Only slightly less than I'd like the mess I'd make when I shot the deer's nose or jaw off. The head's a pretty small target, that move a lot more than the deer's body. A broadside shot behind the shoulder destroys very little, if any, usable meat, and it's a lot easier to make. And if you do miss the intended mark by few inches, you still have a rapidly and humanely killed deer. Do what you want, but if you wound a deer taking what I consider an iffy shot, then you're not much better than a road poacher, IMO.
Mike