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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. | ||
For this we first need to clarify the notations used below: D{{math|n}} represents an {{math|n}}-sided die, {{math|P(i)}} is the probability that a variable has value {{math| | For this we first need to clarify the notations used below: D{{math|n}} represents an {{math|n}}-sided die, {{math|P(i)}} is the probability that a variable has value {{math|i}}, {{math|\mathbb{E} }} denotes the average or expected value of a roll, and {{math|1=\textstyle\sum_{i=a}^b x_i}} denotes the sum of a series of numbers {{math|x}} over an index {{math|i}} with {{math|i}} going from {{math|a}} through {{math|b}}. | ||
The formula to calculate the expected value, {{math|\mathbb{E}[x]}}, of a variable {{math|x}} is equal to the sum of every possible value of {{math|x}} multiplied by the chance for {{math|x}} to have that value. | The formula to calculate the expected value, {{math|\mathbb{E}[x]}}, of a variable {{math|x}} is equal to the sum of every possible value of {{math|x}} multiplied by the chance for {{math|x}} to have that value. | ||
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{| class="wikitable" | {| class="wikitable" | ||
|+ Expected Bonus Damage from Savage Attacker | |+Expected Bonus Damage from Savage Attacker | ||
|- | |- | ||
! | !Damage Die!!Average Bonus Damage!!Average Bonus % | ||
|- | |- | ||
|1d4 ||0.625 | |1d4||0.625||+25.0% | ||
|- | |- | ||
| 1d6|| 0.972 | |1d6||0.972||+27.8% | ||
|- | |- | ||
|1d8||1. | |1d8||1.313||+29.2% | ||
|- | |- | ||
|1d10||1. | |1d10||1.650||+30.0% | ||
|- | |- | ||
|1d12 ||1. | |1d12||1.986||+30.6% | ||
|- | |- | ||
|2d6 ||1. | |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 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]] ( | 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. | ||
==See Also== | |||
* [[List of sources of advantage and disadvantage on attack rolls]] | |||
==External Links== | ==External Links== |