Actualy for pistol rounds it really is quite simple (rifles wounds have extra factors.)
You need a round that penetrates deep enough to reach vital areas to stop an attacker against thier will. While a wound or gunshot will stop some of thier own free will many times (and simply that possiblity even more times), others will be determined and the body actualy needs to be stopped.
For some smaller calibers what penetrates to vital areas can be a FMJ. Many of the calibers used though for self defense have more penetration than necessary to reach vital areas, which is wasted. How do you make good use of that wasted energy? You use it to create a wider diameter wound.
The wider a caliber for a given amount of energy the more resistance the bullet faces, and the less penetration.
Since most defensive calibers penetrate deeper than necessary to reach organs, they benefit greatly from expanding projectiles against the average individual.
There is also the shape of the projectile. Neither JHP or FMJ shapes are ideal shapes for tissue destruction, but JHP is better as it is opening up. Smooth soft edges allow tissue to flow around. Sharp edges and irregular shapes cut even the tissue that flows around the projectile.
So JHP are usualy better for most defensive calibers. They give a wider diameter wound in the more important inches of penetration.
They`re taught that this bullet will normally enter the body at a distance of about 4-6 inches.
Not sure what is meant by that, whether be fired from that distance away (not correct as most gunfights happen from a few few away) or penetrate to that depth. I am going to assume you mean penetrate to that depth, which is actualy more accurate than many here realize.
Most rounds penetrate about 4-8" even though they penetrate 12-16" in ballistic gel. That is because ballistic gel simulates soft tissue, and does not account for bone, like ribs, slightly higher density skin, or changes in medium. When a projectile changes through different density mediums it is also slowed more than taken into account in simple equations. Just like a bullet will travel less distance in water fired from above water into water, than if fired under water. The change between mediums deflects and causes a loss of some energy. Well the body has very different internal mediums, some organs are elastic, some are not, some are light and soft, some are hard and dense.
Some people are built very solid. Some are covered in dense muscle, some more in not dense fat.
Now a round will usualy penetrate more total inches in a fat person because fat is not very dense. So you could say it penetrates 12 in one person, while it woudl go 6 in a thinner more solid individual. So you really cannot make general statements for all people since everyone is constructed differently. There is some very solid thin people, and some very soft large people. You have more lightly built female frames, and denser male frames.
In general though the round will reliably penetrate about 6" of dense tissue in a healthy person even if in gel tests it does near double. It may have to smash into ribs, and go through different mediums. Sometimes it will go further, depending on what is hit. You shouldn't rely on sometimes though. 6 inches of dense tissue is just fine in most cases. Unless they are body builders, or wearing body armor, or as in the case of the North Hollywood shootout are body builders and wearing body armor.
You never know when some massive body builder like a 'Tookie' that normaly just beats people to death in parks may throw on some body armor, grab a shotgun, and kill you because you are "white" or a "Buddha-head" (asian) or something similar. In such cases you may want a little extra penetration. Of course legislation has generaly decided you can't have it in a concealable portable package chambered in common defensive calibers anyways. '18 USC sec. 921(a)(17)'
Most people get so used to citing ballistic gel penetration that they forget it is not the same as human body penetration. Ballistic gel penetration is a very helpful reference point, but not that same thing. Expansion also can be very different when the round impacts clothing, gets slightly crushed and deformed on a rib or other bone, and then enters into tissue. They don't all end up as perfectly opened uniform petals like the pictures of them shot into water or uniform gel.
The best defensive rounds would actualy be those that contain thier own explosive energy. You could fire a projectile with far more energy on target than recoil created at firing. Such projectiles though are also not legal. If they were much weaker calibers would become the minimum reliable defensive calibers. You could have .22 rounds for example that penetrated inches before detonating and creating a small crater in the target. The technology is simple and could be widely fielded tommorrow.
An old grandma with severe arthritis could deliver energy from a .22 pistol that rivals that from much more powerful defensive calibers using traditional rounds.
Our wise overlords though have decided that is unsuitable, and you must deal with increased recoil for increase terminal performance, and citizens must work on improving obsolete bullet designs which are what we call the "latest in bullet technology". Manufactures have created some decent expanding ammunition with those limitations.
The military uses rounds similar to what I described in vehicles known as HE projectiles. They are technicaly banned internationaly for infantry (but not fired from vehicles, the rules are designed to favor the more powerful forces, and limit the less powerful) anti personal roles though there is still some used in that capacity. The Raufoss Mk 211 is used in an anti personal role on occasion and is a similar round.
Similar projectiles in small pistol calibers would be very effective for civilian self defense against a wider range of targets, and could be effectively used from low recoiling calibers.
It really is legislation that limits effectiveness, by limiting the technology that can be employed in projectile designs.
The latest civilian legal rounds are just making the best of restrictive regulations, they are far from ideal, or the best with the technology available.