I agree with Finelyshedded. Every property is different. Every deer is different. Pressure on them will certainly make them move. Different dietary needs will make them shift.
How far? Eh. . . how far would you travel for food? If you are hungry, you go to the food. If you are being bullied by bigger bucks, would you stay? Might depend on the deer again. Some like to scrap. Others don't. Where is the next safe place for them to stay? That might dictate how far they move. how many does in the area? If rut is near, they can go a long way to find some booty. Lots of variables. Disposition of the deer, hunter pressure, available food sources/safe bedding areas, etc., all factor in.