@chmcnm I know exactly what you are talking about. (Needing a shower after an admissions pitch). You are right; they have the data. They know exactly how much discount they need to provide to each applicant ‘cell’ in order to maximize their stats (they live and die based on their rankings) and minimize how much to discount.
The total discount rate increased by 2% again this year (to 52%). As list prices go up, so do total discount rates. Tuition increases are related to many things, least being actual increases in costs to run the college. Parents and prospects believe that a more expensive college is a better one (which is completely false). Why is tuition at all of the Ivies almost exactly the same? Colleges strategically determine their list price and tactically use discounts to improve their class stats (if they do it right). Meanwhile, the more affluent don’t bat an eye at the increases, but those a couple rungs on the ladder down twist themselves in a pretzel to get into that club. A club that the college’s marketing machine (and board) do a fantastic job of convincing us is so, so worth it.
Many private colleges have zero students paying full price. Some colleges have freshmen class which is unprofitable because of a too aggressive discounting year - another reason that tuition needs to increase, to get 2-3% more money from that class each year.
Colleges have NO IDEA how much it costs to educate a single kid. They have their gigantic operating expenses and use every means they have to meet those expenses every year. Those expenses are not just because of professor’s salaries. To compete in the race (before the housing crisis), many expensive )debt service) buildings need to be paid for, still.