Only problem I can see with that is, that passive scores take away from the randomness attributed to DnD but I generally agree with you. I also don’t like rolling checks for my players.
…nonono, passive scores shouldn’t be automatic success or failure: you invert the roll…
…say you want to know whether a party detects traps as they prowl through the dungeon: you subtract twelve from the trap DC, use that as its modifier, and add it to a secret D20 roll which you compare with everyone’s passive perception to determine whether the trap successfully avoids detection…
…as long as you properly account for all applicable modifiers, you can do the same thing for any secret ability check or saving throw, or for a single roll to circumvent the party dogpiling a group check…
…subtracting twelve maintains the same odds with ties ‘succeeding’ for the rolling adversary; some DMs instead subtract eleven and flip ties for the PC to always win, which is mathematically identical, but then you have to keep track of flipping tie-resolution back-and-forth depending upon who’s rolling…
Perception +6, Trap DC 14 = Passive Perception 16, Trap +2
(both have the same 65% chance of detection, 35% chance of staying hidden)
…it becomes a pretty trivial exercise to invert any roll after you’ve done it once or twice…
Only problem I can see with that is, that passive scores take away from the randomness attributed to DnD but I generally agree with you. I also don’t like rolling checks for my players.
…nonono, passive scores shouldn’t be automatic success or failure: you invert the roll…
…say you want to know whether a party detects traps as they prowl through the dungeon: you subtract twelve from the trap DC, use that as its modifier, and add it to a secret D20 roll which you compare with everyone’s passive perception to determine whether the trap successfully avoids detection…
…as long as you properly account for all applicable modifiers, you can do the same thing for any secret ability check or saving throw, or for a single roll to circumvent the party dogpiling a group check…
Hm. That could work. But it would be quite tedious.
Also: why 12 and not 8? Doesn’t a DC calculate 8+prof+ability?
…subtracting twelve maintains the same odds with ties ‘succeeding’ for the rolling adversary; some DMs instead subtract eleven and flip ties for the PC to always win, which is mathematically identical, but then you have to keep track of flipping tie-resolution back-and-forth depending upon who’s rolling…
Perception +6, Trap DC 14 = Passive Perception 16, Trap +2
(both have the same 65% chance of detection, 35% chance of staying hidden)
…it becomes a pretty trivial exercise to invert any roll after you’ve done it once or twice…