I lost my eligibility due to transfer after the season started and I WAS LOST at the new school without a sport to do. I needed to participate in a sport year round. Fortunately the head track coach was the instructor of the gym class I was placed in, and elected one day for the class to do 2-lap races around the skinny and short indoor track. I was paired against what turned out to be pretty fast runner and a head case. He got the jump on me and I didn't know how to safely pass him on the narrow and pretty steeply banked curves. I stayed just behind him and sort of shrugged at the end of the race. Lo and behold the coach immediately approached me and invited me to the indoor track workouts. I was happy though didn't realize he had sprinter in mind rather than distance running.
Point being, come hell or high water I was going to do a sport year round. Played JV football as a sophomore (And marched in the band at the varsity games, BTW) but ran cross as a junior. That same coach that had my gym class had reason to get angry with me later, because I used to bring a basketball to the school early and a bunch of us would play pickup basketball in the gym (in stocking feet). He warned us the first time he caught us, but took my basketball (sniff) the second time. That was the second half of my senior year during which I was ineligible for any sport. I became sports editor for the school paper (a form of compensation, I think), instead.
I don't think it has anything to do with "roundedness". Playing sports is good for the soul.