None of these variables are accounted for by the term, "stopping power". Therin lies the fallacy of such a construct.
You're arguing over the term now. LoosedHorse described "stopping power" as the ability to stop a threat. Therefore, what you hit and how much damage you do does affect stopping power.
Of course, hence the problem with the term "stopping power". It considers very little of what actually happens when bullets hit bodies.
Once again, you're using the term, and ignoring what we're actually talking about.
Almost everything that we deal with in psychology is intangible- feelings, emotions, etc. Here we are dealing with a physical manifestation (incapactiation, tissue damage, death) of an effect or set of effects. Two different disciplines that have little to do with one another.
We are also trying to predict the future, which is intangible. In order to compare how much damage two bullets will do, you have to assume they hit the same spot (otherwise it's like comparing a car drag racing uphill to a car drag racing downhill). In order to really test it tangibly, you'd have to run a computer simulation showing every possible hit (including oblique angles, potential barriers, etc) and see what kind of damage the bullet would cause with such a hit.
You could answer that way, but that ignores what I percieve to be as "a bit warmer than yesterday". If I grew up in a tropical climate and you in an Acrtic clime, your perception may seem negligible to me.
The problem in this case is that, based on the research we have available, everyone values things differently. Some look at the volume of the hole. I personally look more at the surface area of the wound channel as opposed to the volume (which actually puts different calibers closer together). Others look at energy transfer, others ignore everything related to the bullet and instead look at the recoil.
So if I say my formula is Surface Area / Recoil, you may say "nope, only recoil and magazine capacity matter." Or "nope, it's volume, not surface area." Or you may even think recoil doesn't matter because you're only going to shoot once.
EDIT: Loosed, I think you're just taking a step off the end of it. My goal is to stop the attacker. By selecting a handgun caliber, I am trying to select the most effective tool for the job. The tool does its job by penetrating X inches and putting a hole Y wide into the attacker.