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Health makes you stand longer if you have taken damage.
As higher armor also reduces e.g. damage taken from poison, a low health pool with high armor could be more viable.
But since you don't have to decide whether you can have either a lot of armour or a lot of health, both high armour and high health are possible.
Just try it yourself: without having eaten anything (25HP) let a greyydwarf shaman cast the poison thing on you. If do not wear any armor, you will die fast. If you wear some gear, it will take more ticks of the poison DOT to kill your viking.
https://valheim.fandom.com/wiki/Damage_mechanics#Armor
Shields act like a second layer of armor - it works exactly the same way to weaken the damage before it gets to armor, which then weakens that new value further. Small shields ("not-tower-shields") have higher block values when used in a Parry (block action just as/immediately before the attack hits - shields named as bucklers tend to have higher multipliers [x2.5 typically] than ones labeled as round shields [usually x1.5]).
On top of that, some armors will provide a resistance or vulnerability to specific types of damage. A resistance typically halves the damage you take after it's been run through the armor calculation, while a vulnerability typically adds half-again of what got through.
Finally, armor currently also applies to DoT (Damage-over-Time) attacks, lessening the risks of things like fire or poison without needing any specific resistance (as mentioned in the previous paragraph).
so reducing incoming damage via armour is one factor during combat- the other is absorbing stagger, which is dependant on how much max HP you currently have and is visualised by that little red bar that fills up whenever you take a hit. If it fills up completely, you get staggered.
WHEN you get staggered, some very important things happen depending on what you had been trying to do to stop it; plainly blocking, will negate the block armour of the shield and filter the entire attack through just your armour. Parrying will still stagger the enemy, but then you both just sit there pinwheeling your arms until one of you recovers. in one of one encounters this is usually fine, because players recover faster than most mobs. But let's be honest, there's almost always going to be another enemy nearby whose going to punish you for your hubris.
4 damage types generate an amount of stagger equal to the amount of HP they would have claimed; blunt, pierce, slash, and lightning damage all do an amount of stagger equal to the damage you take after armour and shield reductions. All other damage types do not generate stagger.
all stagger generated decays at a rate of 20% of your stagger limit per second. This means big hits and many rapid small hits can overwhelm an opponent( and you) when the stagger limit has been reached.
Almost every entity in the game save for bosses and 9 other mobs have a set amount of hp they can lose in a short period of time before they are staggered and are rendered vulnerable to all sources of damage(barring immunities) for the duration that they are incapacitated.
The player character, for instance has a stagger rate of 40% and when they become staggered, remain so for about 1.18 seconds, which is one of the shortest stagger times outside of mobs that are explicitly immune to stagger. You can have all the armour in the world, but if the damage that does leak through does at least 40% of your max hp, you are rendered helpess for a brief period of time, which given that the player is frequently outnumbered, is often a death sentence. This is why HP foods are so important, because the higher your max HP is, the higher too, your stagger limit will be.
Contrast this to trolls for instance;
base 600 hp, but they have a 33% stagger limit instead, which means for a 0- star troll, you only need to do 180 points of stagger before they are rendered vulnerable to further assault. they are also weak to pierce damage, which will do 50% more damage. They also remain staggered for a whopping 2.74 seconds, and occasionally up to 5.46 seconds randomly during unarmed melee.
This is a big reason why I love the polearms so much; the power attack doesn't do any more damage, BUT the physical damage it does generates 6 times as much stagger as it normally would have. Based off the numbers above, you can reliably stun lock 0-star trolls on demand with the atgeir as long as your lower damage range( the yellow numbers on the weapons item card) is at least 20.
a lot of player will argue in favour of parrying, and in a lot of cases it's generally an excellent go to, but with a polearm, you don't need to wait for a parry opportunity, you just lead with a power attack and you can pull a group of enemies apart faster than you can say "parry bonus"
TL:DR boost armour AND HP in tandem to be more gooder at not dying.