Sure, I can be clumsy and hurt myself around the house, but hand eye coordination is something that can be acquired if you apply yourself. I've been enjoying sports my whole life and I haven't been the type you'd think of as an athlete, what with my other interests and personality traits. I think the truth is that most anybody can benefit from sports and many people on the spectrum can become more coordinated than they first expected.
Between middle school, high school, college, and the gyms I've been to as an adult I've played football, basketball, baseball, rugby, tennis, track and field, and then later on fighting sports with freestyle and greco wrestling, jiu jitsu, boxing, muay thai, savate kickboxing, I've tried it all. And if you met me you probably never would have guessed that I do sports, especially with my hair turning grey.
So to everyone else out there with ASD: you probably can swing a bat. It just takes time and when you apply yourself it's worth the investment in time, in any sport, it's great for your self esteem, confidence, and discipline.
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There is no wealth like knowledge, no poverty like ignorance.
Nahj ul-Balāgha by Ali bin Abu-Talib