I think Questions has it right (as usual)

: DYS wants to admit every child who qualifies and desires to be admitted into the program. They don't list a percentage of applicants admitted because it varies wildly from month-to-month. If everyone who applies in a given month meets the criteria--even if that's 1000 kids--then they'll all be admitted. If they don't, then they won't be.
DYS does not look at local issues at all to my knowledge. "Good" schools or no, they assume that if you apply for your child, then your child can benefit from the program.
This is all about the child and not about anything else.
Factors: test scores, level of work (3+ years above grade level, at least), hobbies and interests, intensity, etc. (Basically, what's on the application.)
Basically, all that matters is if your child is HG+ or not. Whatever you can use to demonstrate HG+ness is what they'll look at. That may be different for different kids.