Paper plate rule...
My Father, used the paper plate rule. His version, anyway. He was an NRA certified instructor, gave Hunter Safety classes for decades, was an active conservationist before the wacko green types gave it a bad name, experienced hunter, and generally gave pretty good advice. I use the same rule.
Our paper plate rule works for deer, with any firearm, at any range. Hitting the plate anywhere isn't good enough, you have to be able to hit near the middle of the plate, consistently.
If you can get a palm size group near the middle of the plate, it passes. Better is, of course, better.
If you can do that at 75yds, for example, but only hit the plate somewhere at 150, then 75yds is your range limit for humane kills, and longer shots are not taken until your personal skill is up to the task.
As others have pointed out, just being able to hit the plate somewhere isn't good enough to ensure a clean kill, because of all the other things involved in a hunting shot. If you can't be accurate enough on the range, odds are very high you won't be accurate enough in the field. And that is a disservice to us all, and dishonor to the deer...