It is said that no land animal can outdistance a well-conditioned human.
A herd of horses, gazelle, etc; can outrun a tribe of humans for days but the persistent humans on the trail will eventually come up on a herd too exhausted to run and can pick off the weakest at will. I'm sure that played a big part in pre-modern evolution even with the questions of shoes, predators, and lack of home base. The problem of home base would be partially solved by running a herd into a valley or perhaps a beach peninsula (which would reduce problems with sore feet and predators).
Sorry about the lack of spell check there...