In terms of statistics to become a barrister, about 1 in 6 of those who apply in any given year are successful. However, lots of good people take two or more attempts to obtain a pupillage, so obviously your overall chances are higher if you keep applying.
The statistics that suggest 1 in 3 of people who pass the BPTC obtain pupillage are slightly misleading (based on c.1500 people passing, and 500 pupillages each year). Don't forget that there are also transferring solicitors (who don't have to do the BPTC) who take a number of those pupillage spots, particularly in the higher paying commercial sets. If you look at the number who are called to Bar each year, it's actually more like 1 in 4 who obtain pupillage in the UK overall. Ex-solicitors are at an advantage with many sets, so that skews the statistics slightly.
Generally, there are so many variables affecting each individual applicant that it's not worth worrying too much about statistics except as an overall picture of just how competitive it is! I think that it's much more useful to apply for pupillage and a scholarship before the BPTC, and use those results as a yardstick to determine if it's worth pursuing this as a career. If you don't get any kind of scholarship or any first round interviews, I think it's a mistake to do the BPTC. You're better off spending another year building up your CV and then reapplying the year after.
PS The BSB website makes interesting reading to bust a few myths about Oxbridge and the Russell Group. It's more like 50% Russell Group (including Oxbridge), and 50% other universities - though of course this fluctuates in any given year.