What are hit points?
The DM’s Guide defines hit points as “The number of points of damage a creature can sustain before death (or optionally, coma), reflecting the character’s physical endurance, fighting experience, skill or luck.”
I have discussed this before ... but admittedly I got distracted by the problem on how to assign hit points, as opposed to what they actually were.
However we may quibble about this definition, we may propose that in D&D the character is an entity made up of corporeal and electrical functions that enable action. Damage is that which disrupts the integrity of these functions. When integrity is reduced to zero, the character dies.
The difficulty is that D&D fails to ascribe any effects at all to the loss of hit points except death. You are either alive or you are dead. If you have 1 hit point, you are alive. If you have no hit points, you are dead. If you are alive, you function at 100% capability. If you are dead, you function at 0% capability. It is very black and white.
I have written rules in the past that have attempted to provide a little grey. This, however, still doesn't explain why a character has the same combat offensiveness at 1 hit point that they had at 30.
The most direct, accurate explanation is that this is a game, dumbass ... and games include all sorts of rules which have little or nothing to do with reality. Why is it I have to randomly stay at hotels in Monopoly? Can't I just walk down the street to where the rooms are cheaper? How is it that it takes the same amount of time in RISK for an army to cross Western Europe as it does North Africa? Why do the East Indies, Madagascar and Mongolia produce the same number of armies as Northern Europe, Japan and the Eastern United States? How come I can't change what I do for a living in the Game of Life? Why does the game end once I've made it to Millionaire Acres? Don't millionaires get married, have children and potentially wind up in the Poor House too? Do I die when I become a millionaire?
On some level, I think people are a little more than mildly stupid when this sort of problem with a game is exhaustively analyzed. Still, I've got some energy, so let's haul it on the slab and gut that puppy.
In the traditional game, if you have 100 hit points, you're going to last longer than a couple of rounds - there are no processes for decimating that many hit points in a single blow. Critical hits and such were added later ... and that does enable you to have a moment of bad "luck" and lose a massive number in a short period of time. So it is possible that hit points represent a statical time period (average damage sustained per round vs. total hit points) before anyone actually lands a blow on you that will kill. When they do land that blow, you die (or you slip into the negatives).
The trouble is that players are aware of how many hit points remain ... which means they can effectively foretell the future; "I haven't been hit up to now, but if I spend three more rounds, I'm dead!" The only way to truly get out of that headspace is to A) never tell the characters how many hit points they have; B) never tell them how much "damage" their hit points have suffered. This would be a very strange way to run ... and might seriously mess with the player's headspace. Just imagine.
You have hit points, which increase with level ... but you never really know how many you have.
You take "damage" that is not actually physical - just a lot of really close calls and weapons that hit your shield or armor really hard. You maybe get a nick or cut, to tell you you're in a fight - but you have no idea if this nick or cut represents a loss of 10 hit points or 1, and you have NO IDEA if 10 hit points is something you can afford to lose right now, or not.
Then, if you really want to FUCK with the player's head, don't tell them when damage has occurred. Play the game so that the nick of a sword doesn't necessarily cause damage ... that's just more general fluff for the campaign world's "feel."
Every round you stay in battle, in that system, is going to bring a level of panic that doesn't exist in the game ... particularly since you don't know if you've taken damage or not. If you've been swinging now for ten or twelve rounds, you're going to get fucking nervous, even if you're seventh or eighth level. Shit, do you have 70 hit points still? Have you even lost a single point? Or are you actually at 3 points right now, and you're going down any second? You just don't know. You'll never know.
Which, if you're going for simulation, IS the shit, baby. Just watch players second guess themselves and run from combats when they can't look at a character sheet and compute their odds with hard facts. Still, the reality, o gentle readers, is that in the middle of a combat YOU DON'T KNOW. You haven't any idea, not really. You could imagine that after breaking your arm, you're probably not long for the slaughter fest. Yet until you've actually been hurt, well guess what: 1 hit point IS exactly the same as 30 hit points, with regards to your combat ability. Which is the D&D idea.
It isn't wrong because the system is irrational. It's wrong because your character knows a lot more than your character should know.