Hampton has 160 seats at 11 plus. Out of this 40 come from Advanced 10 plus and 20 from Hampton Prep school. Which makes it 100 seats to complete out of 700/750 students who gave the 11 plus exam. ( This is straight from head masters mouth !)
My feed back from my son who wrote all the schools
St pauls and Hampton had the maths paper of good or higher standard. YOu need to be at a much higher standard
Hamptons strengths are maths, chess computing. So is St Pauls.
Hampton and St Pauls set their own papers
KCS had papers from GL assessment board. Hence much easier.
KCS / KGS maths papers were so easy ( which makes it difficult in the sense you need to be a top scorer to be called for interview - like scoring 45/50 eg)
My son got Hampton 11plus, KCS 11 plus, St pauls( 13 plus) reserve list but DID NOT GET KGS ( 11 plus) . Was a bit shocking. We did not care much as we never wanted KGS. did not fit in with our requirements.
Interview can be a game changer to get the place or not
I kind of tend to agree with @Summerma in some aspects
Also at the end of the day, luck and a bit of lottery plays a role.