Excuse my ignorance, but what the heck kinda taxes do you have to pay on a baseball that you catch in the stands?
He would have to pay tax on its presumptive worth. Just as if you found a million dollars lying in the street and nobody claimed it, you'd have to pay taxes on that million.
Most of the time we don't hear about this because the people who catch record baseballs can't wait to sell them. This is the first one I can remember who would rather have kept the ball than cash out.