If you know you missed your first shot clean on a big game animal, perhaps the best solution is to decline a hurried follow up shot. A good theory, but in practice, you may not be all that sure what happened with the first shot.
A case in point: when the sun crested the low hill not too far after dawn, I saw the shadow of the little buck in front of me. I turned. He wasn't more than forty yards broadside. I aimed for the chest with my 1895 35 Winchester. I had it loaded with a Hornady 250 grain. I fired. No reaction. The little buck took one step forward and stopped. I couldn't believe I missed. I fired again. This time he took off downhill at a dead run toward me. Just before running over me, he turned. I fired again, and he went down. The last shot was pure instinct. I have no conscious memory of seeing the sights.
I was glad I got the buck, but I was sick. Only one of the shots hit, but which one. I was betting on the second shot. How could I have performed so poorly?
When I checked the buck for bullet wounds, I found three in the chest, close enough to cover with my hand.