Or even more impressively, how you can pick up a random object and throw it with some accuracy.
Catching a ball is easy by comparison, also, my dog is better than I am at this game.
But throwing a random object not only requires an estimation of the trajectory, but also estimating the mass and aerodynamic properties in advance, to properly adjust the amount of force the throw will use as well as the release point with high accuracy. Doing it with baseballs is "easy", as the parameters are all well known and pitchers spend considerable time training. But picking an oddly shaped rock or stick you have never seen before and throw it not completely off target a second later, now we are talking.
Playing Pool is a great example of this because you can math out the angles of a shot relatively easily, but the best pool players do it all intuitively. Some of the greatest don't bother with "advanced" pool tactics. They have spent so much time watching the cue ball strike other balls that they have a tacit understanding of what needs to happen. Part of practicing well is just watching balls hit each other so your brain starts to intuit what those collisions result in.
What is really fascinating for me is that my subconscious will lose interest in pool before my conscious does, and once that happens I struggle to aim correctly. It feels like the part of my brain that is doing the math behind the scenes gets bored and no matter how hard I try to consciously focus I start missing.
Not to mention, you even calculate a probability point map. Like I’m not going to hit the center perfectly but I can calculate the circle with a 90% probability of making the shot, given a distance and an object. And you know how much closer you need to walk to minimize the circle.
Which comes in very critically when chucking away trash overhand in public and you never want to embarrass yourself.
Catching a ball is easy by comparison, also, my dog is better than I am at this game.
But throwing a random object not only requires an estimation of the trajectory, but also estimating the mass and aerodynamic properties in advance, to properly adjust the amount of force the throw will use as well as the release point with high accuracy. Doing it with baseballs is "easy", as the parameters are all well known and pitchers spend considerable time training. But picking an oddly shaped rock or stick you have never seen before and throw it not completely off target a second later, now we are talking.