When I was going through school one thing made me really stand out from my peers and I suspect that it was related to my Asperger's Syndrome (AS). Basically I hated sport and wasn't competitive in any way. I've always been rubbish at anything physical (I know I go to the gym but any idiot can lift something up then put it back down again) or anything that requires co-ordination and teamwork. My non-competitive edge was, I think, partially my AS and partially my desire to avoid the embarrassment of failure.
Sport was mandatory at my school and the sport of choice that was forced on you was almost always football. When forced to play I would simply stand on the pitch making no attempt to go for the ball or even move. If the ball came anywhere close to me I'd still stand there and let it roll by. When they thought they'd be clever and put me in goal they'd soon change their mind when I'd just stand in goal also. If the ball was anywhere near me I'd actually get out of its way.
The school didn't seem to mind, but you can't really force someone to participate, and I think they also knew that my actual punishment would come not from them but from my peers. And of course they were right. Where I grew up football wasn't a matter of life and death…it was more important than that. Football was people's "way out". There was no real employment where I grew up and I went to a school in a disadvantaged area with people whose parents didn't work, were single parents and on benefits. Becoming a professional footballer was their way out of poverty. I always knew that university would be my way out, but by interfering with their precious game I was interfering with their future so it didn't do anything to improve my popularity.
The lack of competitive spirit is something that has stayed with me; however I have found that I can be quite competitive with myself. Getting back to the gym as an example, one thing that drives you on month after month is that you want to beat yourself. You want to lift more this week than you did last week, or lift it better, or lift it more times. It's a gradual process where week by week you improve in increments. When I use the bikes I am constantly trying to burn more calories than I did the week before, keep a higher average RPM, go further. I have all manner of statistics and figures going around in my head and I attempt to better them.
The only thing I've done that comes close to being competitive with others is racing my car. Not on track with other cars…I'm not made of money :) but special timed events where it is just one car on track at a time and your lap times are recorded. It's a good compromise as no-one really wants to race on-track with other cars in their daily driver, but trackdays don't offer any real comparison or competition as they are not timed and you don't "race". This way the only damage you'll do is if you fall off track, but you're still timed so can compare your results to others. Without wanting to blow my own trumpet I was pretty good, usually finishing at the top end of the table, however it was only myself I was really racing. Every lap I just wanted to go faster than my last one. I didn't want to beat others, I went out to beat myself. If I did well compared to others of course that's a good feeling but it's not what I did it for. Alas one of the reasons I stopped racing was the attitude of other drivers. I hated the competitive spirit of others and how it made them behave and act. I hate being around competitive people, I just wanted to get on and do my own thing but it just got harder and harder so ultimately I stopped.
If these things are AS related then if you have AS and want to try sport, or have children with AS and want them to try sport, maybe pick things where you are mainly competing against yourself. Things like golf or snooker come to mind. While they are still against a single opponent, they are mainly against yourself. You can practice both on your own and with golf you aim to get your handicap down and your course score down. With snooker you're trying to improve your break scores, your frame scores, your pots per visit etc. Compare those with something like boxing where it is only ever a competition between you and your opponent and everything is quite subjective.