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Guestx
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I most certainly understand the point you're ultimately looking to debate, but I just think as noted you're over thinking by trying to under simplify, if that makes any sense.
There is no athletic requirement to throw a dart or hit a billiard ball that I can see. The abilities you're noting, perception and coordination here, aren't defined by athletics. Valid skills, absolutely. But hand eye ability or coordination is not directly related to athleticism, at least that I relate it to.
I guess I've always considered a fighter's/player's coordination to definitely be a component of his/her overall athleticism. After all, it's the difference between being able to move gracefully and efficiently and bumbling all around the field, cage or ring.