If fee to grade ratio is the primary measure of school performance, good state grammars will come out miles ahead. QE boys or Henrietta Barnet results are far better than Eton or most other independent schools in the country with 0 fees.
But it's not really a good benchmark - the fee is mainly a function of costs (staff, facilities and so on) while result is mainly determined by how selective the school intake is.
A specialist non-selective (or less selective) private school may have high cost (say, due to high teacher to student ratio and/or specialist sports facilities), and not so stellar result. That doesn't mean it performs poorly, it clearly meets enough parents' needs to make it a viable.