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<blockquote data-quote="NotAYakk" data-source="post: 8146816" data-attributes="member: 72555">Central limit theorem says &quot;nyaaaa&quot; to that.&nbsp; Yes, it is an abuse of statistics.&nbsp; But I'm abusive towards statistics.Stop looking at the shape of the curve and look at the shape of the integrated curve.&nbsp; Gameplay in roll-over is the chance you roll X or higher, not the chance you roll X.And when you graph the chance you roll X or higher, correct for median and standard deviation, you get two curves that are barely separate.I have done this.&nbsp; I described what I did.&nbsp; I checked my work.&nbsp; Do I have to generate the graph for the 50th time?&nbsp; I find it rarely helps.The fastest way to do it is to do this.&nbsp; Graph (1d8+1d12) * (SD of 1d20) - average of that roll, against (1d10) * (SD of 1d8+1d12) - average of that roll, both &quot;roll under&quot;, on a dice rolling website.Here we go: <a href="https://anydice.com/program/1f4db" target="_blank">AnyDice</a>[ATTACH=full]130017[/ATTACH]The curves are basically on top of each other, outside of the &quot;crit hit/miss&quot; stuff.&nbsp; And I rounded the 1.4ish ratio to 1.5; that is where most of the difference between the curves come from.What this shows is it compares resolution mechanics of:(a) d20 game, where modifiers are scaled up by 50% and DCs are scaled 50% further from 10 compared to 5e.(b) 1d8+1d12 game, where modifiers are left just like 5e.Once you patch in a &quot;crit miss/hit&quot; mechanic covering the outermost 5%, it becomes nearly impossible to tell which of the two systems you are using from a description of only the hit/miss/success/failure results of the game.</blockquote>

[QUOTE="NotAYakk, post: 8146816, member: 72555"] Central limit theorem says "nyaaaa" to that. Yes, it is an abuse of statistics. But I'm abusive towards statistics. Stop looking at the shape of the curve and look at the shape of the [B]integrated[/B] curve. Gameplay in roll-over is the chance you roll X or higher, not the chance you roll X. And when you graph the chance you roll X or higher, correct for median and standard deviation, you get two curves that are barely separate. I have done this. I described what I did. I checked my work. Do I have to generate the graph for the 50th time? I find it rarely helps. The fastest way to do it is to do this. Graph (1d8+1d12) * (SD of 1d20) - average of that roll, against (1d10) * (SD of 1d8+1d12) - average of that roll, both "roll under", on a dice rolling website. Here we go: [URL='https://anydice.com/program/1f4db']AnyDice[/URL] [ATTACH type="full" alt="1607804139317.png"]130017[/ATTACH] The curves are basically on top of each other, outside of the "crit hit/miss" stuff. And I rounded the 1.4ish ratio to 1.5; that is where most of the difference between the curves come from. What this shows is it compares resolution mechanics of: (a) d20 game, where modifiers are scaled up by 50% and DCs are scaled 50% further from 10 compared to 5e. (b) 1d8+1d12 game, where modifiers are left just like 5e. Once you patch in a "crit miss/hit" mechanic covering the outermost 5%, it becomes nearly impossible to tell which of the two systems you are using from a description of [B]only[/B] the hit/miss/success/failure results of the game. [/QUOTE]

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