Interesting. Humans have won only a handful of times. And since the horse is carrying a rider, it would be more fair if the human runner was also carrying a proportional weight on their backs.
Or maybe take the rider off and see how well the horses do. 
Particularly throwing. Humans are by far better at throwing (and hitting what they aimed at) than any other animal, even the other chimpanzee species in our immediate family.
More efficient, surely, and that’s something that humans do for day-to-day utilitarian hunting. But if you want to prove your manhood, singlehandedly (or doublefootedly) running down a horse is a pretty good way to do it.
True. But just being part of a consistently successful hunting party would probably get you some 'tang, particularly since it would mean you’d have the surplus calories needed to beat up on other groups.
I’m not disputing that humans are good long-distance runners. And I’m aware some modern tribes do occasionally hunt using the simple exhaustion technique.
What am I saying? I guess that I don’t think a compelling case has been made yet that it was ever our main hunting technique to purely run down our prey (without any aspect of “rounding up”).
The thing is that a ridden horse has a human at the helm, pacing it. Humans are smart and can pace ourselves. We can eat and drink judiciously, surge forward or fall back according to a plan, etc. I suspect a smart human with a plan could outrun a feral unridden horse.
Humans run the 100 mile Western States Endurance Run as fast (and sometimes faster) as trained horses with experienced riders win the Tevis Cup (similar if not identical course - WS100 started when a Tevis Cup participant had his horse go lame and he decided to finish it on foot). That’s strenuous mountain running - 23,000 feet of descent and 21,000 feet of climb.
We’ve done this topic before I know - someone linked to a list of the animals that can outrun a human over long distances (many miles). While it’s not a short list it’s much shorter than people might assume. IIRC there were maybe 20 animals on it.
Of course, we should also include the caveat that “running” means on land. If you include birds, we’re nothing.
I wonder if hunters don’t have an advantage over the hunted, all other things being equal. In other words, if you were ‘it’ in tag, you would be able to catch your double consistently. Angles, and being able to choose a pace, and so on…
[vaguely related trivia] I’ve read in a book about Neanderthals that their physiology made them much more apt at throwing than ourselves [/vaguely related trivia]
As it happens, attracting women does seem to be one of the primary purposes of big game hunting in hunter/gatherer societies. Small game hunting is actually better in terms of how much meat such hunters get (with the exception of whale hunters). But big game hunting means that you can go up to a woman you’re trying to woo and present her with the very best cuts of meat from your latest kill to impress her.
Plus you get a horse out of the deal.
It’s not so much outrun as run down. You never really out run it till the end. And if we’re on the receiving end of a chase we’re going to have a pretty rough go of it.
For some extremely relevant and mind opening reading read “Born to Run” by Christopher McDougall.
Seriously. Read it.
BBC’s Life of Mammals demonstrating a modern kudu persistence hunt amongst the San people of the Kalahari.
I meant in a race, specifically. A well managed horse would do much better than a horse left to its own devices. Which is why those long distance horse/human races aren’t, IMHO, necessarily a good trial of the persistence hunter idea.
I wonder if other well-managed herd animals might also outrun humans, because part of the reason that humans can run them down is because they run in sprints rather than at a steady pace, which is what an unmanaged horse might do. So if you could control all those other species that we can run down as easily as you could a horse, they might not tire so easily.
I’d be interested in seeing a cite for that.
Last I checked, attracting women is one of the primary purposes of nearly everything men do.
*“And in that moment, Dan was reminded once again why he wanted to write in the first place. It’s for the same reason anybody does anything: to impress women.” *- Jeremy Goodwin, Sports Night
Of course, a horse in an organized race probably has someone providing high-nutritional-value feed and fresh water at regular intervals. That I assume is the primary value of a fat-storing omnivore chasing down grass-eating grazers. Grass has very low nutritional value, so grazers spend a huge amount of time eating, even in ideal conditions. Part of the value of continual harrassment is not just to exhaust them, but to leave the animal starved for nutrients and water.
Every seen a horse after an intense workout? The sweat is just pouring off them, not to mention other water-loss processes.
As for dogs - IIRC, a dog does not sweat, it loses heat through its mouth (hence the dog’s head out the car wiindow, tongue drooling in the breeze.) I suspect sled dogs do well in a sled race in snow, but probably suck at endurance running in the African heat. Plus, they need water too.