Although there are always exceptions, most deer only have a vague idea of what the problem is when they are shot.
Running is a natural reflex when they are hit but after going a few dozen yards they will stop to see what is after them.
If the hunter is making a lot of noise, following them they will start to run again.
If the hunter takes his time and quietly reloads his muzzleloader the deer will continue to look around and listen.
That's about the time they realize they don't feel very good and they will often look for a bush or small tree to lay down under.
Once they do that, if the shot was close to the mark, that's where they will be found after a slow, careful search.
The moral of the story is, place the shot right, then give the deer a chance to lay down before trailing it.
Usually, you won't have to go far before you find it.