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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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The default formula that determines AC is:
The default formula that determines AC is:
: {{InfoBlob|10 + [[Dexterity|Dexterity modifier]] + armour bonus + shield bonus + other bonuses and penalties}}
: {{InfoBlob|10 + [[Dexterity|Dexterity modifier]] + armour bonus + shield bonus + other bonuses and penalties}}
The AC bonus from Dexterity modifier may be capped when wearing [[Armour#Medium armour|medium]] and is ignored entirely when wearing [[Armour#Heavy armour|heavy]] armour.
[[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.


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. These are [[Yuan-Ti Scale Mail]], [[Unwanted Masterwork Scalemail]], [[Sharpened Snare Cuirass]], and [[Armour of Agility]].}} whereas 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.
 
Shields will grant the listed AC bonus to whomever equips it, regardless of which weapon slot they are currently using.


=== Other formulas ===
=== Other formulas ===
Unarmoured creatures may use a different formula if they have certain features. Creatures always use whichever formula – which they have access to – would result in a higher AC.{{note|Alternative formulas are only used if {{em|no}} armour is worn in the chest, hands, helm or boots slots.|name=slots}}
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}}


{{SAI|Mage Armour}} and {{SAI|Draconic Resilience}}:
{{SAI|Mage Armour}} or {{SAI|Draconic Resilience}}:
: {{InfoBlob|13 + Dexterity modifier + shield bonus + other bonuses and penalties}}
: {{InfoBlob|13 + Dexterity modifier + shield bonus + other bonuses and penalties}}


{{SAI|Unarmoured Defence (Barbarian)}}:
{{SAI|Unarmoured Defence (Barbarian)}}:
: {{InfoBlob|10 + Constitution modifier† + Dexterity modifier + shield bonus + other bonuses and penalties}}
: {{InfoBlob|10 + Constitution modifier + Dexterity modifier + shield bonus + other bonuses and penalties}}


{{SAI|Unarmoured Defence (Monk)}}:
{{SAI|Unarmoured Defence (Monk)}}:
: {{InfoBlob|10 + Wisdom modifier† + Dexterity modifier + other bonuses and penalties}}
: {{InfoBlob|10 + Wisdom modifier + Dexterity modifier + other bonuses and penalties}}


== Mathematics==
== Mathematics==
Armour Class becomes more useful the greater it is – the difference in effectiveness between 20 and 19 AC is {{em|greater}} than the difference in effectiveness between 15 and 14.
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 +5 (50% chance to hit) to attack rolls, and deals 2 damage per attack, the defender would on average survive for 10 turns.
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).
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).

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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