^^ Correct. Let’s do some math, as this will help drive that point home. Over at Harvard – which has a similar, but lower acceptance rate than Yale – Admissions is on record as saying that 80% of applicants can do the work on their campus, and fully 40% of them are top students with exemplarily credentials.
Now last year almost 40,000 students applied to Harvard. If 40% of them are top students, that means there were 16,000 truly stellar students with top grades, test scores, recommendations and essays in contention for a slot, students who had a big chance. However, Harvard only has enough beds for 1660 students in their freshman class, which means over 14,000 terrifically qualified students – students who had the full package – were rejected. That’s how limited a chance an applicant has when a school has a single-digit acceptance rate.
As the lottery expression goes “You can’t win it, if you’re not in it!”