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Community
General Tabletop Discussion
*Dungeons & Dragons
The mathematics of D&D–Damage and HP
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<blockquote data-quote="fearsomepirate" data-source="post: 8219997" data-attributes="member: 7021420"><p>The underlying problem is a common one. The unspoken assumption is that if something is impossible to measure or compute, it isn't relevant. To compute something analytically, you have to ignore so many important factors just to make the computation tractable that the final result isn't meaningful. This is why analytical probability ends up being an all but useless tool anywhere outside Vegas, and real-world applications use measured statistics.</p><p></p><p>Even in D&D analytics, people ignore monster AC & saves when comparing unlike things. For example, which spell does more damage, Finger of Death, or Disintegrate upcast to 7th level?</p><p></p><p>The correct answer is, "it depends on the monster's CON save, DEX save, how many hit points it has left, how many allied turns there are between you and the monster's next turn, and whether it has Magic Resistance or Legendary Resistance." Against a dragon in the first round or two of combat, the expected damage of Disintegrate is <em>zero</em>. Against a Purple Worm, it is much higher. Against a Marilith, Disintegrate's expected damage is 26, while Finger of Death is about 33.</p><p></p><p>FoD wins, right?</p><p></p><p>WRONG.</p><p></p><p>In D&D, I do not care primarily about the amount of damage I do. I care about killing the monster before it hurts the party more. If our Marilith is down to 70 hit points, the chance that Finger of Death will kill her is less than 1%, and the chance that Disintegrate will kill her is 30%. So, despite FoD doing more <em>average damage</em>, it is not necessarily the "theoretically correct choice" to use it. If the Marilith goes next, it's arguably smarter to use the spell with the most potential to end the threat.</p><p></p><p>(Usual caveat: I may have made errors)</p><p>[URL unfurl="true"]https://anydice.com/program/20fec[/URL]</p></blockquote><p></p>
[QUOTE="fearsomepirate, post: 8219997, member: 7021420"] The underlying problem is a common one. The unspoken assumption is that if something is impossible to measure or compute, it isn't relevant. To compute something analytically, you have to ignore so many important factors just to make the computation tractable that the final result isn't meaningful. This is why analytical probability ends up being an all but useless tool anywhere outside Vegas, and real-world applications use measured statistics. Even in D&D analytics, people ignore monster AC & saves when comparing unlike things. For example, which spell does more damage, Finger of Death, or Disintegrate upcast to 7th level? The correct answer is, "it depends on the monster's CON save, DEX save, how many hit points it has left, how many allied turns there are between you and the monster's next turn, and whether it has Magic Resistance or Legendary Resistance." Against a dragon in the first round or two of combat, the expected damage of Disintegrate is [I]zero[/I]. Against a Purple Worm, it is much higher. Against a Marilith, Disintegrate's expected damage is 26, while Finger of Death is about 33. FoD wins, right? WRONG. In D&D, I do not care primarily about the amount of damage I do. I care about killing the monster before it hurts the party more. If our Marilith is down to 70 hit points, the chance that Finger of Death will kill her is less than 1%, and the chance that Disintegrate will kill her is 30%. So, despite FoD doing more [I]average damage[/I], it is not necessarily the "theoretically correct choice" to use it. If the Marilith goes next, it's arguably smarter to use the spell with the most potential to end the threat. (Usual caveat: I may have made errors) [URL unfurl="true"]https://anydice.com/program/20fec[/URL] [/QUOTE]
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