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{{Hatnote|For a comprehensive summary of the mechanics behind all rolls and modifiers, see: [[Dice Rolls]]}} | {{Hatnote|For a comprehensive summary of the mechanics behind all rolls and modifiers, see: [[Dice Rolls]]}} | ||
'''{{Advantage}}''' and '''{{Disadvantage}}''' are gameplay mechanics that can greatly affect the success of dice rolls. | '''{{Advantage}}''' and '''{{Disadvantage}}''' are terms used for two different gameplay mechanics that can greatly affect the success of dice rolls. First they are used for [[Advantage#Used with two dice|rolling two dice]], second they are used for [[Advantage#Used with contesting ability checks|contesting ability checks]]. | ||
== Advantage == | == Used with two dice == | ||
[[File:Advantage Icon.png|alt=The in-game symbol for advantage.|left]] | |||
[[File:Disadvantage Icon.png|alt=The in-game symbol for disadvantage|left]] | |||
A number of situations and conditions give creatures advantage or disadvantage on d20 rolls. A creature that makes a roll with advantage rolls two d20 dice separately, and uses the higher of the two results. If they have disadvantage, they choose the lower of the two. | |||
Creatures receive no additional benefit or penalty from having multiple sources of advantage or disadvantage on a dice roll, and still only roll twice. Likewise, creatures that have {{em|both}} advantage and disadvantage on a roll only roll a single die, even if they have multiple sources of either. | |||
For an exhaustive list of sources of advantage and disadvantage, see the following pages: | |||
* For attack rolls: [[List_of_sources_of_advantage_and_disadvantage_on_attack_rolls#Advantage_on_attack_rolls|Advantage]] and [[List_of_sources_of_advantage_and_disadvantage_on_attack_rolls#Disadvantage_on_attack_rolls|Disadvantage]] | |||
* For saving throws: [[List_of_features_and_items_that_affect_saving_throws#Advantage_on_saving_throws|Advantage]] and [[List_of_features_and_items_that_affect_saving_throws#Disadvantage_on_saving_throws|Disadvantage]] | |||
Rolling two dice only applies to {{D20}} rolls: [[Attack Roll]]s, [[Saving Throw]]s, and [[Ability Check]]s. They never apply to [[Damage Roll]]s, though other features and effects can make a character re-roll damage dice in other ways. | |||
=== Advantage === | |||
When you roll with {{Advantage}}, you roll two dice and use the '''higher''' result. You either have advantage or you don't: it doesn't stack to grant more than a second die, regardless of how many sources of advantage you have. | When you roll with {{Advantage}}, you roll two dice and use the '''higher''' result. You either have advantage or you don't: it doesn't stack to grant more than a second die, regardless of how many sources of advantage you have. | ||
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*Armour, Weapons, and Spells that grant advantage when attacking enemies of a specific [[Races|Race]]. | *Armour, Weapons, and Spells that grant advantage when attacking enemies of a specific [[Races|Race]]. | ||
==Disadvantage == | ===Disadvantage === | ||
When you roll with {{Disadvantage}}, you roll two dice and use the '''lower''' result. As with advantage, you either have disadvantage or you don't: it doesn't stack to force you to roll more than a second die, regardless of how many sources of disadvantage you have. | When you roll with {{Disadvantage}}, you roll two dice and use the '''lower''' result. As with advantage, you either have disadvantage or you don't: it doesn't stack to force you to roll more than a second die, regardless of how many sources of disadvantage you have. | ||
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*Various spells and abilities that grant Disadvantage. | *Various spells and abilities that grant Disadvantage. | ||
==Advantage and Disadvantage== | ===Advantage and Disadvantage=== | ||
Having both {{Advantage}} and {{Disadvantage}} means they cancel each other out, and you roll one die as if you had neither. Because neither advantage or disadvantage stack, having multiple sources of either doesn't change this: even if you have three sources of Advantage, a single source of Disadvantage will cancel it, and vice versa. | Having both {{Advantage}} and {{Disadvantage}} means they cancel each other out, and you roll one die as if you had neither. Because neither advantage or disadvantage stack, having multiple sources of either doesn't change this: even if you have three sources of Advantage, a single source of Disadvantage will cancel it, and vice versa. | ||
==Math== | ===Math=== | ||
=== Chances of succeeding a specific roll=== | ==== Chances of succeeding a specific roll==== | ||
The benefits of rolling with advantage (or the detriments of rolling with disadvantage) change depending on the target number you need on the 1d20 roll to succeed. The bonus from advantage can be as large as 24-25% when needing a 9, 10, 11, 12, or 13 on the 1d20 roll, and as small as 9% if one needs to roll a 19. | The benefits of rolling with advantage (or the detriments of rolling with disadvantage) change depending on the target number you need on the 1d20 roll to succeed. The bonus from advantage can be as large as 24-25% when needing a 9, 10, 11, 12, or 13 on the 1d20 roll, and as small as 9% if one needs to roll a 19. | ||
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=== Effects on the average of dice rolls === | ==== Effects on the average of dice rolls ==== | ||
