I doubt that any such study has been done.
Personally-
I can't recall a single instance of a first shot miss, with a subsequent kill, by ethical hunters.
If the first shot misses, the animal is gone (generally - on my hunts).
Every successful follow-up shot I can think of came after a connecting first shot. It may have been a bad shot, but it connected.
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One of my brothers has a few mule deer and elk kills that I believe started with missed first shots, but I wasn't there to witness.
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The exceptions I can think of are all related to unethical hunters or unethical/illegal decisions by hunters.
For example... I used to hunt with a two people that, as I discovered in the plains of Wyoming, thought it was perfectly fine to "shoot into the herd" for antelope. I mean that exactly as it sounds: Don't pick out an animal to kill, just sling lead into the mass of hair in your scope and see what gets hit.
Those two hunters, more often than not, would miss one to 3 times before connecting with anything (even when shooting at single animals). And, after all was said and done, to fill their tag, they most likely fired
at least 10-15 rounds. Some years, they would literally shoot 100+ rounds to fill two tags.
Their wonderful decisions in the field, and complete lack of respect for wildlife and other hunters resulted in extra kills, irretrievable wounded animals, and more than one ticket or warning from the game wardens. But, they no longer hunt Wyoming (don't hunt much of anything that's not on a game ranch or in Africa, actually), because they think that wildlife officers are "out to get them". Apparently, it's not
their fault when they "shoot into the herd" and hit a buck, shoot 3 does on two tags, shove a collateral-damage fawn into a badger hole, or take an extra animal "for tags they couldn't fill last year".
It really [peeves] me off, but I'm glad. It's two fewer jerkwads ruining things for the rest of us.
But I truly wish the game wardens would have been much harder on them, and cited them for poaching. Warnings and minor tickets (like 'wrong sex') have their place, but some people really deserve the full force of the law.
"Just sling lead and see what happens!"