Those numbers are generally provided "After" the fact. There's also some other considerations when looking at those numbers. In this case, when they same "2,277 QUALIFIED"; that includes only individuals that can receive an appointment. Meaning, it included individuals who also have nominations. As you all know, no matter how good your application is, you can't receive an appointment without having a nomination. So the 2,277 is the final pool of individuals. But it's not uncommon that there are a lot of "3Q" individuals who didn't receive a nomination, and thus aren't part of that 2,277 number. Just like it's very common for individuals to receive nominations, but the aren't qualified and aren't in that pool.
But assuming you applicant has a nomination and is "3Q" as discussed here, then yes, in theory you would have close to a 50/50 chance. You also need to remember that in this example of 2,277 qualified, throughout the process, that number WAS HIGHER. Between the beginning of the process and the end (June), there will be quite a few individuals who will WITHDRAW from the selection pool. They received offers from other schools, had a change of heart, etc. One thing so many people (Especially on a forum where there's MORE interest in the academy), NOT EVERYONE has the academy as their #1 choice. You hear how people mention on the forum to "Have a Backup" school that you're applying to. Probably 50% or more of the original 9706 applicants that you show, don't want the academy as their #1 choice. The academy is simply another school they are applying to. Possibly their #2 or #3 choice. Those who visit this forum are obviously more interested in the academies. It's probably their #1 choice for college. But think about it; 1% of the 9706 would be 97 people. Are there 97 ACTIVE 2019 applicants on this forum???? No. So that means that MORE than 99% of all academy applicants aren't on this or similar forums. They aren't as GUNG-HO about the academy as you all are here. And for most of them, the academy isn't their first choice.
That's also why the percentage of appointments to those on this forum is obviously pretty high.You have a higher interest in the academies. You are receiving valuable information about applying to the academy that is IMPOSSIBLE to get outside of this forum. Even with some ALO's who are head and shoulders above others; (Like Flieger - Steve), he can only affect a small number of applicants vs this forum. I know a LOT of ALO's and LOD's. Believe it or not, MOST of them don't even know about this forum. And the majority that do know about it, aren't involved with it and don't use it as a tool. (Personally, I think it threatens their EGO, that there's a source of information that is better than them).
Anyway; the point being, in November, December, January, .... April, that 2,277 number is probably much higher. But because of other offers from schools and change of mind, many applicants withdraw from the application process. Remember; the academy is NOT the #1 choice of schools from the MAJORITY of those 9706 applicants. It is safe to say it probably is of the 2,277. So looking back, if you received one of the 1190 appointments, you could say you were in the top 50% of qualified candidates. But at the TIME of the actual selection, there could have easily been 3,000-5,000 qualified applicants. Some become UN- Qualifed. Some didn't receive a nomination. Some withdrew from the process. Of my original slate of candidates, I've had 4 of them WITHDRAW from the process already. 2 of them I could almost guarantee would have been in the top 4-5 for receiving an appointment. So take those numbers with a grain of salt, and remember that they are figured AFTER the fact. Those numbers aren't the same in January.