An MIT Admissions Director probably says it best: http://talk.collegeconfidential.com/massachusetts-institute-technology/939227-reminder-no-one-not-even-me-can-give-you-an-accurate-chance-at-mit-p1.html
Please read his thread to learn why it’s impossible to chance you for Yale.
FWIW: Here’s my take on it. Five years ago, my son was accepted to 10 out of 11 colleges. On every single acceptance letter was a handwritten note from either the Dean of Admissions or the Regional Admissions Director. Each note made mention of my son’s essay, as in “After reading your essay, the committee’s vote was unanimous” or “Loved your essay about your baseball coach” or “Welcome! Based on your essay, we feel you will be a huge asset to our school.” When my daughter applied to college six years ago, she received similar comments on her acceptance letters regarding her essays.
Not one comment on either my daughter or son’s acceptance letters said “Great SAT scores” or “What a wonderful transcript” or “Fantastic EC’s” or “Loved your GPA.” In fact, in all my time on College Confidential, I’ve never heard of any Admissions Officer making comments like that.
So, IMHO, after a student has reached a certain level – say 2250 SAT / 34 ACT/ with a top GPA – it all comes down to your essays and what your teacher and guidance counselor say about you in the letters of recommendation. Do your essays portray you as authentic, compassionate, articulate, likable? Do your essays show strength of “character?” That’s an old fashioned word; it means the way you develop your inner qualities: intellectual passion, maturity, social conscience, concern for community, tolerance, inclusiveness and love of learning. Do your letters of recommendation from your teachers and GC back-up what you have said about yourself in your essays?
Your chances have MORE to do with those subjective qualities than any of the quantifiables you listed above. Here’s a video from a Stanford Admissions Director saying the same thing. My guess is that Yale feels exactly the same way: https://www.youtube.com/watch?v=_UYhTylqC9o&ab_channel=CampbellHallCC.
Best of luck to you in the Admissions process!