I recently had to contend with a muddy run after the ladies scratched all the grass down to nothing (had been waiting for that day to come.. ha!) I read a handful of posts on here that refer to making your run similar to a forest floor and it makes total sense. Utilized pine bark nuggets and cypress mulch, along with some dried, fallen leaves from around my property. Dumped everything inside the run, with some random sticks/twigs, dried grass, plant trimmings. Lots of different things and sizes to facilitate drainage.
We just had 2 days of solid rain from Hurricane Florence leftovers and the uncovered run looks SO much better. It dries out quickly on top and the ladies love to scratch in it and turn the material over.. incorporating their poop too, so zero smell. They're no longer tromping around in consistently wet mud. And as Autumn carries on, I'll continue to add mulched leaves and grass clippings and maybe even try to save some for over winter.