User:Guybrush42/DamageExamples: Difference between revisions

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(Added alternate stats example for damage rolls using multi-axis table and great sword vs greataxe)
 
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''A re-write of the "A bit of Mathematics" section to use a more realisitic example of greataxe vs greatsword.''
''A re-write of the "A bit of Mathematics" section to use a more realisitic example of greataxe vs greatsword.''


Weapons and spells that roll multiple dice for damage do not just have a higher minimum damage. A single die is equally likely to produce any result, since there is exactly one change of getting each one. When adding dice together, there are multiple dice rolls that add up to the same total, meaning that some results - esepcially those in the middle of the damage range - are much more likely. For example, a {{weapon|Greataxe}} does {{DamageText|1d12|Slashing}}, and is equally likely to roll a 1 or a 12 or anything in between. A {{weapon|Greatsword}} does {{DamageText|2d6|Slashing}}, and cannot roll lower than 2 damage - but it is statistically much more likely to roll 7 damage than either 2 or 12.
Weapons and spells that roll multiple dice for damage have higher minimum damage, but also a different probability curve. A single die is equally likely to produce any result, since there is exactly one chance of rolling each number. When adding dice together, there are multiple dice rolls that add up to the same total. Those results are equivalent (ie they have the same functional effect), meaning that some results - especially those in the middle of the damage range - are much more likely to occur.
 
For example, {{WeaponType|Greataxes}} do {{DamageText|1d12|Slashing}} damage, and are equally likely to roll a 1, a 12 or anything in between. {{WeaponType|Greatswords}} deal {{DamageText|2d6|Slashing}}, and cannot roll lower than 2 damage - but they are statistically much more likely to roll 7 damage than either 2 or 12.


This is most easily explained with a table of all possible outcomes:
This is most easily explained with a table of all possible outcomes:


{| class="wikitable" style="text-align: center;"
{| class="wikitable" style="text-align: center;"
|+ Possible results of a 2d6 roll, highlighing results of 7
|+ Possible results of a 2d6 roll<br/>(intersections are totals)
! rowspan="2" | First<br/>roll
! colspan="6" | Second roll
|-
|-
! rowspan=6 ! Second roll
! 1 !! 2 !! 3 !! 4 !! 5 !! 6
! !! 1 !! 2 !! 3 !! 4 !! 5 !! 6
|-
|-
! 1 || 2 || 3 || 4 || 5 || 6 || {{color|red|'''7'''}}
| '''1''' || 2 || 3 || 4 || 5 || 6 || {{color|red|'''7'''}}
|-     
|-     
! 2 || 3 || 4 || 5 || 6 || {{color|red|'''7'''}} || 8
| '''2''' || 3 || 4 || 5 || 6 || {{color|red|'''7'''}} || 8
|-     
|-     
! 3 || 4 || 5 || 6 || {{color|red|'''7'''}} || 8 || 9
| '''3''' || 4 || 5 || 6 || {{color|red|'''7'''}} || 8 || 9
|-     
|-     
! 4 || 5 || 6 || {{color|red|'''7'''}} || 8 || 9 || 10
| '''4''' || 5 || 6 || {{color|red|'''7'''}} || 8 || 9 || 10
|-
|-
! 5 || 6 || {{color|red|'''7'''}} || 8 || 9 || 10 || 11
| '''5''' || 6 || {{color|red|'''7'''}} || 8 || 9 || 10 || 11
|-
|-
! 6 || {{color|red|'''7'''}} || 8 || 9 || 10 || 11 || 12
| '''6''' || {{color|red|'''7'''}} || 8 || 9 || 10 || 11 || 12
|}
|}