A more general way of looking at advantage/disadvantage is calculating the effect on the average of dice rolls. On average, the bonus/penalty is +/-3.325. This makes it more broadly applicable than looking at specific rolls and makes it easier to compare to other bonuses and penalties which may apply to a roll. | A more general way of looking at advantage/disadvantage is calculating the effect on the average of dice rolls. On average, the bonus/penalty is +/-3.325. This makes it more broadly applicable than looking at specific rolls and makes it easier to compare to other bonuses and penalties which may apply to a roll. | ||
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Because of symmetry, having disadvantage instead of advantage means we can simply make the permutation of {{math|\{1, \dots, n\} \to \{n, \dots, 1\} }} for the values of dice rolls and all the calculations will remain the same. Therefore the size of the bonus of advantage is equal to the size of the penalty of disadvantage. | Because of symmetry, having disadvantage instead of advantage means we can simply make the permutation of {{math|\{1, \dots, n\} \to \{n, \dots, 1\} }} for the values of dice rolls and all the calculations will remain the same. Therefore the size of the bonus of advantage is equal to the size of the penalty of disadvantage. | ||
=== Effects on critical successes and failures === | ==== Effects on critical successes and failures ==== | ||
When making an ability check, attack roll or saving throw, a 1 or a 20 will {{em|always}} be treated as a critical failure or success, respectively, regardless of the results after any potential modifiers are added. On a dice roll without advantage or disadvantage, this effectively means there is a {{math|1/20}} (or 5%) chance of either a critical success or failure. | When making an ability check, attack roll or saving throw, a 1 or a 20 will {{em|always}} be treated as a critical failure or success, respectively, regardless of the results after any potential modifiers are added. On a dice roll without advantage or disadvantage, this effectively means there is a {{math|1/20}} (or 5%) chance of either a critical success or failure. | ||
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== Similar effects == | === Similar effects === | ||
While advantage and disadvantage only apply to {{D20}} rolls, some character features can grant a similar bonus to other rolls. The clearest example is [[Savage Attacker]], a [[feat]] which has a character roll all melee damage dice twice, taking the highest result. This is effectively advantage on melee [[damage rolls]], though none of the advantage rules apply: the effect can stack with others that double damage dice, and there is no similar negative effect that gives you the equivalent of disadvantage on damage. | While advantage and disadvantage only apply to {{D20}} rolls, some character features can grant a similar bonus to other rolls. The clearest example is [[Savage Attacker]], a [[feat]] which has a character roll all melee damage dice twice, taking the highest result. This is effectively advantage on melee [[damage rolls]], though none of the advantage rules apply: the effect can stack with others that double damage dice, and there is no similar negative effect that gives you the equivalent of disadvantage on damage. | ||
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Note that Savage Attacker also applies to ALL additional damage dice from ANY source added to a weapon, but not [[Sneak Attack|Sneak Damage]] because those are not bonus dice added to the weapon damage. | Note that Savage Attacker also applies to ALL additional damage dice from ANY source added to a weapon, but not [[Sneak Attack|Sneak Damage]] because those are not bonus dice added to the weapon damage. | ||
For example, the [[Halberd of Vigilance]] (1d10 slashing damage and 1d4 force damage) which was [[Dip#Condition:_Dipped_in_Fire|dipped in fire]] (1d4 fire damage) will, on average, do 1.65 + 0.625 + 0.625 = 2.9 (+27.6%) more damage with Savage Attacker. | For example, the [[Halberd of Vigilance]] (1d10 slashing damage and 1d4 force damage) which was [[Dip#Condition:_Dipped_in_Fire|dipped in fire]] (1d4 fire damage) will, on average, do 1.65 + 0.625 + 0.625 = 2.9 (+27.6%) more damage with Savage Attacker. | ||
== Used with contesting ability checks == | |||
A contest is a special type of ability check where one creature rolls an ability check against another creature's skill. Rather than rolling, the opposing creature uses a ''passive skill'' value given by {{InfoBlob|10 + skill bonus}} with {{Advantage}} on the relevant skill check adding 5 or {{Disadvantage}} subtracting 5. The passive skill value serves as the [[Difficulty Class]] (DC) of the skill check. | |||
:: An example of this with {{SAI|Shove}}. The creature attempting the shove makes an [[Athletics]] check versus the target's passive Athletics {{em|or}} [[Acrobatics]], whichever is higher. | |||
:: Another example is with {{SAI|Hide}} where the sneaking creature makes a [[Stealth]] check against an enemy's passive [[Perception]] while in their cone of vision to avoid being detected. | |||
==See Also== | ==See Also== |
Latest revision as of 23:51, 12 December 2024
Advantage and Disadvantage are terms used for two different gameplay mechanics that can greatly affect the success of dice rolls. First they are used for rolling two dice, second they are used for contesting ability checks.
