Is there any difference between be hit with a ball and be hit by a ball? For example:
One of the players was badly hit with a ball.
One of the players was badly hit by a ball.
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The difference is very slight.
Hit by a ball indicates the ball colliding with the player. But it does not even imply that there was some entity that caused the ball to move at the player. Hit by is indicating that the hitting was done by the ball.
Hit with a ball indicates that there was some entity (presumably a wild pitcher) that did the hitting, and that a ball was used. But this other entity is implied. And not very strongly. It's like there is a very faint odor of pitcher nearby, but nothing specific.
In the hit with form, the by is implied. If it was the pitcher who did it, it could be rewritten as "the player was hit with a ball by the pitcher."
It's really not a very strong inference though. In other situations it might be erased entirely. Hit by a string of bad luck and hit with a string of bad luck are not really different at all. That is because we don't usually assume that bad luck can be imposed by somebody else.