Appropriate tag for a school playing field

I need to tag a school playing field. It doesn’t appear to be marked out for any particular sport at present—it’s just a grassy field with a sign saying “SPORTS PLAYING FIELD” followed by the name of the school it belongs to. What’s the most appropriate tag for this? Leisure=pitch seems closest, except thay any pitch would only occupy part of the area and none is marked. Landuse=grass is true I suppose, but not specific enough. Is there a better tag than these?

landuse=recreation_ground operator= access=private surface=grass perhaps ?

That certainly sounds a bit more accurate. At least if being made to run around in the cold by a teacher counts as recreation . . .