There are the Grammars and then there are the academies of course. Have you factored these in?
The distinction I have made is faith school vs non faith. There are grammar schools and academies in both of those categories, so yes they are included but not separated out as this wasn't the analysis I was giving.
I presume your argument is that grammar schools and academies are more affluent (if so I think it is up to you to provide that evidence), but if so that doesn't really help as although there are faith academies and grammar schools these types of school are more common, proportionately, in the non faith sector which would make the distinction in terms of affluence between faith and non faith schools more stark still.
Academies of course seem to be able to be more selective in which pupils they retain.
Confused statement, and also not true.
Firstly do you mean the pupils they admit, rather than retain.
Secondly, although there are some academies that are partially selective (they cannot be fully selective) that isn't common. Most secondary schools are now academies and many primaries are too. Most aren't selective at all. So as an example - all the secondary schools in my city are now academies - none are even partially selective. Many of the primary schools are academies - none are selective.
The schools my three children attend are both academies - neither are selective.