Whether you stop a threat with the first round depends solely on factors you have not mentioned whatsoever.
You are confusing things here.
There are 2 ways to immediately incapacitate/stop someone, and they are not dependent on which caliber you are using as long as the particular load used allows for enough penetration depth.
The first (a CNS hit) requires enough penetration depth to get there in the first place (and obviously shot placement is a factor, but that is a matter of training and the particular situation) and just that.
If a 22 can get there, even that is very likely to cause quick incapacitation. Same for 5.7 or other such gimmick rounds.
The second is psychological incapacitation and that is a complete and utter wild card one should not rely on as factors you can control (bullet design/caliber etc) don't seem to have anything to do with it.
The 45 has no magical one-shot stop property compared to other calibers.
If you hit a guy's brain with a 45, and compare that to a hit in the heart with a 9, of course the one hit by the 45 will most likely drop instantly vs. the other guy who may well end up shooting you before he is incapacitated much later (barring a psych stop).
The opposite is also the case.
45 makes slightly bigger holes compared to a 9 for example, but for the purpose of immediate incap. that is not particularly important... It's more a factor when it comes to delayed incapacitation (and even then there are so many other factors involved... In reality, there just isn't much of a difference between the two in terms of how much tissue they crush. Not enough to affect which gun to choose... Pistols suck at reliably stopping threats quickly no matter the caliber)
Frangible ammo? Do you mean training ammo or RRLP? Why would you want to use that for self defense? RRLP has some specialized uses, but frangible training ammo behaves (from what I can remember) like FMJ's when used against human targets/soft tissue, no?
And again, there is no magical one-shot stop property of a bullet. "one-shot stop" is meaningless anyway. How long did it take to stop the threat after it was hit? Where was it hit? Etc.
Before you at least seperated immediate incapacitation and delayed incapacitation. This time you did not.
I'm not sure if this was said in jest or not?
.410 was an inferior self defense choice even before someone went and put it in a badly designed revolver to cash in on people's ignorance...
Overall, no disrespect intended to you, devildog_jim. Kind of feels like I'm attacking you or singling you out, but that is not my intention.
This is, however, exactly why we need to have a thread about terminal/wound ballistics. That stuff is quite well researched and documented (and of course there is an overhelming amount of misinformation out there as well). We do basically know how incapacitation happens and what bullets do, though the information is sadly not nearly as wide-spread as it should be, both among the general public as well as soldiers and LE personell, lawyers and people serving on juries on cases related to shootings etc...
Anyway OP, I'm hoping that Robert A or someone else will post the links for me...