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Damage
For a comprehensive summary of the mechanics behind all rolls and modifiers, see Die Rolls.
A Damage Roll happens when the game wants to determine the damage done by a successful attack, area of effect spell, trap, and so on. It can involve one or many dice of any type. This is not to be confused with the Attack Roll, which is a D20 roll deciding whether the attack hits at all.
For example, a successful hit with a Dagger will lead to a D4 being rolled to determine the damage (referred to as 1d4 damage), whereas a successful attack with a Greatsword will lead to two D6 being rolled (referred to as 2d6) for a total damage of 2 to 12. Being caught in a Fireball will cause 8d6 points of damage, though a successful Saving Throw can reduce it to half.
Modifiers
For Weapon attacks, the attacking creature's Ability Score Modifier for Strength or Dexterity can affect the total value of the roll. For the damage of spell attacks, including Cantrips, no such modifier exists, unless explicitly granted by a magical item or class feature, such as the Warlock's Agonizing Blast.
The Proficiency Bonus and Advantage system don't apply to Damage Rolls at all.
Ability Score Modifier
A bonus or penalty may be applied to the result of the roll based on either Strength or Dexterity. For rolls involving multiple dice, such as 2d4, the dice are rolled together, and the modifier is applied to the total result, not to each die.
Whether Strength or Dexterity is used depends on the weapon. Usually, it's Strength for melee weapons, and Dexterity for ranged weapons. The exceptions are Finesse weapons, where the higher one of Strength and Dexterity will be used; and Thrown weapons, which use Strength for both melee and ranged attacks. If a weapon is both Thrown and a Finesse weapon, it will use the higher of Strength and Dexterity both for melee and ranged attacks.
Some examples, to make the possible combinations of Finesse and Thrown easier to understand:
- Using a Maul for a melee attack always uses Strength.
- Using a Rapier (Finesse) for a melee attack uses Strength or Dexterity; whichever the attacking creature has a higher score in.
- Shooting a Longbow for a ranged attack always uses Dexterity.
- Throwing a Handaxe (Thrown) for a ranged attack uses Strength.
- Throwing a Dagger (Finesse & Thrown) for a ranged attack uses Strength or Dexterity; whichever the attacking creature has a higher score in.
If you use a weapon in a way it's not designed for at all, such as throwing a Maul at someone, or hitting someone over the head with a Longbow for a melee attack, then no Ability Score Modifier is applied at all. That being said, Improvised Weapon Proficiency can negate this penalty.
Whether it's Strength or Dexterity that ends up being used, the following table defines the value of the modifier:
| Ability score | Modifier value | Ability score | Modifier value | |
|---|---|---|---|---|
| 1 | -5 | 16-17 | +3 | |
| 2-3 | -4 | 18-19 | +4 | |
| 4-5 | -3 | 20-21 | +5 | |
| 6-7 | -2 | 22-23 | +6 | |
| 8-9 | -1 | 24-25 | +7 | |
| 10-11 | +0 | 26-27 | +8 | |
| 12-13 | +1 | 28-29 | +9 | |
| 14-15 | +2 | 30 | +10 |
A bit of Mathematics
Note that due to the mathematics of dice rolls, the difference between, say, 1d8 and 2d4 is more than just the higher minimum value of 2 on the 2d4 roll. With the d8, you have an equal chance of getting, say, a 5 and an 8. On the other hand, the 2d4 roll is statistically more likely to lead to a total value of 5, than a total value of 8. This is most easily explained with a table of all possible outcomes:
| First roll | Second roll | Total value |
|---|---|---|
| 1 | 1 | 2 |
| 1 | 2 | 3 |
| 1 | 3 | 4 |
| 1 | 4 | 5 |
| 2 | 1 | 3 |
| 2 | 2 | 4 |
| 2 | 3 | 5 |
| 2 | 4 | 6 |
| 3 | 1 | 4 |
| 3 | 2 | 5 |
| 3 | 3 | 6 |
| 3 | 4 | 7 |
| 4 | 1 | 5 |
| 4 | 2 | 6 |
| 4 | 3 | 7 |
| 4 | 4 | 8 |
Notice how often the 5 appears in the possibilities for the total value (4 out of 16 possibilities) vs. how often the 8 appears (1 out of 16). This means a 2d4 roll has a 25% chance of resulting in 5 points of damage, but only a 6.125% chance of resulting in 8 points of damage. Meanwhile, the 1d8 roll actually has a higher chance of resulting in the maximum damage value of 8, since 1 out of 8 possibilities (12.5%) result in an 8.