Intake is key. I positively hated school through to 16 when I then went to a separate Sixth Form College to do my A-Levels - and suddenly all the knobheads were gone and I could actually enjoy myself for the first time.
You always get knobheads, no matter the intake. If 3% of people are knobheads, with a class of 30 there's a 60% chance of having at least one knobhead. With a class of 20 it's 46%, with a class of 15 it's 37%.
You seem to be assuming that admissions is based on a lottery and expulsion cannot occur.
You might note that at what are considered "good schools", not only are neither of those things true, but trying to implement either would cause the school to be quickly abandoned.