A group, not a page
Most social-only leagues in this directory at least have a page, which is a public-facing object. South Ardmore has a group -- a container designed for conversation between members, often requiring approval to enter and frequently invisible to anyone outside it.
Facebook returns a bad request to non-browser requests regardless, so the distinction is academic from here. Nothing can be read.
But it matters for what the league is choosing. A page broadcasts. A group converses. A league that lives in a group is one where everybody already knows everybody, which works beautifully until it needs a new player and has no way to be found by one.
A High Cheese league page is the broadcast half the group cannot do: a permanent address with the schedule, the standings and every roster rendered as pages, findable by a stranger. The group can carry on being the dressing room.
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