Used with two dice[edit | edit source]
A number of situations and conditions give creatures advantage or disadvantage on d20 rolls. A creature that makes a roll with advantage rolls two d20 dice separately, and uses the higher of the two results. If they have disadvantage, they choose the lower of the two.
Creatures receive no additional benefit or penalty from having multiple sources of advantage or disadvantage on a dice roll, and still only roll twice. Likewise, creatures that have both advantage and disadvantage on a roll only roll a single die, even if they have multiple sources of either.
For an exhaustive list of sources of advantage and disadvantage, see the following pages:
- For attack rolls: Advantage and Disadvantage
- For saving throws: Advantage and Disadvantage
Rolling two dice only applies to d20 rolls: Attack Rolls, Saving Throws, and Ability Checks. They never apply to Damage Rolls, though other features and effects can make a character re-roll damage dice in other ways.
Advantage[edit | edit source]
When you roll with Advantage, you roll two dice and use the higher result. You either have advantage or you don't: it doesn't stack to grant more than a second die, regardless of how many sources of advantage you have.
Example: You roll two d20 for an Attack Roll, the results are 16 and 4. Your effective result is 16.
Having advantage raises the average of your roll by 3.325 to 13.825. (For the math, see below.)
Examples of situations that grant Advantage on attack rolls:
- Attacking an enemy that is under these conditions: Restrained, Prone, Sleeping, Entangled, Paralysed, Off balance, Enwebbed, Blinded.
- Attacking an enemy while being Hidden or invisible.
- Armour, Weapons, and Spells that grant advantage when attacking enemies of a specific Race.
Disadvantage[edit | edit source]
When you roll with Disadvantage, you roll two dice and use the lower result. As with advantage, you either have disadvantage or you don't: it doesn't stack to force you to roll more than a second die, regardless of how many sources of disadvantage you have.
Example: You roll two d20 for an Attack Roll. The results are 16 and 4. Your effective result is 4.
On a D20, having disadvantage lowers the average of your roll by 3.325 to 7.175. (For the math, see below.)
Examples of situations that grant Disadvantage on attack rolls:
- Trying to make a ranged attack against an enemy that is within 5ft and making you Threatened.
- Various spells and abilities that grant Disadvantage.
Advantage and Disadvantage[edit | edit source]
Having both Advantage and Disadvantage means they cancel each other out, and you roll one die as if you had neither. Because neither advantage or disadvantage stack, having multiple sources of either doesn't change this: even if you have three sources of Advantage, a single source of Disadvantage will cancel it, and vice versa.
Math[edit | edit source]
Chances of succeeding a specific roll[edit | edit source]
The benefits of rolling with advantage (or the detriments of rolling with disadvantage) change depending on the target number you need on the 1d20 roll to succeed. The bonus from advantage can be as large as 24-25% when needing a 9, 10, 11, 12, or 13 on the 1d20 roll, and as small as 9% if one needs to roll a 19.
Target on 1d20 | Normal Roll | Roll With Advantage | Roll With Disadvantage | Gap between Normal and (Dis)advantage |
---|---|---|---|---|
1 | 100% | 100% | 100% | 0% |
2 | 95% | 99.75% | 90.25% | 4.75% |
3 | 90% | 99% | 81% | 9% |
4 | 85% | 97.75% | 72.25% | 12.75% |
5 | 80% | 96% | 64% | 16% |
6 | 75% | 93.75% | 56.25% | 18.75% |
7 | 70% | 91% | 49% | 21% |
8 | 65% | 87.75% | 42.25% | 22.75% |
9 | 60% | 84% | 36% | 24% |
10 | 55% | 79.75% | 30.25% | 24.75% |
11 | 50% | 75% | 25% | 25% |
12 | 45% | 69.75% | 20.25% | 24.75% |
13 | 40% | 64% | 16% | 24% |
14 | 35% | 57.75% | 12.25% | 22.75% |
15 | 30% | 51% | 9% | 21% |
16 | 25% | 43.75% | 6.25% | 18.75% |
17 | 20% | 36% | 4% | 16% |
18 | 15% | 27.75% | 2.25% | 12.75% |
19 | 10% | 19% | 1% | 9% |
20 | 5% | 9.75% | 0.25% | 4.75% |
Effects on the average of dice rolls[edit | edit source]
A more general way of looking at advantage/disadvantage is calculating the effect on the average of dice rolls. On average, the bonus/penalty is +/-3.325. This makes it more broadly applicable than looking at specific rolls and makes it easier to compare to other bonuses and penalties which may apply to a roll.
