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<blockquote data-quote="NotAYakk" data-source="post: 8647727" data-attributes="member: 72555">A d12 has a variance of 143/12.&nbsp; A d20 399/12, and 3d6 a variance of 105/12.So in a roll over/under system, 3d6 modifiers away from average are &quot;twice as large&quot; as d20, and d12 are 1.7x as large as d20.&nbsp; (how big modifiers are scales with standard deviation, the square root of variance).Ie, a system with DCs scaled 40% towards 10, then being 4 lower and modifiers 40% smaller would feel about the same.&nbsp; Attributes from -3 to +3, proficiency from +2 to +4, naked being 6 AC and plate+shield being 12 AC.We can add +4 to the system by making attributes range from +1 to +7 (no minuses) with +4 being average human.&nbsp; Set proficiency to +2 to +4.&nbsp; DCs are 4+prof+attribute.&nbsp; unarmored is 6+dex, light armor is 7+dex, medium is 11+dex/2 (+1 if bulky), and heavy is 15.&nbsp; Shields grant +1 AC.&nbsp; Magic items cap out at +2 instead of +3.&nbsp; Etc....The interesting thing happens when you add not roll over/under mechanics.&nbsp; Up to that, we just get modifier tweaks.&nbsp; While muliple dice are &quot;curvier&quot;, when you reduce it to roll under/over and scale by the SD, the only substantial difference happens in the top/bottom 5%ish (the crit hit/miss territory).&nbsp; Integration makes things smoother, and &quot;roll under/over&quot; is integration of probability.</blockquote>

[QUOTE="NotAYakk, post: 8647727, member: 72555"] A d12 has a variance of 143/12. A d20 399/12, and 3d6 a variance of 105/12. So in a roll over/under system, 3d6 modifiers away from average are "twice as large" as d20, and d12 are 1.7x as large as d20. (how big modifiers are scales with standard deviation, the square root of variance). Ie, a system with DCs scaled 40% towards 10, then being 4 lower and modifiers 40% smaller would feel about the same. Attributes from -3 to +3, proficiency from +2 to +4, naked being 6 AC and plate+shield being 12 AC. We can add +4 to the system by making attributes range from +1 to +7 (no minuses) with +4 being average human. Set proficiency to +2 to +4. DCs are 4+prof+attribute. unarmored is 6+dex, light armor is 7+dex, medium is 11+dex/2 (+1 if bulky), and heavy is 15. Shields grant +1 AC. Magic items cap out at +2 instead of +3. Etc. ... The interesting thing happens when you add not roll over/under mechanics. Up to that, we just get modifier tweaks. While muliple dice are "curvier", when you reduce it to roll under/over and scale by the SD, the only substantial difference happens in the top/bottom 5%ish (the crit hit/miss territory). Integration makes things smoother, and "roll under/over" is integration of probability. [/QUOTE]

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