DND_Reborn
The High Aldwin
Let's see how each of these options fares at achieving the goals and avoiding the side effects that I think we agree on as criteria.
Makes rogue strictly weaker than RAW, thus violates side effect #3.
Given the other features I would be adding to rogues to make them perform skills better in other ways, overall they would not be weaker than RAW, simply stronger in other ways. Since I don't like the high potential for expertise, I don't see this as a bad thing.
Interesting. Makes expertise better at lower levels but with a lower ultimate ceiling. Could work.
I just thought of this one today, actually. I like it, but have a hard time justifying the reason to base it off of ability. Also, in the case of rogues with STR 10, expertise in athletics would offer no benefit at all, so I probably won't be using it.
All of these go in the wrong direction for your stated goals, I think. Setting hard floors on rolls, or making low rolls less likely while leaving the ceiling the same as proficiency, makes easy things easier, and makes hard things harder, for characters with expertise. So you wind up with more medium difficulty scenarios (such as stealth around enemies with low to moderate perception) where the rogue has no chance of failing, not less, and you lose the expert's higher ceiling, which wasn't one of the problems in the first place.
Yeah, in some ways it messes with things, but it was still a good idea and I was summarizing everything (well, most of it) from the thread. But I don't mind losing the expert's high ceiling, that is an issue I have trying to remove.

Has many of the same issues as the last category, since it makes it harder to get a low number, and also removes any incentive in-game to try to get advantage other ways, thus taking away an avenue by which fellow party members who aren't skill-focused can participate in the skill sphere by buffing the primary skill character.
We actually tried advantage once but ended up rejecting it. Again, it is part of the summary of peoples' ideas.
So here's the proposal I've been working on. I'm still looking at the math to calibrate it, but the design goals are as follows:
1. Expertise should have less of an impact on easy to moderate difficulty tasks than it currently does, so as to avoid the bounded accuracy problem of saturating success rates.
2. Regular proficiency should feel more meaningful for easy to moderate difficulty tasks than it currently does.
3. Expertise should not be weakened in general, since doing so makes two classes weaker relative to other classes.
4. These criteria lead me to posit that the gap between proficiency and expertise should be widened compared to RAW for high difficulty tasks. This reflects the colloquial meaning of being an "expert": your specialized training will be most apparent when doing particularly complex or difficult things.
5. But we don't want the expert to start doing really difficult things too routinely. So if we want to widen the gap between expertise and proficiency at high DCs, that suggests making it harder for the merely proficient to do those things and keeping the expert close to where they are now, under RAW.
6. Even though I'm weakening proficiency at high DCs, the strengthening at moderate DCs will be felt more, on balance, since those things come up more often.
Unfortunately, our design goals differ in some key points.
1. Expertise (as the rogue/bard feature) should offer options available to those classes which make using their skills more versatile and offers a greater degree of success, but without granting them potential beyond other classes.
2. I agree with this for proficient over non-proficient characters. That is why I did like #8b from my post, making a minimum of 5 + bonuses if you have proficiency. Even with modest bonuses, it makes moderate DC of 10 automatic, and with higher bonuses even DC 15.
3. Here we definitely disagree. I see expertise as is as too powerful compared to other features, and reigning it back only brings these classes back in line compared to others. I really don't mind them potentially being a bit better (up to +2), but more than that is unbalancing as our table has seen.
4. This is exactly the opposite of what I want LOL! Expertise is a feature offered (for rogues anyway) at level one. Yet, because it is based on proficiency, it continually gets better. That is what makes it so powerful compared to other features other classes get, such as Fighting Styles (which don't improve). In your view, this is what makes them a key feature, but makes it too strong in my view. Your definition of "expert" is spot on, but again why should rogues and bards be experts compared to other classes. Widening the gap just makes it worse IMO.
5. It is already hard for proficient characters do to hard and nearly impossible, even at the highest levels. Of course, at lower levels, those tasks are literally impossible. Someone with expertise should have a chance. One option I forgot to list before was for someone with expertise, a natural 20 should always succeed regardless of the DC. This could even be expanded at higher levels in some fashion.
6. Proficiency shouldn't be affected, only expertise.
With that logic in mind, here's what I came up with:
1. Skill checks use 2d10 instead of 1d20.
2. We adopt the variant rule that makes proficiency add a die instead of a fixed value (1d4 corresponding to +2, 1d6 to +3, etc.)
3. Ability score modifers are dropped by 1 across the board: 8-9 is now -2, 10-11 is -1, 12-13 is 0, etc.
4. The expertise feature grants a second proficiency die, but only if the base roll is 11 or higher. So, roll 2d10 first. If the natural result is 2-10, just roll a single proficiency die as normal. If the natural result is 11-20, roll two proficiency dice.
Here are the success rates at level 5 for an ability score of 12 for this scheme in graph form by DC, compared to RAW, and comparing no proficiency to proficiency to expertise.
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The system adds too much complexity for me, anyway. First, adding dice rolling takes time and for our group, adding a variable result from several dice would take way too long LOL! Compared to rolling a single d20, rolling a proficiency die, 2d20, and possibly another proficiency die for expertise would definitely be rejected at our table.
I don't mean to sound ungrateful for all the obvious thought and effort you've put into this, but it isn't heading in the direction we want. In the OP, the idea was to increase proficiency while decreasing ability and expertise; going from the +6/5/6 model to something like +8/4/4 or +9/5/2, etc. Since I have long been advocating for reducing the effect of expertise, I am not sure where you thought increasing it was my goal.