The only reason I would go to a baseball game is for the atmosphere, I've learned it's fun to go just for that. I don't GAF about sportzing. So, I'd give the ball to a kid, but only if one nearby was trying to catch it, too. I wouldn't just hand it over to any random nearby kid, if they didn't even make an effort.

However, if I knew the ball I caught (like that would happen, me actually catching a ball) might have some value because of who hit it, etc. Then, I'd probably keep it. Assuming I caught it fair and square.

I have an agreed plan with my spouse. We usually go to the ballpark together. If one of us catches the ball, we give it to the other, who is supposed to react all excited, and we say happy birthday to pretend it's their birthday.