First of all, no team sports, no sports "scholarships," and no NCAA-type intercollegiate competitions. The NCAA is a corrupting influence in American higher education (for examples, see here, here, and definitely here). And, team sports such as football and baseball mostly involve standing around and doing nothing, as the Wall Street Journal recently demonstrated (see "NFL Games have 11 minutes of action").
On a daily basis, freshmen should run (up to 10 miles), swim (up to 1 mile), and/or hike (up to 25 miles). They should learn to throw the javelin, shotput, and discus. They should learn to box and wrestle. They should learn archery.
Sophomores will learn horsemanship and fencing. They will continue their martial arts training, adding perhaps judo and kendo.
Juniors will learn ju-jitsu, karate, and other fighting arts, as well as be trained in pistol and rifle shooting. Swimming, running, and hiking will continue throughout all four years. Intracollegiate competition in Modern Pentathlon will begin.
Seniors will compete in Modern Penathlon, endurance running, open water swimming, and multi-day wilderness trekking.
Somewhere along the line, students should learn to sail and to handle small boats, to row, and to dance. They should also learn some gymastics.