For this we first need to clarify the notations used below: D represents an -sided die, is the probability that a variable has value , denotes the average or expected value of a roll, and denotes the sum of a series of numbers over an index with going from through .
The formula to calculate the expected value, , of a variable is equal to the sum of every possible value of multiplied by the chance for to have that value. In the case of an -sided die, D, this becomes:
For a regular dice roll the probability distribution is uniform, which means for any , and using , we get
For a dice roll with advantage the chance to roll the number is equal to the chance that the first die rolls multiplied by the chance that the second die rolls or less, multiplied by 2 (because the 2 dice are interchangeable), minus the chance of both dice rolling (because we counted that possibility twice by multiplying by 2). This gives
Applying that to the formula of an average of a die D we get
Here we can use that the sum of squares is , which gives
To know what bonus having advantage gives to our roll, we calculate
When we apply this expression to a d20 we get that having advantage is equivalent to an average bonus of +3.325.
Because of symmetry, having disadvantage instead of advantage means we can simply make the permutation of for the values of dice rolls and all the calculations will remain the same. Therefore the size of the bonus of advantage is equal to the size of the penalty of disadvantage.
Effects on critical successes and failures[edit | edit source]
When making an ability check, attack roll or saving throw, a 1 or a 20 will always be treated as a critical failure or success, respectively, regardless of the results after any potential modifiers are added. On a dice roll without advantage or disadvantage, this effectively means there is a (or 5%) chance of either a critical success or failure.
Having advantage or disadvantage can drastically increase or reduce the chance of critical successes and Failures. For example, when rolling with advantage, the only way to get a Critical Failure is to roll two 1s at the same time. The odds of this result is (or 0.25%). Conversely, rolling a Critical Success is far more likely - out of the 400 possible dice roll outcomes, 39 will result in a 20 (rolling 20 on the first die and 1, 2, 3, ... 20 on the second die, plus rolling 20 on the second die and 1, 2, 3, ... 20 on the first die, minus one so that the result of two 20s is not doubly-counted). The odds of this result is (or 9.75%). The opposite is true for rolling with Disadvantage: a Critical Success has a 0.25% chance and a Critical Failure has a 9.75% chance.
Effectively, rolling with advantage means that critical failures are 20 times less likely and critical successes are almost twice as likely, and the inverse is true for disadvantage.
Outcome | Normal Roll | Roll With Advantage | Roll With Disadvantage |
---|---|---|---|
Critical Failure (1) | 5% | 0.25% | 9.75% |
Critical Success (20) | 5% | 9.75% | 0.25% |
Similar effects[edit | edit source]
While advantage and disadvantage only apply to d20 rolls, some character features can grant a similar bonus to other rolls. The clearest example is Savage Attacker, a feat which has a character roll all melee damage dice twice, taking the highest result. This is effectively advantage on melee damage rolls, though none of the advantage rules apply: the effect can stack with others that double damage dice, and there is no similar negative effect that gives you the equivalent of disadvantage on damage.
Using the result of the calculations above to see what the average bonus to our damage becomes, depending on what dice the weapon uses.
Damage Die | Average Bonus Damage | Average Bonus % |
---|---|---|
1d4 | 0.625 | +25.0% |
1d6 | 0.972 | +27.8% |
1d8 | 1.313 | +29.2% |
1d10 | 1.650 | +30.0% |
1d12 | 1.986 | +30.6% |
2d6 | 1.944 | +27.8% |
Note that Savage Attacker also applies to ALL additional damage dice from ANY source added to a weapon, but not Sneak Damage because those are not bonus dice added to the weapon damage. For example, the Halberd of Vigilance (1d10 slashing damage and 1d4 force damage) which was dipped in fire (1d4 fire damage) will, on average, do 1.65 + 0.625 + 0.625 = 2.9 (+27.6%) more damage with Savage Attacker.
Used with contesting ability checks[edit | edit source]
A contest is a special type of ability check where one creature rolls an ability check against another creature's skill. Rather than rolling, the opposing creature uses a passive skill value given by 10 + skill bonus with Advantage on the relevant skill check adding 5 or Disadvantage subtracting 5. The passive skill value serves as the Difficulty Class (DC) of the skill check.
- An example of this with Athletics check versus the target's passive Athletics or Acrobatics, whichever is higher. . The creature attempting the shove makes an
- Another example is with Stealth check against an enemy's passive Perception while in their cone of vision to avoid being detected. where the sneaking creature makes a
See Also[edit | edit source]
External Links[edit | edit source]
- The unexpected logic behind rolling multiple dice and picking the highest by Matt Parker
- Advantage and Disadvantage in D&D Next: The Math by The Online Dungeon Master (Michael Iachini)
- D&D 5e: Probabilities for Advantage and Disadvantage by Bob Carpenter