Your profile sketch is certainly in the ballpark for accepted students at HYP. However, because there are so many other variables, it's extremely hard to predict who will get in and who won't. This is known as the "elite crapshoot."
I see recs and essays as two of the most critical variable elements in elite admissions because the applicant has a reasonable degree of control over them. Many times, though, a rec writer isn't articulate enough and doesn't provide enough anecdotal evidence to support his or her glowing words of reference.
Of course, if the applicant isn't a strong writer, his or her essays aren't going to help much to break a tie with another equally qualified applicant. The weakest link in the chain for most applicants, in my view, is the essay. Most seniors just don't know how to find their writing voice, let alone use it to elaborate who they are to the admissions committee.
Your class rank will be viewed in relation to the overall competitiveness of your school. HYP's admissions offices will know how tough your school is from its profile and past experience dealing with your school's graduates. Don't be overly concerned with your rank. Your ECs seem very strong.
If you have covered the bases well in the areas of recs and essays, and placed special emphasis on marketing your overall profile, then I believe that you stand just as good a chance as any other equally qualified applicant at HYP. Does this mean that you'll be admitted to any or all of them? No, it doesn't, unfortunately. That's the misery of today's elite admissions arena.
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