Long story short, deterrence is only half of the equation.
Statistically speaking, it's about 90% of the equation because that's the rough percentage of the time that a defensive gun use is resolved successfully either without a shot being fired or without the assailant being hit by a shot.
Even in the cases where the gun alone isn't sufficient deterrent and the assailant is actually shot, the FBI acknowledges that in the majority of cases "psychological/mental incapacitation" results from the assailant's decision to cease hostilities. In other words, capitulation is not an actual physical necessity due to the injury/damage caused by the bullet--the person gives up because he decides to, not because he has to.
It's only rarely that incapacitation results as a direct consequence of damage that renders the attacker unable to continue attacking. In short, caliber rarely enters into the equation because it's only rarely that physical incapacitation happens or is necessary to end an attack.
That doesn't mean one should ignore caliber or expect someone to automatically run at the sight of a gun--far from it. But it's important to maintain a reasonable perspective.
With higher calibers, you're deciding the outcome for them.
That's a dramatic overstatement.
The bottom line is that if you have to physically break an assailant down with a handgun, you're in a pretty bad spot regardless of what the bore diameter is. Cirillo pointed out in his books that during his numerous shootouts he saw failures to stop with virtually every firearm they employed--up to and including 12ga shotguns.
Handgun bullets, even from the more commonly recommended self-defense pistol cartridges only damage a very small percentage of an adult human male attacker. Relying on the size of the bullet to do the job is largely wishful thinking. The key to success is
which part of the attacker is destroyed far more than it is
how much of him is destroyed--at least on the scale of tissue destroyed that we're talking about.
And that comes down to skill and probably a lot of luck too. The idea that one's choice of caliber "decides the outcome" is not at all realistic.
That said, I'm NOT saying that rimfires and very small calibers are a good choice for self-defense nor that they give up nothing to larger calibers. Clearly neither of those statements is true.
I never
initially recommend anything smaller than a .380ACP for self-defense and even then, the .380ACP gets some caveats due to its tendency to underpenetrate with expanding ammunition. Sometimes people can't or won't carry/shoot something that large, and then I'll try to help them find something that will work for them.
The point is that even a pistol in a small "ineffective" caliber can be a lifesaver--it's really sad when well-meaning advisors convince people that if they can't/won't carry/use "Caliber X" that they might as well not carry any gun at all.
When my wife made the decision to carry 100% of the time, she chose a .32ACP. I wasn't thrilled with that decision, but I was happy that she was able to shoot her chosen weapon competently and that because of the size & weight of the pistol she was able to carry it comfortably enough that she didn't look for excuses to leave it home.
After some years of carrying, she's decided to move up to a .380ACP pistol. I might have been able to push her into that decision initially, but the odds are that because the decision to "upgrade" is hers, she'll be much more invested in making her new choice work for her. Just as she was invested initially because she picked out the gun she has been carrying for years now. I consider it very likely that she would have become discouraged and stopped carrying had I tried to coerce her to initially carry a gun she thought was too big or kicked too much.
