Re CAT scores, I agree with everything @LondonGirl83 says. Most importantly, CAT and ATOM scores are not interchangeable. CAT4 uses four 'batteries' to test: VR, NVR, spacial and quantitative; ATOM mock ISEBs tests in maths, English, VR and NVR. The simplest way to distinguish them is ATOM is more about attainment whereas CATs are more about intrinsic potential.
In theory, you can't tutor for CAT4 but I think scores can be improved on any computerized test with enough practice. However, I don't think it would be useful to attempt to increase a child's CAT score artificially, as one of the key purposes is to benchmark their score against under-achievement which can uncover things like SEN.
And despite the clever marketing, we shouldn't make the assumption that ATOM is directly comparable to ISEB. For DD, we used ATOM for a few weeks before she sat the real ISEB; however, after a while the same questions came up on ATOM which made DD's scores inflate beyond what she would have achieved in an unseen test. So that was the point to pull the plug!
I think the information up the thread about average SAS scores for those selective London girls' schools is probably about right. SAS scores for the intake in SW London independent schools will be above the national average for all kinds of reasons, but it's unrealistic that a whole year group would score above say 135 on CAT4 tests. There will be a range of ability.
Like others have said, I agree that there will be a lot of bright children this year who slipped through the cracks in the process which is desperately unfair. Hopefully there will be a shakeup with waitlists in the spring...
One thing that strikes me is the fundamentals of demand and supply for London independents haven't changed. i.e. there hasn't been a massive influx of extra children into London. If anything, due to the pandemic, many families have left London (although conversely, a few parents have moved their children to indies because of patchy provision in some state schools). Therefore the higher number of candidates this year must be primarily down to parents applying to multiple schools - and as we all know, they can only go to one school!
Sorry about the rant! There is so much mis-information on MN and other sites about the distribution of cognitive scores, so I just needed to unload that here... 