Stan, welcome to College Confidential!
As a new member, please take a look at this post from an MIT Admissions Director on chance posting, as everything in it applies to Yale as well: http://talk.collegeconfidential.com/massachusetts-institute-technology/939227-reminder-no-one-not-even-me-can-give-you-an-accurate-chance-at-mit-p1.html
You seem like a wonderful candidate, as are the thousands of other students who apply and are rejected. As Yale receives more applications from qualified applicants than they have seats in the freshman class, Admissions uses a student’s essays, teacher recommendations, guidance counselor report (SSR) and interview report to select one high-performing student over another. As you haven’t posted that information (nor should you), the only way you’re going to find out your chances is by submitting your application. Best of luck to you!