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Message: <blockquote data-quote="Ovinomancer" data-source="post: 7891474" data-attributes="member: 16814">I focus on it because it's a key indicator that you aren't comparing the same things.  Here's a great example using the OP's first example.  I'll repost it for ease:Alright, this is a true statement -- these things have similar probabilities (~1% different).  But, what happens if we alter this highly contrived example just a touch?  Let's give the Fighter STR 20, and the target a ring of protection.  This makes the normal attack bonus +11 against normal AC 27.  Need a 16+ on 3d6, or a 4.64% chance of success. Now, if we do the doubling, it's an attack bonus of +22 (4 less) against an AC of 44 (2 more).  You need a 22 on a d20, for a 0% chance of success.Before you start, sure, 5e has a 20 always hits rule, but that's not part of the distribution -- it's actually breaking the statistical analysis -- so it cannot be used to justify a system based on an incorrect assumption of similarity in statistical behavior.The difference in spacing is a critical indicator that such breakpoints exist, this one just barely off of the example put forth to show just how similar the systems are.  If you, instead, reduce the difference by 2 instead of increase it, the delta is on 3d6 a 50% chance and on the doubled d20 a 45% chance.  Reduce another 2 and it's 74% to 65%.  You have a non-linear rate of change, which makes it obvious these two things are not, at all, alike.Math tip:  that equation simplifies to 2*DC-10.  Much easier to write.  It's also slightly off from what the OP suggests, but pretty close, for AC.  For DC, it's more (DC-10)*2+6, or 2*DC-14.  Still not quite what is suggested, but pretty close.The OP actually suggests using ability-10 as the bonus rather than 2*ability bonus, which increments in possible single steps rather than by 2's all the time.  Not sure why they felt the need for that bit of granularity while just doubling everything else, but hey, it's good.I do find it odd that you think I misunderstood what the OP was suggesting.  I didn't.  It's just not based on good math.This does pretty much nothing for increasing correctness, but it does immediately show how sensitive the analysis is to the arbitrary selection of offset.  Your suggestion now only lines up at 2, where the graphs cross, and then almost again at 13 and 14 on 3d6 (which get close to 15 and 17, respectively, on the d20).  No, the OP wasn't "off by one" as that actually makes the artificial comparison strictly worse.  You'd need to choose a different scalar to align at 11 rather than 10.  Which, interestingly, while the OP chose 10 as the center for the scaled 3d6, he left 10.5 for the d20 center, meaning the graphs don't even have the same mean value.  The warning signs for bad math are just all over this -- and, indeed, it's terrible math.</blockquote>

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