User:Guybrush42/DamageExamples: Difference between revisions

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→‎A note on multiple damage dice: New draft

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 ''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:
 {| 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 roll
+! rowspan="2" | First<br/>roll
 ! colspan="6" | Second roll
 |-
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 |}
-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.