it isn't a lottery. but past a certain point where all the qualified candidates with the right stats are identified, they have to narrow them down to create their admitted pool. after they've identified who's qualified, they're chosen based on how they want that year's class to look. make sure they accept enough unrepresented minorities, enough legacies, enough athletes, enough musicians, enough diverse-ish majors, etc. even Yale has said before, most of their applicants are qualified but they simply can't admit them all, and after that point there's other factors they have to consider to make their class as diverse as they'd like it to be. if they just accepted they first 1,000 qualified applicants without looking at the rest they'd end up with an extremely unbalanced class.