So, the assumption made of spray and pray not being a reliable strategy can be questioned.
Probably valid enough to do so, because here's the question.
In a moment of extreme danger under extreme duress, does a human have the capability to bear down on his sights and accurately place one shot (low number of shots with the aim essentially being to stop with one shot)
Or
Because of the blurred vision/tunnel vision, shaking from adrenaline, and so on, will firing volume be the way to the promise land?
That is to say, if I put you under extreme danger and duress, put a baseball at 20 yards, are you more likely to hit that target by taking your time and sending one shot, or by dumping your mag? (regardless the fact that you're only getting 2 seconds here anyway)
Now, the answer here may actually be multiple shots, because in that condition we may not realistically be able to focus on our sights to precisely place the one shot, but there's an asterisk here.
So, if we say multiple shots, now we have a problem of, can we get off multiple shots while maintaining a degree of accuracy, pulling the trigger so fast you clip your own chin doesn't do you much good. This is a big question too, if a bear is going to cover 15 yards or so per second, can you hit the baseball at 15 yards? How many shots can you get off in one second?
Now, the asterisk on the one shot scenario.
The one shot can be whenever, you can wait until the bear is 5 feet away, can you hit that baseball now... this may be statistically the only "right" answer to this conundrum.
Now the bear is bigger than a baseball, but the "stop zone," may only be baseball size territory, again, hitting the bear doesn't necessarily matter, you have to stop it, we don't care if the bear dies eventually, you must live.
Again: all this while under extreme danger and duress
So, at what range can you reliably hit a baseball, how many shots would it take you at 15 yards? How many shots can you get off in the one second that bear travels 15 yards?
How many shots will it take you at 30 yards? How many shots can you get off in the 2 seconds it takes the bear to cover that distance?
Plan for the worst hope for the best may really turn up that the answer is one shot, you HAVE to hit the brain, you have one shot, doesn't matter if he starts 30 yards away, shoot him 3 feet off the end of your gun if you have to, but one shot in the brain is it.
That may statistically be it, scary or not.
And yes, even so, there will be bears killed with 22s, people that sling volume of shots and stop the bear, people that quick draw and stop the bear stone dead at 20 yards.
The question here is if we had 10,000 bear charges and we could only chose ONE method of defense, what method, statistically, keeps the most people alive. ( I know not all charges are the same, some never get the opportunity to shoot, some get off several shots, plan for the worst means we plan for no shot, but that gives us nowhere to go, so we have to plan for at least the opportunity to shoot)
Is it "spray and pray," or is it "one and done."
Now, if the answer is spray and pray, I've got to think that then the question of gun and caliber become easier. Gun, well, it's spray and pray, you want all the rounds you can get in the gun, not on your hip in an additional magazine. And reliable of course, but 20 rounds beats 10 here. Comfortable, great pointing in your hand, fast shooting, many rounds, bullet that will penetrate through skull. More caliber than is needed means more recoil than is needed which isn't what we want for this strategy. Many shots on target very quickly is the key
If it's one and done, you need to come to terms with one shot is all you're taking, doesn't matter if you can't fire a 500 S&W 10 times in a row, you're relying on one shot, can you hit that baseball with that 500 S&W once, at whatever distance, 5 feet, dead bear is dead bear, you walk away is the point.
But I suppose at that point, one and done could be done with smaller too, heck, if you're hitting the brain you're hitting the brain, you just need to know you'll get the straightline penetration needed to go through the skull.
500 may allow a little more wiggle room in terms of the size of that bullseye though. As in, you didn't directly strike the brain like you would have needed to do with the 10mm, but because of the forces at play, blowing his head apart by hitting any meaningful mass of it means killing the bear, thus you now have a ... grapefruit sized bullseye
Add into all that, this, penetrating bullets are non-expanding bullets. So, does something like the 500 S&W, because of the drastic increase in energy, temporary and permanent wound channel, bone busting power, create the option to go center chest and stop the bear too?
If the bear is 30 yards out, can someone with a 500 or like, center up the chest and maybe have a secondary bullseye that's... IDK, a volleyball or what not size? Do the bigger bores create another opportunity not present with the smaller calibers.
So, quick first shot center chest, now focus on this next shot being the last, wait for a guaranteed hit of that baseball in between his eyes and quickly jerk the trigger.