So the scenario is that you have applied to a middle school, not got a preferred place and are now on the waiting list?
You are hoping that someone will not accept their place and thus you will be offered it?
If that is the case, I presume, as with all admissions, it will depend where you are on the waiting list. If you are 7th, then that requires 6 people to turn offered places down ...
AND there is the issue of late applicants who might 'jump' you in the queue due to being higher up the oversubscription criteria - so you can be 7th in the waiting list on offers day, but 9th a month later, if 2 children move into the area and live closer to the middle school in question.
So the admissions dept is quite right in making it sound vague - it is a slightly 'how long is a piece of string' question. If you are first on the waiting list, there is some movement most years AND nobody moves in closer to the school, it may be quickly, as it only requires 1 person to turn down their place. However, in other scenarios it may be months, or never... (though since infant size regs don't apply, appealing is more straightforward as it is a balance of prejudice case)