Another way to think about it--i.e. hoofed animals can only walk or sprint. Humans can jog, so as long as a human hunter can pick up the trail after the animal sprints out of sight, the jogging will eventually win out.
I did horse riding for a bit, that is not true. There is a lot of speed ranges you can choose from
The linked paper in the parent comment has a graph on page 347 (page 2 of the content). The human's walk curve is substantially more efficient than the other gaits, included on the graph, which is the point I was trying to make. Humans best their caloric/distance ratios over time ("endurance hunting").
Horses have more than two speeds. They can walk, trot, gait, gallup.
> Although not extensively studied in non-humans, endurance running is unique to humans among primates, and uncommon among quadrupedal mammals other than social carnivores (such as dogs and hyenas) and migratory ungulates (such as wildebeest and horses)
Anyway I was attempting a clumsy metaphor to aid someone's understanding, not trying to be pedantic. It's easiest to compare sprinting and not-sprinting.