"If the intake of a school is in the bottom 5% but by the time the kids leave school they are in the bottom 25% then the school has increased their expected results by a factor of five which is miraculous and implies incredible teaching"
But again that depends on the stats you use. What does bottom 5% mean, for example? And bottom 25% again? And 5th percentile to 25th percentile is not a factor five, that's meaningless. It might be that such a change puts the school in the top 0.1% (just for random example), which means that the school is more effective BY THAT MEASURE than 999 out of 1000 schools.
And it's unlikely that the teaching is miraculous/incredible. Good results come from good management. And in particular, when you have known stats to target then an effective management can work directly on those stats. The school's management doesn't have to say 'Hmm, Joe wants to be a car mechanic, he should do X, Y, Z', it can instead say 'If we put Joe in lunchtime GCSE English crammer classes, then that should boost him a grade and add 1 point to our value-added bottom line'. That doesn't mean the school is doing a good job by Joe, necessarily.
Of course in reality the schools that do a good job on stats are usually teaching well as well, and on top of that good results will attract a better intake.
"If the intake of a school is in the top 5%
and by the time the kids leave they are in the top 10%
then the school has allowed half of its pupils to slide back significantly
so is failing them and clearly not helping them reach their capacity
the kids are above average
but the school should be graded below average for teaching"
Or it might be that the school doesn't bother to target the stats directly, because it's complacent, because of it's intake. The second school likely has very good teaching and teachers.
If your child is of low ability, then the first school is almost certainly better. But if he is of high ability, then the second school is more likely to be appropriate, because the curriculum is more likely to be appropriate for a high ability child.
It's all very well to say 'this school is doing fabulously for value-added' in respect of a school with low GCSE pass rates, but the problem is that the parents posting on Mumsnet (or similar) are disproportionately of high ability, because parental interest is a good predictor of academic success.
You have to look EXTREMELY carefully at a school in the first category if you child has high ability, because if most of the intake is of average + below ability, then it might not cater for high abilities. It might do, but it's not essential, in order to show up as doing well by value-added - they can achieve that by catering for the 90% of average + below pupils, and let the high ability coast.