Bear in mind that a PAN of 150, and 162 girls placing them as first preference does not mean there are only 12 girls who placed it first and did not get it. There will be plenty in the 150 who have been allocated places that did not place it first on their CAF. For instance, Pate's qualified 230 children and most (but not all) of those will have put it first on their CAF. A number of them won't have got it (I know at least 3 personally) and so will have been allocated their 2nd preference school, which (if they were girls) may have been SHS, DRHS,Ribston or Crypt, for which they will have been relatively highly ranked. I also know of someone who put Denmark Rd first, but didn't end up getting a place, so was allocated her second choice, SHS. And so on. They will be allocated places before those who are ranked lower, even if those others put SHS first on their CAF. Therefore there will be more than 12 of those that put it first but did not get it.
That said, you are right that sometimes schools do make a mistake and effectively 'run out of children'. That happened to Crypt last year (even before March 1st) and to Pate's a couple of years ago. In both cases they hadn't qualified enough children, so had to go back to people after March 1st and 'qualify' a few more, encouraging them to apply (for Pate's it was only a handful, but for Crypt they qualified an extra 200 and still took lots on appeal). Since then Pate's have increased their qualifying rank to 230, and Crypt increased theirs from 600 last year (originally) to about 925 this year, and both seem to have avoided the problem happening again.
It's fascinating and unpredictable. No one seemed to expect that SHS would need to go so far down their list on March 1st this year. Whether that is because there has been a 'swing' back towards DRHS and Ribston, and of course Crypt taking more girls (we don't yet know how many this year), or whether as someone else suggested, there were more people that shared with SHS- perhaps due to the excellent exam results last year- that ultimately decided distance was too far etc and did not name it on their CAF, I don't know!
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