I've found that I pick up sports very quickly...at school when we did something new, I was always the best after 2-3 sessions. I was lucky in that we did a load of different stuff like fencing and lacrosse. At some point though, I'd hit a wall and end up right in the middle of the class after a few weeks.
The way I always figured it was that my speed of thought and ability to quickly grok the concepts and rules gave me an initial advantage, but my general clumsiness and/or lack of fine motor coordination stopped me from becoming accomplished. I think it holds for other stuff than sports as well. At various times, I've been reasonably good at soccer, badminton, basketball and fencing and I've also played trombone, tuba, timpani, drums, bass guitar and electric/acoustic guitar. With all of them, I've reached a decent standard quickly and then failed to improve despite a lot of effort. If you can settle for being average and accept your limitations, you can still accomplish a lot.
Another part of it is choosing your battles, I think...I knew I was never going to be a skillful, technical footballer so I worked on using my fitness and physical size (I'm 6'4") to become and rough-and-ready central defender. Same with basketball, I was never going to be a Michael Jordan, but i won plenty of leagues and competitions by aiming to be more like David Robinson. I tend to leave the highlight-reel stuff to other people.
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I find the main advantage of having Aspergers Syndrome to be my ability to focus completely on one subject to the exclusion of...OOOH SHINY THINGS!!