I live in a grammar county so no grammars are super selective and even have a smattering of middle achievers. I have looked at the results for my area. They seem to follow instinct on which is a good school - more or less!
All the 4 grammars are above average progress 8. One out of 7 secondary moderns is above average (a C of E selective secondary modern) two are average and the others below or well below. So it is the grammar school children or the church selected children who make the most progress.
I would suggest this is largely down to the majority of the secondary schools just not being very good and really having problems getting their lower attaining pupils and PP pupils to make good progress. There are few PP pupils in the grammar schools but where there are, they make excellent progress.
It is often thought it is more difficult to get good progress in grammars but this is not the case here. There are relatively few privately educated children going into the grammars. I would not have thought grammars could just make up a KS2 score though but I am not sure about this. I think, here, that the grammars are largely outstanding schools and only one secondary is. All the others have been in and out of RI or worse and it shows!