If the pee is flowing to a ditch, then everywhere it was has a layer of pee on it. Same with droppings, which don't flow away, but get walked on. Pee is not clean water, to not leave a nasty residue. Even a layer of absorbant paper would be better than nothing. Would you pee on a slanted floor and walk around barefoot? Even though the pee mostly flowed off the floor to one side, there's still some there.