Put simply, Damage Reduction (often abbreviated "DR") is an indication of how much physical damage a character sucks up before it actually starts to subtract from their Hit Points.
Though used primarily in Role-Playing Games, DR can be found across many different media. In games, DR typically is the very first thing calculated, right after base damage is assigned, and before any multiplicative or additional damages are added into the equation.
In most Tabletop RPGs, this usually tops out at numbers less than 10, since even 30 damage in pen-and-paper games is enough to kill most low-to-mid-level, non-fighter characters. Electronic and MMORPGs on the other hand, can easily have DR hitting double or even triple digits.
Most systems with a DR mechanic are also systems without Scratch Damage, which means the target cannot be hurt at all if the attacker can't overcome the DR.
One very important to note is that, most of the time, DR reduces only physical damage — that means that, typically, there are one or more ways to get around a DR-based Damage Sponge: Elemental Powers almost always bypass DR, and if Magic Damage is different than Physical Damage, suddenly spamming the hell outta Magic Missile seems like a really, really good idea. Even if neither exist in the setting certain weapons or environment hazards can bypass the effect. DR can also manifest in different types, making some enemies very resistant against magic but weak to physical attacks and so on. Attacks that are specifically designed to ignore Damage Reduction tend to be Armor Piercing Attacks.
The Trope Maker here is a little hard to place, as many/most Tabletop Games miniatures games use some sort of Armor Rating to reduce damage, but the Trope Codifier is without a doubt Dungeons & Dragons (third Ed and above), which uses it to a large extent, and is responsible for the tradition of "magic fire beats DR."
- Tunnels & Trolls (1975) contained the Ur-Example of this trope in tabletop RPGs, replacing D&D's (the only other RPG in existence at the time of its release) armor-as-likelihood-to-miss with armor-as-damage-reduction.
- In GURPS, the primary benefit of wearing/installing armor is reducing damage received. DR is also an advantage that can be purchased by characters, races, etc. One to three points of damage reduction seems to be the "realistic" limit for natural DR, possessed by real animals with thick hides/scales or purchasable by players without needing specific GM approval. Previous versions featured the Toughness advantage, a more expensive DR with a two point Cap specifically for human use, with the base advantage restricted to supers or races.
- Armor piercing attacks generally take the form of a divisor, reducing DR by half or more.
- The Damage Resistance advantage also has a host of options to modify it's function, in particular conjunction with Damage Typing. The advantage could be used to simulate anything from thick skin to magical resistance against a given element to an ablative force field that needs recharging.
- In The Witcher: Game of Imagination armour, both natural and crafted, works this way. If the target is hit, the damage is reduced by a certain value, depending on the type and/or layers of armour. Can lead to situations when no damage is dealt at all. Shields are special in this regard, as they both provide armour value and rise defenses, making it in the same time harder to hit their wielders.
- Dungeons & Dragons makes extensive use of this trope. Damage reduction is generally not provided by wearing armor, even magical, and is usually an ability granted to monsters. Said monsters oftentimes have a weakness that bypasses their DR, usually written as "DR Value / Weakness"* . Some materials or enchantments do provide DR on equipment and some class features also grant it.
- Hardness is a variant used only by inanimate objects, for when players decide to smash down doors, sunder enemy gear, or otherwise wreck their environment. Most objects have little to no armor class and surprisingly little HP compared to a player character. Hardness makes them difficult to actually damage. In theory, this should prevent anyone from just carving a new door through a wall, because standard attacks won't overcome hardness and will never cause hit point damage; in practice, most characters can easily overcome the hardness of stone and players agree to not abuse those rules most of the time.
- Early versions of D&D averted the trope. A creature hit by an attack would most often take either full damage normally or else be flat-out immune no matter how hard it would have otherwise been hit (the latter in particular with regard to insufficiently magical weapon attacks); some cases of half damage would pop up as well, but generally no fixed resistance values whatsoever. It took until the third edition for D&D to employ DR as seen today, long after other games had already used the mechanic for years.
- "Damage reduction" applies to weapon attacks only; energy attacks (acid, cold, electric, fire, and sonic) ignore it. To reduce damage from fireballs and lightning bolts, you need "energy resistance", often provided by spells or as a special quality of creatures. Speaking of which, natural resistance to sonic damage is quite rare.
- Arkham Horror features a few options for DR. The mobster investigator has it as his special ability. A few items and spells allow for it, including a variation of Hyperactive Metabolism were food provides DR rather then healing.
- New Horizon has armor... and specific attacks penetrate the armor, as well as attacks that go overboard.
