Not meaning to stress you - because I know you very much want your DD to make Handworth Girls (and I sincerely think she will - maybe not on offer day if it goes up a lot from last year's 219 cut off - but I certainly think she has a great chance from the waiting list). - So although I generally agree with what you posted regarding chances in relation to first choice - I think you do have to consider savvy parents playing their options: So knowing they haven't made KEFW or KECHG but putting them above Handworth Girls on the basis of 'it can't hurt'. Therefore you can't just go by first choices and do really have to consider all choices - as you posted originally in another discussion on preferences:
KEHGS 936 decrease of 12% 112 less applied
KECHG 863 increase of 7% 57 more applied
SCGS 1151 no change
KEFW 1877 increase of 27% 500 more applied
HGS 1047 increase of 2% 22 more applied
KEA 1097 increase of 5% 58 more applied
KECHB 778 increase of 4% 32 more applied
BV 1009 decrease of 6% 65 less applied
Fairfax 1248 increase of 8% 103 more applied
Arthur Terry 1085 increase of 9% 93 more applied
So Camp Hill Girls in 2015 had 863 people put it down as a preference (at whatever rank on the CAF) and there are only 150 places (I think it's 5 forms of 30 but may have that wrong).
863 divided by 150 = 5.75 (but as 3/4 girls don't exist) let's call it nearly 6 applicants for every place.
Now - who choses CHG as their first preference - parents who want a girls school/ parents who live nearby/ all sorts of reasons.....
But some parents may fundamentally prefer a mixed school and KEFW has a slightly higher cut off score (recently) - so they may put FW 1st choice/ then CHG/ then just in case the scores really sharply rise - maybe Handsworth girls or if they're closer may put Sutton Coldfield.
So although it may seem logical to you to look at the score and choose x or y school on that basis - even you've admitted above that you've put 3 grammar schools down (which assuming you're playing odds means Handsworth is probably 3rd choice on your CAF and you've taken the 'you never know' approach - which to be fair I did with little fish whislt suffering from Precious First Born secondary transfer shock & close but no cigar syndrome in relation to her 11+ result).
I also agree with ToadMum - Birmingham LEA and our primaries could be doing a lot more to explain clearly how this system operates. Interestingly - little fish and small fry have been in different schools for Y5/ Y6 due to house move. Little fish's school circulated KE Grammars flyer and open days flyer in Y5 and at start of Y6 sent out a letter telling us we had to submit our CAF form by beginning of October even though the city council website said end October. [I suspect high numbers for FW/ CHG/ CHB for 2014 entry may have reflected the fact that some parents were bounced into submitting their CAF before KE grammar scores were known].
2 years later and at a different school - the HT organises for small fry's Y6 cohort to have HTs from all local secondaries come and speak to parents/ children about secondary transfer. It included a briefing and worked examples of how to fill in the CAF and openly talked through the scenario of a borderline grammar school score.
Schools can do more - if they want to...
Finally what I will say is that I don't envy the secondary transfer team at Birmingham LEA (or indeed the KE foundation office - by the way the sparkly my little pony is in the post! [please visualise sparkly pony emoticon - how's that coming moderators?
]) - It's a massive enterprise and my experience of the system to date is that it has worked incredibly smoothly. So a very hearty WELL DONE to you all!