The wizard took so many cuts and bruises, yet did not care. If there was still a scrap of life left, that’s all that matters. One more damage and the wizard died, thus concluding the match of Magic: the Gathering.
The joke in MtG is that all hit points are irrelevant. except the last one. The game can be seen as a race to achieve victory before your life runs out. Often this entails directly attacking the opponent’s life total, some other times it’s way more complicated.
D&D feels sort of the same, sometimes. The narrative of HPs is that they are not simply wounds, but a mixture of stamina, bruises, tenderness, encroaching disabling pain, and real wounds. And until they all are gone characters can perform.
Perform normally? Probably not. Truth is, humans can take stupid amount of damage before stopping. I walked a week on a broken leg. A few years later, while bouldering, I had a bad fall and broke two ribs, yet I kept on climbing, even if in pain. I discovered my ribs were broken only weeks later, when I went to the hospital as the pain was still intense. I was informed that my lungs were not collapsed, which is great because it happens quite often when you break your ribs. No, most people do not notice. And these experiences are completely normal. I might say they are even quite mild.
Probably at that last HP you can hear your heart pumping like crazy, you are gnashing your teeth to avoid screaming in pain, and you might be about to faint, Still, you are holding on to dear life, trying to keep stabby sharp metal away from your body, running even if your legs are burning and your lungs have given up, in the hope that you’ll make another day. Because that is the kind of otherwise insane tenacity dying people routinely display. They will keep on going until they collapse, are overwhelmed by pain, their limbs give up, or their morale breaks. If they do not, and are in a dangerous situation like a melee, falling down, or slowing down, or routing is as good as dead.
There are ways to get better at this. The little martial arts I’ve done (some karate, a few months of HEMA, and an exercise routine that often was “20km on the bike and then punch the sack 600 times because I cannot punch bullies”) seems to point in the direction of familiarizing yourself with pain, and normalizing it. At some point you give up not being in pain when you exercise or when you spar. It’s in a way similar to the typical workout soredness, and similarly you learn to push through it, but the kind of it’s sharper, longer, and for what I’m concerned entirely different in its essence. That kind of pain is just in the nature of spending time being in fights: you train to fight and get covered in bruises while doing so, and then train covered in bruises. Sparring is soaking in pain: fighting will be carried out in pain too.
And this is why fighters have more hit points, by the way. They are just used to having the living crap beaten out of them, can stab you even when stabbed, and are less overwhelmed by the terrifying taint of approaching death.
Ok, now some rules on HPs that I have been using for the past 5 years or so. They give the player the certainty that they are really out of everything and the next blow is going to put them down:
You can perform normally even at 0 HP. If you were to go under 0, if the blow was hella mighty you just die, otherwise you stay at 0 HP.
At 0 HP, however, you know another wound will be your end. If you are hit at 0 HP you will definitely die, or if you are lucky you will collapse and/or be mutilated. In the latter case, use this table.