I dont know about stamina efficiency, humans superpower is that we can get rid of heat efficiently. Take wolves, they can only sweat thru their paws, and their main way to lose heat is by panting, which they cant do while running. So if you were to just keep after them, even if your slower, they will eventually pass out from heat stroke. The same applies to other animals.

Meanwhile the human is jogging after them, sweating all over, the faster they run the more efficient the sweat evaporating is, and they can drink or pour water over them selves as well.

Thats why we win persistance hunting.