You have never gone hunting have you.
You do not run after deer, although that does work with horses, actually walking is better. You spook the herd and follow them, you do that a half dozen times and you can walk right up to them and select which one you want for dinner.
Lions are short distance runners. We are built for endurance. Which means we can out last almost any animal.
Drive a number of sharpened stakes in the ground, drive a group of animals towards them and you will get at least one.
And the stakes are reusable.
I had heard of "the follow until exhaustion method". I only used it once. A bird had gotten into the office, so I propped open the front door to let it out. The stupid bird sat on the window above the door, so I tried to shoo it downward. It flew back into the office, so I found it and shooed it back to the door, which it sat above again. After about a half dozen round trips it was too tired to fly so I grabbed it and carried it outside. If I wanted a sparrow snack I could have had it.