Similar here. Ridiculously competitive, and though I had inconsistent physical results, I enjoyed learning strategy as well as making physical progress.
I personally found great intellectual stimulation and feelings of satisfaction from one-on-one sports such as tennis, table tennis (ping pong), badminton, racquetball, and wrestling. I also played team sports quite a bit, and enjoyed being a student of those games, but I tended to prefer pursuing mastery of one-on-one sports (edit to add: though I've never come close to mastery).
By distilling the experience down to a one-on-one competition, I find I'm able to focus more on the intellectual pursuit, as opposed to the intellectual+social pursuit of team sports. Handling social dynamics can sometimes overwhelm me when I attempt to focus on the strategic and the intellectual.
Everyone's experience and taste is different, of course. Many paths can lead to happiness :)