I've had all sorts of reactions, too. The last doe I shot was a broadside double lung. At the shot, she made one big leap and just stood there. After a few seconds, she started to walk off and simply fell over. I shot her from about 16 steps, and she never got more than 30 yards from me. Field dressing revealed my arrow had slipped between the ribs on both sides.
If I look back, I think that every time I've hit a bone, or if the arrow stayed in, the deer took off. The ones I've shot that just stood there, the broadhead slipped between the ribs and completely passed through.