Marlowe1, I love your analogy to probabilistic distribution of ideal gas molecules with respect to probability of busting financial aid budgets, it brings back warm memories of Chemistry and why these U of C threads are unlike any other.
My only point was a college is truly need blind insofar as its fixed financial aid budget. If Chicago has a target class size of 1700 and its tuition is $50K, then Chicago is truly need blind is its financial aid budget is $85 million. However, the reality is all admissions offices are given both an annual financial aid budget and a tuition revenue budget by the President, Provost, and Board of Trustees and Dean Nondorf is expected to meet both of those numbers, which I am sure he does with superb accuracy.
Yes, I agree with everything you posted that, in reality, wealthy students will inevitably comprise X% of the class because they will have stats and accomplishments that are disproportionate to their demographic numbers, but I am also very confident that no admissions office will ever find itself in a position where it “accidentally” exceeded its annual financial aid budget by >5%, forcing it to ask the President and Board for more money to support needy admits. Bottom line, Nondorf and his peers all have to meet their target numbers (both aid and tuition) and they do so in a very calculated and deliberate way.