I'm sure recruited athletes have an advantage, but saying it's "especially large" because a pool of applicants hand picked by coaches have a high admit rate doe

I'm sure recruited athletes have an advantage, but saying it's "especially large" because a pool of applicants hand picked by coaches have a high admit rate doesn't make any sense. They are doing more analysis than you suggest. They are looking at Athlete admits, and comparing their scores in other categories like academics, and noting they are much lower than other admits. I.e., the paper is not just looking at admit rate. Recruited athlete admits are universally weaker than non-ALDC admits on these ratings. This is not surprising, given that we know athletes are stronger on the athletic rating. But for some race and rating combinations, the differences are striking. At most, 28% of white athlete admits receive a 2 or higher on the academic rating. In contrast, 89% of white non-ALDC admits receive a 2 or higher on the academic rating. 78% of Asian American non-ALDC admits receive a 2 or higher on the extracurricular rating, while at most 12% of admitted Asian American athletes receive a similarly high extracurricular rating.