How can I clean off my black wooden baseball bat?

I just got a Derek Jeter Black Ash Baseball bat and I’ve been using it for a month now. I’ve been playing at the park with friends and everytime I hit a baseball, it gets a white mark on it. By now, I have a ton of white marks on my bat. I’ve tried alcohol but it doesn’t work. How can I clean it off without using water or damaging it?

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