Wouldn't it be neat to invent a new schoolyard game? One where players don't just focus on one ball, but consider multiple things in a dynamic situation. Actually the game came from an abstract grid and dice board game concept, but this inspiration, including quidditch, was in the air.
This is a game of tag. Two teams of five, starting on either side of a dividing line. One dog, one cat and three rats per team. Rats tag dog, dog tags cat, cat tags rats. D -> C -> RRR -> D. You win by A) tagging the opposing cat or B) tagging all the opposing rats.
When a rat is tagged, the rat is out of the game. When a rat tags a dog, the dog must sit down, until the dog is no longer being touched by a rat. The briefest touch from a rat requires sitting down before getting up again.
Optional (but recommended):
A tag that ends the game would be announced with "checkmate". A tag that does not end the game would be announced with "check". Rats would check, dogs would checkmate, cats a bit of both. Saying this is not required for a tag to take effect.
The game has not been tested.
It would sort out naturally into two largely separate games, with the cats doing most of the work. The cat had better have some success.
A game would be fairly brief, more like a round, but if you think about it the game would not be won right away.
We'll have to do something with out of bounds.
Would the play area work better if there are obstacles, specifically trees?
With all these players moving around on their separate agendas, there might be a safety problem, or at least reason to argue.
This business of rats touching the dog while the cat is in close proximity might get a little weird. I could picture rats policing a sitting dog ("You're not going anywhere") rather than touching him.
This isn't British Bulldog; it's not so straightforward to teach and learn.
You could have one colour shirt for each type of animal.
What would conversation be like after a round?