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Ironeye |
The system is set up to benefit the active entity over the passive entity when they both have equivalent bonuses ("active" being whichever one is allowed to touch the dice). As previously noted, +0 vs. DC 11 is "balanced" insofar as the CF/F/S/CS chances are symmetric at 5%/45%/45%/5%, but the actual "equal bonus" situation is +0 vs. DC 10, thereby favoring whoever holds the dice. (Contrast, for example, +0 Deception vs. +0 Perception and +0 Perception vs. +0 Deception.) Given that the passive entity effectively "Takes 10," if anything, all of the cutoff points (DC, DC - 10, DC + 10) should "round down" to the worse outcome, rather than only DC - 10 rounding down to Critical Failure.
Having the "passive" die result being the actual average of 10.5 would dodge this whole "which way to round?" business entirely and smooth out the math in the process, but then we'd all be running around with fractional AC's, and I don't think anyone wants that.
As it stands, the intuition behind the most common interpretation for the cutoff points seems to be to "round away" from the theoretically boring Failure result. I find universally "rounding up" to the more beneficial result to be more intuitive (and mathematically tidy), but the math would then suggest 11 as the passive baseline, not 10.
All that being said, what makes the math "correct" may very well be different for actions that cost significant resources (e.g., spell slots, actions in combat) vs. actions without significant cost.
If neither side has a resource crunch, the balanced 5%/45%/45%/5% result on equal skill should be independent of who's rolling, since the active entity is taking no more risk and incurring nor more costs than the passive entity. Similarly in that case, we'd ideally want a "symmetric" result where the active entity's +1 bonus causing a 5%/40%/50%/5% mirrors the passive entity' +1 bonus causing the active entity to get 5%/50%/40%/5%.
On the other hand, if the active entity is expending resources, it may very well make sense to give them the advantage of the passive entity "Taking 10" in order to compensate for the cost of the active entity's resources to take the action. In that case, DC - 10 "rounding down" for the active entity serves as a small check on the "free" +1 they get for being the one touching the dice. (This gets interesting for effects with Save DC's, since the targets get the free +1 for being active even though they're usually not expending actions.)