We present a method to compare different qualifications for entry to higher education by studying students' subsequent performance. Using this method for students holding either the International Baccalaureate (IB) or A-levels gaining their degrees in 2010, we estimate an "empirical" equivalence scale between IB grade points and UCAS points whereby, for similar students in the same universities and subjects, final degree performance is independent of the type of entry qualification. The empirical equivalence scale suggests that the official UCAS tariff is too generous to IB students in the allocation of UCAS points. We also compare the points of IB students with the UCAS scores of A level students in the same university. We find that the amount that the official tariff is adjusted by universities is approximately correct in the low-to-middle part of the range (IB points in the low 30s). At the top end of the scale, however, universities have adjusted too far away from the official mapping. Oxford and Cambridge are exceptions, owing to their intensive recruitment methods; yet their tendency to ask for very high IB points, but not very high A level UCAS points, remains a puzzle. (Contains 2 figures, 5 tables, and 8 notes.)