My approach to hit dice in D&D has always been that they reflect primarily the life energy, the force, will and mana, that each character (whether PC or NPC, monster or other) has. From this I differed from Gary Gygax who saw them reflecting and abstracting various trinkets, skills and improvements a character obtained as the character reached higher levels combined with the physical presence/size of the character.
Gary was right that D&D works the way he saw it. You can run Runequest vs. D&D character melee (and Runequest is clearly a model that embraces a mostly Gary Gygax view of character leveling) and it works very well. The D&D hit points and armor class pretty much work against the parry, etc. so that (after taking into account that the RQ character has improved will/POW with higher “levels”) it is pretty transparent.
When Steve Perrin pointed that out, I was amazed, then impressed. The active avoidance of Runequest vs. the passive incorporation of it all as hit dice/hit points really works either way.
That said, that wasn't my approach. Instead of approaching hit points as an approximation, I approached them as a measure of the additional life force one gained with leveling. That fits many culture myths and legends very well. Characters who have overcome and "leveled up" have superhuman vitality and personal force in such myths.
In that light, I approached magic items, especially +0/+1/+etc. weapons as an extension of life force and energy. (Silver = +0).
A living weapon, whether it be a werewolf’s claws or a dragon’s bite, allowed the application of the magical force of the character against an opponent. That fit in well with every few levels or so ~ +1 weapon for hitting things that require magical weapons to hit.
There are many variations to this.
Thus a hero/4 hit dice creature can hit things that require silver/+0 to hit – if they hit with their bare hands/teeth/fangs/etc. 0-4, can’t hit. 4-8 hit things that require +0. 8-12 hit things that require +1, etc. Perhaps with some tweaking or adjusting to the scale.
Or, to go to the rules, the most common variation is that 1-4 hit dice creatures using their natural weapons hit as +0/silver weapons, 4-6 hit as +1, 6-8 as +2, 8-10 as +3 and 10+ as +4 weapons for figuring out what they can hit.
You can this starting with Chainmail, where a “hero” can hit and kill some magical creatures, with or without a magic weapon. The charts seem natural to carry over to the Brown Box set and the “fights like a hero” or “fights like a superhero” categories as characters progress.
Thus variations on the rules allowing more hit dice/levels allowing characters and creatures to hit things that otherwise require magic started with Chainmail and made it into various editions of the rules. This got into the rules without much explanation as to why, other than to avoid problems such as where a dragon could be slaughtered by a two or three hit dice creature or creating special cases (such as PC races with shapeshifting being able to hit things requiring magical weapons while shapeshifted) or or creating consistency with prior rules.
But the general rule and rational I liked was that immunity to normal weapons had to do with the magical nature of the creature with the immunity, coupled with it possibly not being completely present on the physical plane. The power of magical weapons to hit such creatures had to do with the magical weapon being alive in a sense, the same for silver weapons that channeled the power of the moon through the magical correspondence with silver. Thus the more alive a weapon was, the more things it could reach and hit.
Monsters with natural weapons worked into that system well. PCs? Well, they had to hit things with their hands (unless they were shapeshifters). Just because they could hit things, did not mean that they wanted to. Monks and Mystics aside, a DM would look at a player and ask “Do you really want to hit that wraith with your hands? Life drain works on contact after all. It drains you every attack, you drain yourself every time you hit back.” Makes for a short and brutal melee if the character decides to go with fists instead of a holy symbol or fleeing. Which reminds me, an interesting tweak in Chainmail is that a wight is inferior to a wraith at everything except fighting wraiths.
I had meant to write that approach up into a rule, but it is one of the things I never got done – for good reason.
There were distractions, and the rational for it was not one that everyone agreed on.
Everyone was pretty clear that higher hit dice creatures should in general be able to hit magical things because most higher hit dice creatures were higher hit dice creatures because they were intensely magical (think Balrogs). But did that general condition that really mean that a blue whale could hit anything just by virtue of being large and thus having lots of hit points, or was there more to it?
Should you use a sliding scale so that each size above “normal” you slide the critter doing the hitting down a few hit dice for figuring out what it can hit with natural weapons? Where did each approach take you, where did each explanation lead? Was this a rule that really needed an explanation or that was better for having a rationale? Was it better off as just a rule of thumb without explanation?
In this essay you can see my rationale. If you’ve played in games I’ve run you’ve seen how I make it work, which is it rarely matters, but it provides the flavor for why the rules are as they are. You can also see the official rules that eventually got written and put into print in the various editions.
You can make your own determination as to what you want in your game.
I know I do. I know Gary hoped that everyone would make their own determinations and find what made the game more engaging and fun for them. I hope this helps you find the approach and variations that fits what makes it fun for you and that you feel empowered to choose what you prefer rather than what someone tells you to do.
And that is what I was trying to do when I had rules, and did not have them.