The 7 appears as the result in 6 out of 36 possible rolls, while the 12 appears only once. This means a 2d6 roll has a 16.6666% (1 in 6) chance of resulting in 7 points of damage, but only a 2.7777% (1 in 36) chance of resulting in 8 points of damage. Meanwhile, the 1d12 roll actually has a higher chance of resulting in the maximum damage value of 8, since 1 out of 12 possibilities (8.3333%) result in an 8. This is also true of the lowest damage, though, and the lowest value is lower for 1d12. So a greataxe and other single die weapons are "swingier" - more likely to deliver very high or very low damage damage - while a greatsword and other multiple dice weapons are more consistent - more likely to produce a result in the middle of their damage range.
The 7 appears as the result in 6 out of 36 possible rolls, while the 12 appears only once. This means a 2d6 roll has a 16.6666% (1 in 6) chance of resulting in 7 points of damage, but only a 2.7777% (1 in 36) chance of resulting in 12 points of damage. By contrast, a greataxe actually has a higher chance of rolling maximum damage, since 1 out of 12 possibilities (8.3333%) result in an 12. But it has an equal chance of rolling a 1.
 
Thus greataxes and other single die weapons are equally likely to deliver medium, high or low damage, and feel "swingier" or more random. Greatswords and other multiple dice weapons are more consistent: they're more likely to produce a result in the middle of their damage range, and only rarely roll very high or low.

Latest revision as of 07:42, 5 November 2023

Test run for damage example tables.

Damage Expressions[edit | edit source]

The intent is to replace the paragraph of examples in the Damage rolls article with a table, so that the full in-game style damage expression can be shown for each example.

Table of examples[edit | edit source]

Examples of damage expressions
Source Simple expression (no modifiers) Dice Damage range
Daggers Dagger
D4 Piercing.png 1d4 (1~4) Damage TypesPiercing
One four-sided die 1 to 4 piercing
Greatswords Greatsword
D6 Slashing.png 2d6 (2~12) Damage TypesSlashing
Two six-sided dice 2 to 12 slashing
Fireball Fireball
D6 Fire.png 8d6 (8~48) Damage TypesFire
Eight six-sided dice 8 to 48 fire

Current example paragraph[edit | edit source]

For example, a successful attack with a Daggers Dagger does a base of 1d4Damage TypesPiercing damage (1~4). This means a single four-sided die D4 Piercing.png is rolled to determine the damage, for a total of 1 to 4 piercing damage. Most weapons use a single damage die, but some two-handed weapons use two: a successful attack with a Greatswords Greatsword does 2d6Damage TypesSlashing damage (2~12), rolling two six-sided dice D6 Slashing.png for a total of 2 to 12 slashing damage. Damaging spells typically roll more dice: for example, being caught in a Fireball Fireball will cause 8d6Damage TypesFire damage (8~48), though a successful Saving Throw can reduce it to half.

A note on multiple damage dice[edit | edit source]

A re-write of the "A bit of Mathematics" section to use a more realisitic example of greataxe vs greatsword.

Weapons and spells that roll multiple dice for damage have higher minimum damage, but also a different probability curve. A single die is equally likely to produce any result, since there is exactly one chance of rolling each number. When adding dice together, there are multiple dice rolls that add up to the same total. Those results are equivalent (ie they have the same functional effect), meaning that some results - especially those in the middle of the damage range - are much more likely to occur.

For example, Greataxes Greataxes do 1d12Damage TypesSlashing damage, and are equally likely to roll a 1, a 12 or anything in between. Greatswords Greatswords deal 2d6Damage TypesSlashing, and cannot roll lower than 2 damage - but they are statistically much more likely to roll 7 damage than either 2 or 12.

This is most easily explained with a table of all possible outcomes:

Possible results of a 2d6 roll
(intersections are totals)
First
roll
Second roll
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12

The 7 appears as the result in 6 out of 36 possible rolls, while the 12 appears only once. This means a 2d6 roll has a 16.6666% (1 in 6) chance of resulting in 7 points of damage, but only a 2.7777% (1 in 36) chance of resulting in 12 points of damage. By contrast, a greataxe actually has a higher chance of rolling maximum damage, since 1 out of 12 possibilities (8.3333%) result in an 12. But it has an equal chance of rolling a 1.

Thus greataxes and other single die weapons are equally likely to deliver medium, high or low damage, and feel "swingier" or more random. Greatswords and other multiple dice weapons are more consistent: they're more likely to produce a result in the middle of their damage range, and only rarely roll very high or low.