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Armour Class: Difference between revisions

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(an attack roll that equals the AC hits, so a +5 attack has 55% chance of hitting a 15 AC, not 50%. +4 is what works with the rest of the math here)
 
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{{ up to date | 2023-08-18 }} <!-- Date format is YEAR-MONTH-DAY, like 2023-08-07. -->[[Category:Gameplay Mechanics]]
{{guidenote}}
'''{{ArmourClass}}''' ('''AC''') is a measurement of how difficult a creature is to be hit by an attack. AC can be increased by equipping [[Armour]] and [[Shields]], by selecting certain [[Feats]] when leveling up, or utilizing certain Magic [[Spells]].
'''Armour Class''' ('''AC''') is a measurement of how difficult a creature is to be hit by an attack. In order to successfully hit a creature, the results of an [[Attack roll|attack roll]] must have a number equal to or greater than the target's Armour Class. AC can be increased by equipping [[Armour|armour]] and [[Shields|shields]], by selecting certain [[Feats|feats]] when leveling up, or utilizing certain [[Spells|spells]].


The formula that determines AC is:
== Formulas ==
The default formula that determines AC is:
: {{InfoBlob|10 + [[Dexterity|Dexterity modifier]] + armour bonus + shield bonus + other bonuses and penalties}}
[[Armour#Medium armour|Medium]] armour caps the Dexterity Modifier to +2.{{note|The [[Medium Armour Master]] feat increases the cap from +2 to +3.}}{{note|Four rare armours have an "Exotic Material" trait that allow the wearer to get the full Dexterity bonus to AC, namely [[Yuan-Ti Scale Mail]], [[Unwanted Masterwork Scalemail]], [[Sharpened Snare Cuirass]], and [[Armour of Agility]].}} [[Armour#Heavy armour|Heavy]] armour ignores the modifier entirely.


<center>Armour Class = {{InfoBlob|Base Armour Class + [[Dexterity#Dexterity Modifier Chart|Dexterity Modifier]] + Other Bonuses and Penalties}}</center>
Shields will grant the listed AC bonus to whoever equips them, regardless of which weapon slot they are currently using.


*Base Armour Class is the number seen in shields in the descriptions of armour. When unarmoured, most creatures naturally have a Base AC of 10.
=== Other formulas ===
**[[Mage Armour]] sets the base armour class to 13 if the target isn't wearing any armour
Unarmoured creatures may use one of the following different formulas if they have certain features. Creatures always use whichever formula would result in a higher AC among those they have access to.{{note|Alternative formulas are only used if {{em|no}} items are worn in the chest, hands, helm or boots slots which are labelled as armour. The Monk version also stops working if a shield is carried.|name=slots}}
*The AC bonus from Dexterity Modifier may be capped when wearing heavier types of [[Armour]].
** Light Armour doesn't cap the Dexterity AC. Clothing doesn't either, but they don't count as armour at all.
** Medium Armour typically caps the Dexterity Modifier to +2 
*** The [[Medium Armour Master]] feat increases the cap from +2 to +3
*** A few rare armours have an "Exotic Material" trait that allow the wearer to get the full Dexterity bonus to AC. These include [[Yuan-Ti Scale Mail]], [[Sharpened Snare Cuirass]], and [[Armour of Agility]].
** Heavy Armour ignores any bonus (or penalty) from the wearer's Dexterity.


* The final term, "Other Bonuses and Penalties" is a very valuable source of AC, it is subject to the least amount of restrictions, but also are relatively rare, demands certain trade offs, or otherwise require the expenditure of [[Resource|Resources]].
{{SAI|Mage Armour}} or {{SAI|Draconic Resilience}}:
** [[Shields]] will grant its listed AC bonus to whomever equips it. This means the user's off hand will be occupied, denying the bonus they would get for two-handing a versatile weapon, and wouldn't be able to equip a two-handed weapon or an off-hand weapon.
: {{InfoBlob|13 + Dexterity modifier + shield bonus + other bonuses and penalties}}
** Certain Clothing and Armours grant bonus AC outside of their Base AC. [[Potent Robe]] is an example of this.
 
** [[Barbarian|Barbarians]] and [[Monk|Monks]] have access to the [[Unarmoured Defence (Disambiguation)|Unarmoured Defence]] feature. Allowing them to add their Constitution Modifier and Wisdom Modifier to AC respectively, but only when unarmoured.
{{SAI|Unarmoured Defence (Barbarian)}}:
** [[Fighter|Fighters]], [[Paladin|Paladins]], and [[Ranger|Rangers]] have access to the '''Defense [[Fighting Style]]''' feature, which grants +1 AC if the they are wearing armour.
: {{InfoBlob|10 + Constitution modifier + Dexterity modifier + shield bonus + other bonuses and penalties}}
** The [[Defensive Duellist]] feat allows a character to spend their [[Reaction (Resource)|Reaction]] to functionally add their [[Proficiency Bonus]] to their AC for a '''single''' incoming attack. The character must be wielding a [[Finesse]] weapon they are [[Proficiency|Proficient]] in. (This is actually implemented by imposing a penalty to the incoming attack roll.)
 
