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General Tabletop Discussion
*Pathfinder & Starfinder
Monte Carlo versus "The Math"
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<blockquote data-quote="Cadfan" data-source="post: 4983322" data-attributes="member: 40961"><p>No, no. The DPR analysis works just fine because its being compared to other DPR values. The relative relationship between two character's DPR calculations and the relative relationship between their "rounds of combat" calculations should be so similar as to be indistinguishable in casual discussion.</p><p></p><p>Try an example, done mathematically. You've got character A, and character B, with DPRs of 9 and 7, respectively. DPR wise, we expect character A to kill monsters approximately 28.6% faster than character B.</p><p></p><p>Now imagine they're each fighting a monster with 60 hp.</p><p></p><p>Using what you call the DPR approach, we expect Character A to kill the monster in 6.667 rounds. But if we were to make our analysis more specific, we'd determine that Character A expects to kill the monster in 7 rounds- 6 rounds to get to 54 damage, then one more to get to 63. The remainder is rounded up to the nearest whole number.</p><p></p><p>Using what you call the DPR approach, we expect Character A to kill the monster in 8.571 rounds. But if we were to make our analysis more specific, we'd determine that Character A expects to kill the monster in 9 rounds- 8 rounds to get to 56 damage, then one more to get to 63.</p><p></p><p>Well, lets check our ratios to see whether these forms of analysis generated significantly different outcomes.</p><p></p><p>DRP ratio, 6.667/8.571 = .77786</p><p>Round analysis, 7/9 = .77778</p><p></p><p>There you go.</p><p></p><p>For reference and full disclosure, lower hit points and higher damage (ie, fewer rounds needed to kill the monster) will generate more variability in the comparison of the DPR and Round analysis. This is because the remainder makes up a larger portion of the division of HD/DPR. </p><p></p><p>Using a mathematical expression for the round analysis instead of relying on DPR as an average will also introduce more variability. But that variability averages out and shouldn't affect overall conclusions.</p></blockquote><p></p>
[QUOTE="Cadfan, post: 4983322, member: 40961"] No, no. The DPR analysis works just fine because its being compared to other DPR values. The relative relationship between two character's DPR calculations and the relative relationship between their "rounds of combat" calculations should be so similar as to be indistinguishable in casual discussion. Try an example, done mathematically. You've got character A, and character B, with DPRs of 9 and 7, respectively. DPR wise, we expect character A to kill monsters approximately 28.6% faster than character B. Now imagine they're each fighting a monster with 60 hp. Using what you call the DPR approach, we expect Character A to kill the monster in 6.667 rounds. But if we were to make our analysis more specific, we'd determine that Character A expects to kill the monster in 7 rounds- 6 rounds to get to 54 damage, then one more to get to 63. The remainder is rounded up to the nearest whole number. Using what you call the DPR approach, we expect Character A to kill the monster in 8.571 rounds. But if we were to make our analysis more specific, we'd determine that Character A expects to kill the monster in 9 rounds- 8 rounds to get to 56 damage, then one more to get to 63. Well, lets check our ratios to see whether these forms of analysis generated significantly different outcomes. DRP ratio, 6.667/8.571 = .77786 Round analysis, 7/9 = .77778 There you go. For reference and full disclosure, lower hit points and higher damage (ie, fewer rounds needed to kill the monster) will generate more variability in the comparison of the DPR and Round analysis. This is because the remainder makes up a larger portion of the division of HD/DPR. Using a mathematical expression for the round analysis instead of relying on DPR as an average will also introduce more variability. But that variability averages out and shouldn't affect overall conclusions. [/QUOTE]
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