I've just finished OAA stage 1 and thought I'd share the following:
They said that every online application was given a mark/score based on how good it was. At the moment 30% of applicants have been invited to stage 1 (or have completed it).
There will be an email between 4-6 Jan inviting successful candidates to the next stage.
Last year OAA got 44% of BA's future pilots, and they believe the reason is because of 'head of OAA recruitment lady' - who previously worked for BA. Apparently she knows exactly what BA are looking for and will invite everyone that has potential back for the next stage. (she said "if there are 400 good candidates, then I will see them all", so it doesn't seem like they have a certain number of seats to fill for stage 2)
In response to comments about BA favouring UK nationals: I counted 13 people present at the assessment and about a third of them were from outside the UK.