>Once scholars control for all these factors as best they can, they find that coaching has a positive but small effect: Perhaps 10 or 20 points in total on the SAT, mostly on the math section, according to careful work by Derek Briggs of the University of Colorado Boulder and Ben Domingue of Stanford University.
[1] https://slate.com/technology/2019/04/sat-prep-courses-do-the...
I attended a small state school for undergrad, and a top school for grad school. There were no extraordinary students at the small state school. I was top of the class. When I went to grad school I was quickly humbled as very much average in that selected group. Everyone studied/research all day long in grad school, it wasn't really a matter of who was more driven, everyone was driven.
All my point is and has been, is that extraordinary people self select to go to good schools. That brings up the average overall compared to low rank state schools.
I attended a top school. I can assure you my classmates weren't on the whole more intelligent. They did have more drive, better study habits, more external forces (parents) pushing them. Some were extraordinary, but not the average. I would have trouble saying as a body they were more intelligent than say those that went to large state schools.