I can only answer his as a native Russian speaker: you can say this sentence with "есть" or without, both are grammatically correct. But there's a slight difference in the meaning of both:
1) у баскетболиста мяч = here the fact that he's holding a ball (not a flower, not a can) is a bit more important. For example, if your friend is asking "who among these guys there is a basketball player?" And one of them is holding a ball and you try to emphasise this fact with your answer. ".... а у хоккеиста шайба"
2) у баскетболиста есть мяч - the word "есть" is more important here as to emphasise the fact of having itself. Like "the basketball player has a ball in case you need one". Hope it helped a bit.
Could the difference be 1) he owns a ball in general or 2) he physically has the ball - during the game, for example? (Or maybe the other way around...)
uhm..no=). I'd say "есть" in both cases. as i said you put Есть if the fact of having itself is more important. Imagine we're having breakfast.
And i say "Can i pour you some tea?"
1) you can answer: Нет, у меня есть чай. (I already have it thank you)
2) or you answer: Нет, у меня кофе (I don't need your bloody tea, i already have some coffee in my cup). "есть" is skipped here.
is it any clearer now? No?)
How come there's no есть here?. A ball is a physical object that you can hold.
I think it's omitted because it's implied. Chances are you can see the basketball player holding the ball, so the ball's existence is implied.
"Мяч в баскетболисте" I think. However in such a case, the player would be dead or in critical physical condition.