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I am designing a poster for a softball game between all the coaches.

Do I refer to it as a "Coaches' Game", or as a "Coaches Game"

Thanks for any input.
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Both are fine. I suggest that the one without the apostrophe is the easier.
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Students: Are you brave enough to let our tutors analyse your pronunciation?

the apostrophe changes the definition

Next to the coaches office or next to the coaches' office