The loss of hit points is represented most viscerally by a notation on a piece of paper. That is caused by a die roll mediated through someone's brain and thereby interpreted as a certain sort of "move" in a game. The die roll is in turn triggered by an action declaration, typically "I attack it".
Whether or not that notation on a piece of paper also represents something in the shared fiction of the game is a further question. Many people take the view that not all such notations do represent something. For instance, many people doubt that writing down XP totals actually represents something in the fiction. Similarly, I don't think anyone thinks that initiative scores represent anything in the fiction (they're just a metagame ranking device for making the action economy work).
Sure, XP represents something in the fiction: the gaining of
experience that leads you to being stronger, better, faster, etc. Your character at 100 XP is different in the fiction than your character at 10,000 XP. It's the Hero's Journey (or some other character development) as a point total! At the very least it represents the
amount of story that has happened to the character.
And Initiative represents something in the fiction, too: who acts before who in the attempt to beat someone else to the punch.
Given that reducing the hit point total does move the target closer to defeat, we can confidently say that a hit point loss represents that much, namely, that the opponent who made the attack - ie who engaged the target in combat - has pushed the target closer to defeat. Whether the hit point loss corresponds to any discrete injury is not a question we can answer just from considering the mechanical situation (unless of course the hit point loss reduces the target to 0 hp). It seems to me largely a matter of taste.
In basic D&D, this kind of "defeat" is equal to physical, corporeal death. Something that defeats a creature by reducing its HP is something that can kill that creature. It's not a matter of taste: the rules dictate what happens at 0 hp, and it is exactly one kind of defeat, and that is death (or, depending on how gentle your dying rules, damn close to it).
If you wanna play with other defeat conditions at 0 hp, that's awesome, but it's clearly giving up the claim of being basic/traditional/classic D&D. Which is fine (that label can do more harm than good), but it probably be something you want to enable as an option, not something you assume everyone is doing just by playing D&D. In designing D&D (as opposed to any other RPG), death is what you need to assume is at risk of happening at 0 hp in pretty much everyone's game (and an option to change that is certainly worth consideration).
D&Dnext seems to default to the assumption that if you're not bloodied yet, then hit point loss does not correlate with injury, but if you are it does. That doesn't particularly suit my taste, and I think it can cause some other wonkiness, but it's not an obviously flawed approach. Others who want to argue that every hit point loss event at the table corresponds to an injury event in the fiction are of course free to take that approach, but I don't think the mechanics in any way mandate, or even speak in favour of, that approach rather than the D&Dnext default or (what I take to be) the 4e default that the only injuries are those which correspond to condition infliction (including "bloodied" and "dying") as opposed to simple hit point loss.
As long as HP loss can kill you, things that cause HP loss need to be potentially deadly. Playing around with other "conditions" can be cool, but by that point you're giving up claims of being traditional D&D. Which is awesome, but not something that should be expected of every group.
The mechanic only exists to resolve the question of "I do X. What Y happens?" The mechanics do not resolve the question of "Y happened. What X did I do?"
Says who? (Other than you, obviously.)
Causality, mostly. With a dash of player empowerment.
Gygax clearly had a different view, in relation to attack rolls: you don't know exactly what you did until attack and damage are resolved; and in relation to saving throws, where again you don't know exactly what you did until the saving throw is resolved. And it's not as if Gygax didn't know a thing or two about how D&D mechanics might work!
I've probably never played D&D As Gygax Intended. I'm not even 100% convinced that Gary played D&D As Gygax Intended. One of the big strengths of the game is that there's no One True Way!
You can treat it that way. I think it's most neutrally interpreted as answering the question, "As I engage the goblin in melee while wielding a sword, who is being worn down?"
That doesn't sound like a game of action and adventure, to me. It sounds like what happens during a tough day at the office.
Without that try, there's no roll of the dice. There's no outcome to resolve if there is no cause that creates the potential outcome.
You can treat it that way. Or I could say: without that
conflict, there's no roll of the dice. Nothing in the mechanics speaks in favour of your treatment over mine.
Your treatment is a subset of mine. Without action, there's no conflict.
The player announced what his character hopes for - say, defeating the goblin in melee - and the resolution tells you to what degree, if any, that hope was realised.
...
Sure, the player does a thing. That may or may not correspond to the character doing a thing at the same time that correlates in any meaningful way. The player can declare "I roll an attack". In the fiction, that corresponds to "My guy engages that guy in combat and tries to defeat him", but in D&D at least it's hard to be much more specific than that until the action is resolved.
If the player hopes to defeat the goblin in melee, they best be
doing something to accomplish that goal. Hoping at it isn't going to do squat.
What does that engagement look like? What do you do, specifically, to engage the creature? What are you trying to do, specifically, now, in the moment, here with the goblin in front of you snarling and the sweat on your brow and the stink of its warren permeating your nostrils. Give me some concrete
actiion.
It's a rule from improv: be specific. Be present. Make statements. Give detail. The more concrete things that people have to hang their vision of the scene on, the better anchored everyone is to make future decisions. The less detailed and specific and realized a given action is, the more nebulous and wobbly it all is, the less you suspend your disbelief, the less "real" it feels, the closer we all are to realizing we're grown adults sitting around a table pretending to be magical elves.
Hey, maybe some groups have a lower threshold for that suspension of disbelief, or prefer to play the game at a higher level of remove, or whatever. But I don't think the rules can presume that most people can live with nebulous general goal statements. Certainly an audience at an improv show wouldn't be able to live with "I hope to defeat this opposition!" for very long before they just want to see someone
do something.
I want to encourage my players at every turn to take definitive, discrete action, to do a thing, so that I can respond, and so that we can get on with it. If the player can't pass the Journalism 101 test when they declare their action (Who? What? When? Where? Why? How?), it's not useful to me. It doesn't give me anything specific to work with to inform my response.
This seems to presume that the output is determined before the input, that we know the effect before we know the cause
Correct. Unless your PC is wielding a vorpal sword, until you roll the damage roll, and we thereby learn whether or not the enemy has been reduced to 0 hp, we can't know whether or not your blow struck his/her neck with enough force to sever it.
But we can know that your PC tried to cut off the enemy's head. Just because we don't know the success of an action before dice are rolled doesn't mean we don't know what actions were taken.
But nothing in either the general idea of RPG mechanics, nor in the particular design of D&D mechanics, pushes in favour of your preferred approach. You might wish that D&D was a different sort of system (perhaps more like Runequest, say). But it's not. Gygax's way isn't the only way, but it's not like he was wrong about how his game system was meant to work.
The only points I have in my favor as a default are points of psychology and D&D history: Injury makes you die, and specific is more interesting and grounding than general.
Which isn't to say that's what it's always tethered to. That's just probably what the game should embrace as a default, IMO.