** A few spells grants bonus AC: [[Barkskin]], [[Shield of Faith]], [[Shield|Shield(Spell),]] [[Mirror Image]], and [[Haste]]. But all of these either don't last long, requires concentration, or are otherwise limited in its bonus.
{{SAI|Unarmoured Defence (Monk)}}:
** Spells that decreases AC are even rarer: [[Slow]] can do this directly, but is subject to a saving throw; [[Chromatic Orb: Acid]] and [[Melf's Acid Arrow]] can achieve this via an [[Acid Surface]], but can be swiftly negated when the victim leaves the surface.
: {{InfoBlob|10 + Wisdom modifier + Dexterity modifier + other bonuses and penalties}}
In order to successfully hit a creature, the [[Attack Roll]] must have a number ''equal to'' or ''greater than'' the target's Armour Class. This means, typically, each point of AC makes a creature 5% harder to hit.{{GameplayNavbox}}
 
== Mathematics==
Armour Class becomes more useful the greater it is; for instance, the difference in effectiveness between 20 and 19 AC is {{em|greater}} than the difference in effectiveness between 16 and 15.
 
To illustrate this, if a defender has 15 AC and 10 HP, and the attacker has +4 (50% chance to hit) to attack rolls, and deals 2 damage per attack, the defender would on average survive for 10 turns.
 
If the defender's AC was increased to 16 (45% chance to be hit), they would instead survive for an average of 11.1 rounds (an 11% increase in effectiveness).
 
Meanwhile, if the defender has 19 AC (30% chance to be hit), they would survive for an average of 16.66 rounds. If their AC was increased to 20 (25% chance to be hit), they would be able to survive for an average of 20 rounds (a 20% increase in effectiveness).
 
The difference between 25 and 24 is even greater, with a {{em|100%}} increase in effectiveness (50 vs 100 rounds).
 
== Footnotes ==
{{notelist}}
 
{{NavGameplay}}
 
[[Category:Gameplay mechanics]]

Latest revision as of 18:41, 7 October 2024

Armour Class (AC) is a measurement of how difficult a creature is to be hit by an attack. In order to successfully hit a creature, the results of an attack roll must have a number equal to or greater than the target's Armour Class. AC can be increased by equipping armour and shields, by selecting certain feats when leveling up, or utilizing certain spells.

Formulas[edit | edit source]

The default formula that determines AC is:

10 + Dexterity modifier + armour bonus + shield bonus + other bonuses and penalties

Medium armour caps the Dexterity Modifier to +2.[note 1][note 2] Heavy armour ignores the modifier entirely.

Shields will grant the listed AC bonus to whoever equips them, regardless of which weapon slot they are currently using.

Other formulas[edit | edit source]

Unarmoured creatures may use one of the following different formulas if they have certain features. Creatures always use whichever formula would result in a higher AC among those they have access to.[note 3]

Mage Armour Mage Armour or Draconic Resilience Draconic Resilience:

13 + Dexterity modifier + shield bonus + other bonuses and penalties

Unarmoured Defence (Barbarian) Unarmoured Defence (Barbarian):

10 + Constitution modifier + Dexterity modifier + shield bonus + other bonuses and penalties

Unarmoured Defence (Monk) Unarmoured Defence (Monk):

10 + Wisdom modifier + Dexterity modifier + other bonuses and penalties

Mathematics[edit | edit source]

Armour Class becomes more useful the greater it is; for instance, the difference in effectiveness between 20 and 19 AC is greater than the difference in effectiveness between 16 and 15.

To illustrate this, if a defender has 15 AC and 10 HP, and the attacker has +4 (50% chance to hit) to attack rolls, and deals 2 damage per attack, the defender would on average survive for 10 turns.

If the defender's AC was increased to 16 (45% chance to be hit), they would instead survive for an average of 11.1 rounds (an 11% increase in effectiveness).

Meanwhile, if the defender has 19 AC (30% chance to be hit), they would survive for an average of 16.66 rounds. If their AC was increased to 20 (25% chance to be hit), they would be able to survive for an average of 20 rounds (a 20% increase in effectiveness).

The difference between 25 and 24 is even greater, with a 100% increase in effectiveness (50 vs 100 rounds).

Footnotes[edit | edit source]

  1. ↑ The Medium Armour Master feat increases the cap from +2 to +3.
  2. ↑ Four rare armours have an "Exotic Material" trait that allow the wearer to get the full Dexterity bonus to AC, namely Yuan-Ti Scale Mail, Unwanted Masterwork Scalemail, Sharpened Snare Cuirass, and Armour of Agility.
  3. ↑ Alternative formulas are only used if no items are worn in the chest, hands, helm or boots slots which are labelled as armour. The Monk version also stops working if a shield is carried.
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