I have no backup but I think that humans can run down (over hours or days) anything on the African savanna. I've seen documentaries of Bushmen running in the sun for many, many hours until they have an antelope staggering and just walk up and spear it.
Wolves are only good for a shortish run (again no backup). I don' know about deer. My only source is a documentary showing a wolf after a young caribou. The claim was the wolf had to get it in the first mile.