First, I don't think that age alone would be an issue. There could be a maturity issue -- that would be reflected in recs, mostly from teachers.
As for one quality vs. many -- that's really not an easy question. One great quality will not overcome deficiencies across the board. So, for example, fluency in Arabic might be a desirable quality. However, if your grades aren't very good, you don't participate in sports, and you haven't shown much leadership, your language ability probably won't help all that much. That said, when evaluating a lot of very strong candidates, having one really great attribute could well tip the balance.
In terms of the whole person multiple, the most important thing is your h.s. classes and your class rank. Taking the hard math, science, English, history, and language classes and standing out among your peers is the most important thing you can do. I really wouldn't fret about one sport vs. three.
Finally, please recognize that no one other than the folks at USNA who reviewed your record can make any meaningful judgments about why you or someone else did or didn't get in. And this includes your BGO, who can make an educated guess but doesn't see 98% of your packet let alone the packets of the thousands of other candidates. There are so many factors that go into a decision that go well beyond numbers and lists of activities -- for example, your teacher recs.
What I'm saying is not to rush to judgment. If you get a TWE, I strongly suggest that, come June (because CGO is less busy in June), you call CGO and speak to your Regional Director. Ask him/her what kept you out and what you can do to improve your chances, if you still have the desire to attend. Whatever the reason, I'm pretty sure it won't be that you played one sport instead of three or weren't the team captain.
