You cannot replace the d20 and expect everything else to just fall in line. Here's an example of what I had to consider when I decided to build around a 3d6 bell curve rolle as the core mechanic.
At its most fundamental level, the original core mechanic of the game has you roll a single die, adjust the number with any relative modifiers, and compare it to a target number which represents the difficulty of resloving a task or action. The single die creates a linear progression with an equal distribution probability for any result. That made it very easy to adjust and maintain balance within the game.
A bell curve roll, however, works quite differently. (Check out this page for some probability charts!
Link)
The majority of rolls are more likely to produce results between 9 and 12 before modifiers, while rolls above 15 and below 6 are very rare. This doesn't eliminate the randomness of the dice completely, however. It simply reduces the unpredictable nature of an extremely high or low result. Less emphasis gives more control to the players and power to their choices, as well as the DM. So how does that affect the target difficulty numbers? This is where I start looking at the different editions.
Fourth edition (4e) had everything on a sliding scale. When you character levele up, they got most of the same bonuses as everyone else in their primary abilities. And the monsters did, too. So when you gained another +1 modifier to your skills, DCs and monster bonuses also went up. At one point, I had stopped looking up DCs and bonuses at the table and just assumed any roll over 12 was good. No one seemed to notice, or cared.
In 5th edition, its simple to remember because it stays consistent throughout the game at every tier. That is in part how bounded accuracy was designed. Smaller numbers for modifiers that were never expected to exceed a particular number, thus target numbers remained relevant even as the characters progressed. The DCs for level 1 to 20 are the same, from very easy to nearly impossible: 5, 10, 15, 20, 25, 30.
With a bell curve, numbers below 3 and above 18 don't exist on the possibilities of rolls without any modifiers. So numbers above or below the median (below 6 and above 15) become either extremely easy or extremely difficult to beat.
Furthermore, modifiers need to be reigned in significantly. A simple +/- 1 won't break anything, but each +/- compounds the weight of the modifier. Suddenly, your 9-12 expected range becomes 12-15 with a +3. And we all know that +3 is minimal at any level in D&D. So that is something else I'll need to look into. For now, I know that my modifiers are going to be smaller (and more meaningful) than usual.
So here's what I came up with in terms of target values for difficulty. Mind you, this is for scale and general reference. Numbers do (and will) exist in between.
Target DC | Difficulty | Average Roll Needed | Modifier |
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8 | Easy | 3, 3, 3 | -1 |
12 | Medium | 4, 4, 4 | 0 |
16 | Hard | 5, 5, 5 | +1 |
20 | Very Hard | 6, 6, 6 | +2 |
24 | Nearly Impossible | 6, 6, 6 | +6 |
This also tells me that a +4 modifier is significant. That is the threshold I'm looking for to separate the average heroes and monsters of one tier to the next. Starting characters should probably have only a +4 in their specialty skill, including their attributes. So the question is, when does the each significant tier of their adventuring career begin and end?