A man can run a horse down even if the horse can outrun him (by some amount, say 50%). Firstly he could ambush the horse, injuring it; but let's ignore that an

A man can run a horse down even if the horse can outrun him (by some amount, say 50%). Firstly he could ambush the horse, injuring it; but let's ignore that and say it starts off fairly. He surprises the horse, it spooks and starts running. It won't run at a measured pace, it will tend to run either too fast or too slow. Psychologically it is going to be in a panicked state for an extended period of time, it's not going to operate close to peak performance as it would with a rider. After that the man can also both use his brain to drive the horse towards a desired location as well as his determination and knowledge of previous hunts to win the race.