The athletic hook
There is no better hook for being admitted to highly selective schools than to be a recruited athlete. College trustees at both private and public colleges and universities value the brand name recognition that successful athletic teams generate. That in turn leads more students to apply, thereby lowering the number they can accept which makes them more selective, allowing them to attract better students and faculty, and generate greater contributions from proud alumni. Even Division III colleges value successful athletic performance as they want students who excel in whatever their interests are.
As a result, Admissions officers, who do not have the ability or time to determine which athletes are most likely to be contributors to their teams, delegate that responsibility to their coaches. Admissions has standards they apply to who will be admitted but for many schools in many sports, it is only the minimum standard applied by the NCAA, basically a sliding scale of GPA in 16 core courses and the SAT, ranging between a 2.0 and 1010 SAT for critical reading and math. But as the colleges become more selective and admit fewer of those that apply, there are more demands placed on the coaches to meet higher academic standards. But even in those cases, in order for highly selective school coaches to have enough talent to be able to compete effectively at their division, the standards must be lowered. In general, an athlete can be recruited at a level where the 25th percentile of the school's students fall in terms of SAT, for example. They are qualified to do the work but can't all be expected to perform at the level of their brightest students since they put so much time into trying to perfect their sport that they can't be held to the same standard as other applicants, especially if the school hopes to compete nationally.
Private colleges value diversity and definitely support the applications of alumni children but not nearly as highly as they do recruited athletes. As one example, last year Dartmouth College, an Ivy League school, accepted only 9.7% of all those that applied. But included in that amount were some of the 222 athletes they invited on official visits last fall. Of those 222, 106 ended up applying. Of those 106 that applied, all 106 were admitted So even at the most prestigious and selective colleges, being a recruited athlete is the best hook.