- Dark Heresy, Rogue Trader, and Deathwatch all have this in the form of both Armor and Toughness. Very few attacks ignore this, though many weapons have Armor Penetration (which ignores a certain amount of Armor) and some have the Felling quality (which ignores a certain amount of "Unnatural Toughness"). Their parent game, Warhammer 40,000, uses a combination of Toughness Values and Armor Saves, though it's a certain chance to ignore damage, rather than reducing it. The Feel No Pain rule is described in the fluff as a more straight example, but again it's an additional chance to ignore damagenote .
- Any game with damage soak rolls, such as Shadowrun, either version of The World of Darkness, and West End Games' D6 system such as the Star Wars d6 RPG. After establishing the damage of the attack, the thing being attacked rolls to reduce the amount of damage actually taken, in terms of their own innate difficulty to damage. Armour may either provide extra dice or reduce the target number of the roll to reduce the damage, depending on system.
- Exalted also has a "hardness" trait for armour, meaning that if the raw (pre-soak) damage doesn't reach the threshold designated by the hardness of the armour, no damage at all is rolled. This, however, is a fairly low number, and if the raw damage reaches or surpasses this threshold it isn't taken into account at all, instead you have to soak for any damage reduction.
- The Hero System's version of defenses functions a touch differently. A character can have both Defenses and straight Damage Reduction; Defenses outright subtract damage from the roll and can reduce it to zero, while Damage Reduction applies after Defenses and cuts the damage received by a straight percentage. Damage Reduction is one of the "warning sign" powers in the book; characters are expected to have fairly limited Damage Reduction, such as having it only apply to certain types of damage, and across-the-board Damage Reduction is mostly the domain of supervillains expected to take on entire teams of heroes singlehandedly or Nigh Invulnerable extreme-power characters like Superman.
- In Magic: The Gathering there is the Absorb mechanic, which allows you to just prevent a certain amount of damage dealt to a creature that has the ability.
- In Spycraft, damage reduction is the armor mechanic, with "armor" and "armor penetration" forming a parallel defensive system to the usual d20 armor class stuff.
- In Numenera, all armor works this way.
- In Ponies & Parasprites damage is reduced in two ways. The first is via use of "Buffer Exhaustion", which allows a character to absorb a certain amount of damage before they are affected by it. The second (such as the Earth Pony's Tough as Nails ability and Celestia's Inescapable Corona of Justice) simply reduces the amount of incoming damage. These two abilities explicitly stack with one another.
- In Palladium's "Mega-Damage" RPGs like Rifts, Robotech, and Splicers, this is pretty much how Mega-Damage works. Normal attacks, which inflict SDC(Structural Damage Capacity)/HP damage, cannot harm MDC materials unless they can inflict around a hundred points of damage or more in a single hit or burst (effectively DR 100/MD). Mega-Damage, however, also works in reverse: a single point of MD is equal to 100 SDC/Hit Points.
- In Eclipse Phase armor reduces damage by a quantity equal to its armor rating, and each type of armor has two ratings, one for kinetic damage and one for energy damage. But, most weapons also have an Armor Piercing rating that subtracts from the armor's effective rating.
- Sentinels of the Multiverse has a few ways for both heroes and villains to do this. Most of the heroes' damage reduction, is personal, like armor equipment or a power, though some heroes can give someone else damage reduction. Generally, -1 reduction is equipment or a power that can stay out indefinitely without penalty. -2 reduction either only lasts a turn, only affects the next damage taken, or is only applicable to damage of 5 or more. And they can stack. The villains' DR often applies to their whole deck, or a group within their deck. Grand Warlord Voss takes the cake. For every minion he has out, he reduces all damage to himself by 2, making him effectively invincible if there's more than two or three minions in play.
- The chief purpose of armor in Planet Mercenary is to reduce incoming damage by the listed Damage Reduction value.
- Kingdom of Loathing has three forms of this. The first, actually called Damage Reduction, subtracts damage taken by a set amount, and the second is Damage Resistance, which reduces damage taken by a percentage at certain levels. Notably, they reduce all types of damage, regardless of element or type. The third, Elemental Resistance, reduces damage of a specific element by a percentage at certain levels.
- Armour in Fallout titles typically have two stats for each type of damage: Damage Threshold and Damage Resistance. Damage Threshold reduces all damage received by a certain amount, while Damage Resistance reduces what's left by a percentage. Fallout 3 only used Damage Resistance, but New Vegas brought back Damage Threshold with one quirk. It reversed the calculation order, so that DR reduces incoming damage before DT. Appropriately, DR is a lot harder to come by, banished to the realms of Med-X and select NPCs. Another change is that the minimum amount of damage you can take is 20%, rather than the 15% of Fallout 3. Of course you could always mod it...
- Similarly in Front Mission, Wanzers have a built in armor plating that reduces damage from any one of the three attack elements (namely Impact, Pierce and Flame). More generally, Wanzer pilots can equip skills that reduce incoming damage or cut certain amounts of damage altogether. The former is great against single shot, high attack power weapons while the latter is excellent against burst fire weapons.
