Another factor to bear in mind: the lack of a D1 sports program at UChicago, which means that they don’t admit nearly the number of low-stats revenue sports athletes admitted to peer schools. UChicago doesn’t release a Common Data Set that you could use to analyze this, but if you compare published information from HYPS you can see the kind of “stats tax” this can impose.
Because S for decades has had the best overall athletic program in the country, there seem to be significant allowances made for athletes with regard to standardized testing. Between about 2.75% and 5.73% of students of students enrolled at S who took the SAT have a score of 599 or below on at least one section, and 13.48% scored 29 or below on the ACT composite (including 1.12% who scored between 18 and 23). At H, for example, those numbers are 0.99% and 3.68% for the SAT and 9.98% for the ACT, with no one below 24. At Y, it’s 2.00% and 2.00% for the SAT (they use different bands for the ACT). At P, the numbers are 1.58% and 3.27% for the SAT and 7.94% for the ACT, again with no one below 24. It seems likely that there are a lot more athletes in the lower reaches at S (because they’re not bound by the same Academic Index requirements for athletes as the Ivies). Put another way, there are 50-100 kids per class at S who would be excluded from HYP on the basis of test scores alone.
Given that HYP field 30-40 D1 sports teams each (some of which compete for national championships, go to the NCAAs, etc.), compared to UChicago’s 18 D3 teams, I can only think that there would be a similar, proportional difference between them and UChicago in this area which would reduce the average stats of the former relative to the latter.