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For a comprehensive summary of the mechanics behind all rolls and modifiers, see: Die Rolls
An Attack Roll happens when the game wants to decide whether an attack will hit its target. This is different from a Damage Roll, which instead determines the amount of damage done. The Attack Roll uses a D20 and can be affected by Modifiers such as the Ability Score Modifier and Proficiency Bonus of the creature making the attack. The result of the roll, after Modifiers, is compared to the Armor Class of the target. If the Armor Class is reached or exceeded, the attack is a successful hit and the game proceeds with a Damage Roll.
As a special case, a roll of 1 means that the attack fails regardless of bonuses and target Armor Class. This is called a Critical Miss. Likewise, a roll of 20 means the attack succeeds regardless of the target's Armor Class. This is called a Critical Hit. A critical hit also affects the result of the Damage Roll, though the details of how this will be implemented in the finished game are not known yet.
Attacks done with Weapons always use an Attack Roll to determine success. Some spells also use an Attack Roll to determine whether they hit their intended target (such as Fire Bolt or Eldritch Blast), though other spells hit the target automatically (such as Magic Missile or Fireball). A spell that hits its target automatically may allow the target to make a Saving Throw instead.
The Ability Score used for the Modifier depends on the type of attack that's being made. Melee and ranged weapon attacks use Strength or Dexterity, depending on the weapon. For spells, the Ability Score used for the Modifier generally depends on the class of the caster:
Intelligence | Wisdom | Charisma |
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