Shortcut to assessing "competitiveness" of various competitive full tuition or better scholarships?

texaspg has most of the process of how scholarship recipients are chosen correctly stated.

USC receives around 30,000 applications before their Dec 1 scholarship deadline, so the % eventually being offered the big scholarships is somewhat higher.
There are more than 150 students who are offered the big scholarships after they have been interviewed. USC assumes correctly that they will not enroll 100% of all who are offered the top scholarships. We read on CC each year about students who decide to go to HYPSM, etc instead of USC. So their yield ends up with around 150 full tuition scholarships /year.

But this is correct-

“I believe the break down of full scholarships for each school and how each school distributes them within the school in terms of majors will determine how the kids fare. Being top 1% of the nation or top 1% of the school’s applicants still does not get you close to the full scholarship. Where you stack up in the applicants within the school you apply to determines whether you will make that cut.”