I was told reliably by someone at an independent school in Northen London that given the fact thant the same crowds (i.e. pupils) appear in the exams taken by independent schools in certain areas the true ratio of success of a pupil from the test stage to actually securing an offer in at least one of the schools (s)he has applied to is around 1 in every 2.5. So the odds are not as daunting as they may intially sound. I suppose they transform this statistic in each school into forming their offer policies accordingly plys by taking into account their reputation factor (some schools are aware that they are more likely to be first choices than others, and hence less likely to receive a rejection to an offer they make).
I know another London independent which interviews about 300 out of 600 candidates who take the exam, and they have about 80 external places up for grabs.
What would be a really interesting statistic to know would be the number of offers they normally make per available place. Clearly they offer more places than available because, as noted above, they know that most candidates will have also applied to other schools. Anyone know of any ratios, eg 2 to 1 or 2.5 to 1? Clearly it will be slightly different for different schools.