@GMTplus7, while the very top students will have their pick of schools, there is also plenty of probability involved for the next or next next tier of students. Hypothetically, let’s say Harvard ranks all the students based on their “desirability” to the school from 1 to 40,000. Let’s say Harvard shuffles all the applications and ranks them again. The order is going to change depending on many factors, like “phase of the moon”. While it’s unlikely for an applicant ranked 10,000th to move up to 1,000th in the second time, it may very well be 8,000th or 12,000th which I agree wouldn’t make a difference. On the other hand, someone ranked 1,800th may be 2,200th or vice versa, which could be the difference between an acceptance and rejection assuming the school admits 2000.