70 range: at that point it’s about 50:50 for interview invitations.
Irl, a TSA score over 66ish + your stats and a strong LoR is likely to get you an interview invitation, but after that all bets are off. You can assume that all interviewees have very high stats & TSA scores, and are considered strong applicants going into interview., yet roughly 2/3 of them will not get an offer.
FWIW, in the 2016/2017 application cycle 605 of the 1983 PPE applicants were non-EU internationals; they received 175 of the 705 interview invitations; and 53 of the 274 offered places.
As @Conformist1688 indicates, Math is seen as an important component. Although it is not required, 93% of successful applicants in the 16/17 cycle had maths to A-level or comparable.