- Mechs in Super Robot Wars titles can have physical shields or Deflector Shields that reduce damage by a percentage or a set amount. Larger units also take less damage from smaller ones, and certain pilot skills also reduce damage (usually one named "Guard", and some character-specific things).
- Defense works this way in Super Mario RPG, the Paper Mario series, and Mario & Luigi: Superstar Saga (but not its sequels). Both Super Mario RPG and Paper Mario use a simple attack power - defense formula for damage, though RPG has separate physical and magical stats (magic defense is generally lower), and all attacks will inflict at least one damage. Superstar Saga is a bit more complicated - POW and DEF are multiplied by different values before subtraction occurs. For enemies, it's always 0.4*POW - 0.2*DEF, with POW being different depending on the attack. Mario and Luigi have constant POW, but their multipliers vary a lot depending on which attack is used and how well you do the Action Commands.
- Defense in Terraria works like this. For every 2 Defence a player or enemy has (or 1.5 in Expert), they take one less damage from attacks. Attacks will still deal at least one point of damage, however.
- Most forms of defense in XCOM: Enemy Unknown work by either making a unit harder to hit (cover, various abilities) or adding Hit Points (most armor). The exceptions are the Hardened trait (shared by most units on both sides that are incapable of taking cover) and Resilience skill, which grant immunity to Critical Hits, effectively reducing their damage back down to normal levels, and two unique MEC trooper skills which reduce damage by 2 for 2 turns after a successful hit, and reduce any hit that would take off more than a third of their life down to a third.
- The Long War Game Mod adds a specific damage reduction with its own icon, granted mainly to machine/armored enemies as well as units in cover.
- XCOM 2 adds an armor mechanic, most often seen on mechanical units or units wearing Power Armor. Each point of armor reduces damage from weapon attacks by one point. Certain attacks can "shred" targets, reducing their armor value for the rest of the mission.
- Characters in Nexus War have a Soak value for each type of damage, reducing the damage received by a flat amount. For example, a character wearing a chain-mail shirt would suffer reduced slashing damage from a sword strike but take full damage from an acid spell. Resistance is a percentile reduction applied after Soak, only available through certain skills. Scratch Damage applies in that the target will always suffer at least 1 point of damage if not completely immune to the damage type.
- In Ancient Domains of Mystery, this is how armour works: it mostly grants "Protection Value", and your Protection Value is your amount of damage resistance. (There is also "Defensive Value", which makes you harder to hit.)
- In Warframe, this is the purpose of armor for players and enemies alike. Unlike most examples, it's a percentage-based modifier, with the fraction of damage received decreasing asymptotically as armor increases. Notably, it only reduces the damage taken to health; shields get no benefit whatsoever. It also alters the effectiveness of different damage types. There are still ways around it: Corrosive procs, Corrosive Projection, and certain Warframe Augments can permanently reduce enemy armor, while Finisher damage ignores it outright.
- Iji has the "Suppression" trait, unlocked by maxing out the Health stat (to a maximum of 20HP), which reduces any HP damage by one, to a minimum of one. One boss has a 5HP attack that has both a flag for ignoring all defenses (Mercy Invincibility, Suppression, etc.) and a special code for not ignoring Suppression after all.
- Armor in Overwatch works by subtracting 5 from any instance of incoming damage, or halving it, depending on which would result in damage reduction having the lesser effect.
- There are also several buffs that reduce a percentage of incoming damage. The most interesting examples are Orisa's Fortify, which halves incoming damage for a few seconds (among other things), and Ana's Nano Boost, which applies a buff to an ally which halves incoming damage for a few seconds (among other things). Consider not only that these stack, but that Orisa has the aforementioned armor, and you can see how a nigh-unkillable Orisa can exist.
- The Final Fantasy games typically has the Protect and Shell spells, which reduces damage from physical and magical damage respectively.
- Final Fantasy XIV have tanks that have abilities whose purpose is to reduce incoming damage for a few seconds. Since a tank's job is to soak up damage, having damage reducing abilities makes their job easier. Healers have barriers which absorb a certain amount of damage before the barrier breaks.
- In Sins of a Solar Empire, capital ships and bigger things get damage reduction from two sources: armor and shields (while they're up). Between the damage reduction and self-repair, putting down a capital ship and higher is a pretty tough task.
- Fire Emblem Awakening and Fire Emblem Fates have a couple of skills that work like this. Pavise can potentially halve the damage from an incoming physical attack, while Aegis can halve magical damage.
- Pokémon has the Barrier, Reflect, and Light Screen moves. The former two reduce physical damage, while the latter reduces special damage.