Most of the deer that I shoot are calm and do not know that I am there so therefore I usually can wait until I can get a good shot. Most of the deer that I have shot have shown sign of being hit if they run off. If a deer starts running off after the shot, even if I think I hit it good, I will attempt to put another round in the lungs IF I can get another shot. Most the places that I hunt are brushy and in the woods so therefore its hard to get more than one shot. I try to make that first shot count. Usually by the time that I bolt another round into the chamber and get the deer back in my scope, the deer is down on the ground. Most of mine have ran 50 yards or less.
If I was hunting running deer in front of dogs, I would rather have a good shotgun shooting #1 buckshot because it makes it easier to hit the deer and if you are within shotgun range the deer just about drops in their tracks.