In combat, there are different ways that an attack can affect a character. The following are optional alternatives to taking a whack to your HP for you to choose if the situation seems right.
Armor Damage
A character that is wearing armor (defined as something that protects them by adding to their AC) can choose to allow their armor to take the brunt of a critical hit, reducing the armor's AC bonus by 1 to reduce damage from the attack to 0.
This cannot be used against critical sneak attacks, and once the armor has lost all AC bonuses it is broken beyond repair.
Anything other than complete damage to the armor can be repaired at a smith/armorer for the cost of 10gp per AC point restored, or 15gp for armor with magical properties. (As with any business venture, characters can try to haggle this like normal.)
Elemental Alternatives
Acid
The corrosive spray of a black dragon’s breath and the dissolving enzymes secreted by a black pudding deal acid damage.
Consumed - Acid eats away at the targets’s defenses, reducing AC by -1 until they can repair the damage at a smith/armorer. (See above for costs.)
Bludgeoning
Blunt force attacks—hammers, falling, constriction, and the like—deal bludgeoning damage.
Pummeled - The attack overwhelms the creature, knocking it prone.
Cold
The infernal chill radiating from an ice devil’s spear and the frigid blast of a white dragon’s breath deal cold damage.
Frostbitten - Cold creeps into the creature's muscles and its movement is slowed by 10ft for until the end of its next turn.
Fire
Just as red dragons breathe fire, many spells conjure flames to deal fire damage.
Set Ablaze - The target catches fire and takes additional burning damage (1d6) at the start of the next turn unless it uses an action to put itself out. Flammable objects may also be destroyed.
Force
Force is pure magical energy focused into a damaging form. Most effects that deal force damage are spells, including magic missile and spiritual weapon.
Pushed - the target is pushed back back 10ft by telekinetic energies. If the target cannot move 10 feet due to an obstruction, taking 1d4 bludgeoning damage for each 5ft of movement it was blocked from, to represent the force of hitting an obstruction. If this obstruction is another creature, each takes 1d4 of bludgeoning damage.
Lightning
A lightning bolt spell and a blue dragon’s breath deal lightning damage.
Shocked - The target is shocked by the attack and can’t take reactions until the end of its next turn.
Necrotic
Necrotic damage, dealt by certain undead and a spell such as chill touch, withers matter and even the soul.
Withered - The target is afflicted with decay and can't regain hit points until the end of its next turn.
Piercing
Puncturing and impaling attacks, including spears and monsters’ bites, deal piercing damage.
Pinned - The attack pins the target, and it suffers disadvantage on dexterity saving throws until the end of its next turn or until the weapon is removed.
Poison
Venomous stings and the toxic gas of a green dragon’s breath deal poison damage.
Weakened - The attack wears at the body's poison tolerance; take the next poison save at a disadvantage.
Psychic
Mental abilities such as a mind flayer’s psionic blast deal psychic damage.
Dumbfounded - The target’s mind is overwhelmed and it has disadvantage on ability checks until the end of its next turn.
Radiant
Radiant damage, dealt by a cleric’s flame strike spell or an angel’s smiting weapon, sears the flesh like fire and overloads the spirit with power.
Dazzled - An intense flash temporarily blinds the target, granting advantage on next attack against them.
Slashing
Swords, axes, and monsters’ claws deal slashing damage.
Hamstrung - The attack caught a tendon, rendering the character's next attack less effective; take disadvantage on the next attack.
Thunder
A concussive burst of sound, such as the effect of the Thunderwave spell, deals thunder damage.
Disoriented - The sudden boom of sound throws the target off balance and deafens them until the end of them next turn. A deafened creature can’t hear and automatically fails any ability check that requires hearing.
