Yeah, I noted that as a benefit in the other thread. I've made my peace with the change in the context of advantage being able to stack. I just think, apart from that aspect, there's a mismatch between the solution and the examples you gave for why you think a high modifier is a problem.
I don't think it makes sense to think about the chances of an outcome when you've conditioned on one of the rolls being high (or low). I think you should only be considering the overall chances of being noticed.
If you assume the rogue rolls well, for a suitable definition of well, then a nat 20+perception is not enough to notice them unless the perception mod is nearly as high as the stealth mod. For a stealth mod of +7 and a perception mod of +2, say, the rogue makes the perception roll irrelevant if they roll a 16 or higher. If the rogue's mod were +10 they'd need only a 13 to render the perception roll irrelevant... but 16+ with advantage is more likely than 13+ without.
But that's a silly way to analyze the situation. It doesn't matter how often one side's roll is rendered meaningless; all that matters is how often the rogue is noticed. You should think of the opposed check as a single random event,
If you keep the same progression of proficiency bonus as RAW, the benefit of expertise as advantage over RAW expertise is:
+2 | d20 rolls 4 to 18 (78.75%) |
+3 | d20 rolls 5 to 17 (68.25%) |
+4 | d20 rolls 7 to 15 (47.25%) |
+5 | never (they tie on a roll of 11) |
+6 | never
|
So, yes, in many ways our expertise rule works to the player's advantage (no pun intended), but since it keeps the floors and ceilings lower that RAW, it accomplishes the balance I was shooting for.
In the example you wrote, yes the advantage over RAW is 43.75% to 40%, slightly better but hardly a big factor. When you get to something like a DC 25, the RAW still has a 30% chance to hit it, the +7 is still close (just under 28%).
What IS a big factor IMO is the +10 has the potential to reach 30, making it nearly impossible for most monsters to every notice them (the ceiling) and also making his minimum of 11 beat many monsters with passive scores of only 10 or lower. At 4th level, it is too much to have automatic success. With only +7, there is a chance, however small, that monsters with passive scores might notice him if he rolls low enough.
The goal with the advantage house-rule is also to make it so rogues (yeah, and bards...) cannot inherently hit higher DC than other classes. I am fine with them getting a chance to do better (it is a class feature after all), but not get high enough that others have no chance to even compete.
Anyway, the gang will arrive soon. As I have said before, if things don't work out with it, we'll go back and try a different approach, but last session it worked well IMO. And, as you said before, I don't see much point in going over ALL the math again!
