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Every elk and deer we've hit in the liver have died in less than an hour. My sons bull this year was dead 40min after the shot when we found him.
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I think with any of these comments it's valuable/important to mention whether you are talking about archery hunting or rifle hunting. Of course, the OP is talking about rifle hunting so it would be natural to throw in rifle scenarios as most relevant. But we definitely have some archery stories being included.
There is a pretty big difference between slicing the liver a little with an arrow and blowing it up with an expanding bullet and the associated concussion. A bullet could reasonably turn most of the liver into jello, and open up all the arteries going to and from it. That could definitely be a pretty quick death.
With an arrow, it's pretty well-documented that a liver hit can take hours and hours to kill an animal, and I have seen it happen several times. Archery situations are also quite a bit different because if it's going to take the animal four hours to die, you better give it four hours. Because if you bump it, it's highly unlikely you're getting a follow-up shot with a bow. Whereas, jumping it with a rifle isn't the end of the world because odds are high/good you can put another round in it to finish the job.
With basically any rifle hit on public property, especially in the rain, I don't typically wait around before pursuing a hit animal. Maybe I should, but the only rifle-hit animal I have lost remains a huge mystery- it was pouring rain but I'm pretty sure the hit was good and I found about a 1" piece of lung that blew out of his chest cavity. It was a big spike buck and to this day I have no idea where he ended up or how I couldn't find him.