The concept of a “passive Perception score,” although somewhat derived from the Take 10 mechanics of 3rd Edition, was introduced in the 4th Edition of D&D. The basic concept is that, instead of having the PCs make Perception checks to see whether or not they spotted something, you pre-calculate a static value (10 + their Perception modifier) and simply compare that score to the DC of the Perception task.
Frankly speaking, it’s a bad mechanic that got even worse in 5th Edition.
First, there’s no variation in result: PC A will always have a higher score than PC B, so PC B will never spot something PC A doesn’t see. This not only eliminates novelty (which can be valuable in its own right), the lack of variety is also inherently stultifying, making it more difficult for different players to take the lead in reacting to different situations.
Second, it combines poorly with bounded accuracy. The basic concept of bounded accuracy is that you push all the DCs into a small range with the expectation that the d20 roll will be relevant and then remove the d20 roll. The Dungeon Master’s Guide, for example, says “if the only DCs you ever use are 10, 15, and 20, your game will run just fine.” But any 1st-level group, of course, will almost certainly have multiple PCs with a passive Perception score higher than 15.
Which brings us to the biggest problem, in my opinion, which is that in actual practice the whole thing is a charade. You, as the DM, will very quickly learn what the highest passive Perception score in your group is, which means that whenever you’re deciding what the Perception DC is, you’re really just deciding whether or not the DC is going to be higher or lower than the party’s score.
There’s nothing wrong with GM fiat, per se, but the passive Perception score ends up being this weird fake mechanic with a bunch of extra bookkeeping trying to mask what’s really happening. “No, no,” says the DM. “I didn’t arbitrarily decide you didn’t spot the trap! I decided that the DC to spot the trap was higher than your passive Perception score! Totally different!”
So, personally, I recommend that you don’t use D&D’s passive Perception scores. For a better way of handling perception-type checks — which can be used in a wide variety of RPGs, not just D&D — I recommend checking out Rulings in Practice: Perception-Type Tests.
With that being said, if you nevertheless want or for some reason need to use D&D’s passive Perception score, there are some best practices you can follow to do so to best effect.
MAKE A LIST
Ask your players for their passive Perception scores, write them down on a Post-It note, and attach that Post-It note to your GM screen.
This may seem obvious, but I’ve played in any number of games where the DM was constantly asking us what our passive Perception scores were, and there’s absolutely no reason for it. Collect them once, then use them instantly every time. Both the pace and the focus of play will be immensely improved.
Random Tip: While you’re doing this, go ahead and grab the PCs’ armor class, too.
Watch out for changing Perception scores. Some spells, abilities, and magic items may modify a character’s Perception score, grant them advantage on Perception checks, or the like. You’ll need to make sure to track this. (And, of course, you’ll also want to make sure you update your list when the PCs level up.)
In some groups, you may also discover that your players challenge surprise. When players see the mechanics being invoked, even if that’s just the DM asking for their passive Perception score, they’ll accept the outcome; but if it’s all being done invisibly behind your DM screen, some players will worry that they’re getting screwed over. “Did you remember that I have advantage on Perception checks in forests?”
The best way to handle this is to (a) make sure you’re getting it right, (b) reassure them, and (c) if it continues, have a transparent discussion about why you’re handling the passive Perception checks this way and how you’re doing it. You might find it effective to make a point of confirming their passive Perception scores at the beginning of each session, and you can also ask them to notify you whenever their passive Perception scores shift during a session.
(The next technique can also help with this, since they’ll at least hear the mechanics being invoked.)
REMEMBER DISADVANTAGE
One of the most overlooked rules in D&D 5th Edition is that characters who are “distracted” are supposed to be at disadvantage on their passive Perception checks, which means that they should suffer a -5 penalty on their passive Perception score.
I recommend applying this aggressively in any situation where the PCs are not explicitly keeping watch and/or paranoid. Creeping down a dungeon passageway in hostile territory? On watch at night? You specifically said you were going to keep a lookout on the door while Arathorn ransacks the room? Great, you get your normal passive Perception score.
Arathorn, though? Apply the penalty. Also apply the penalty if the PCs are just walking down the street in a friendly city without any expectation of trouble or hanging out at a tavern with their friends.
In practice, this blunts the problems with how bounded accuracy interacts with passive Perception scores. It also encourages the players to be more specific with how they interact with and observe the world, instead of just coasting through the game on auto-pilot. (This is particularly important in making traps work right, for example.)
ROLL THE DC
You can sidestep the system being a camouflage of busywork for DM fiat by assigning a modifier and then rolling the DC of the check instead of assigning a static DC.
Basically take the DC you would have assigned (10 = Easy, 15 = Moderate, 20 = Hard, etc.), subtract 10, and use the remainder as the modifier for a d20 roll. (You can do the same thing with prewritten adventures that list a static DC.)
This is what you already do with Stealth checks, of course, but it may feel weird doing it for something like noticing the rune faintly inscribed on the ceiling.
The point, of course, is to reintroduce variability to the check so that you can make non-fiat rulings. (For example, I can decide the run is moderately difficulty to notice with a +5 check; but I don’t know whether or not the rogue with a passive Perception score of 18 will spot the rune or not.) But you nevertheless retain most of the advantages of using passive Perception scores, because you’re not making a roll for every individual PC (which would be time-consuming and also have a drastic impact on the probability of the check.)
RANDOM SPOTTING PRIORITY
Once the Wisdom (Perception) DC is set, you’ll know which PCs, if any, successfully noticed whatever the target of the check was.
If there are multiple PCs who succeeded on the check, randomly determine which of them noticed the target first.
This is a simple way of systemically spreading the “spotting something” spotlight around, giving different players an opportunity to call attention to a cool tapestry, sneak a gem into their pocket, or determine what the group’s reaction to approaching goblins might be.
Is this “fair” to the PC with the highest passive Perception score? Frankly, yes. Note that they’ll still get spotting priority more often than anyone else in the group, because (a) they’ll participate in more spotting priority checks than other PCs and (b) there will be some checks where they’re the only PC to succeed.
Alternative: If it’s a combat situation — or a potential combat situation — you might use Initiative checks to determine first spotter.
VARIANT: LET PERCEPTION RIDE
An alternative method for passive Perception scores would be to have the group roll Perception checks at the beginning of a delve, raid, or session and then let the result ride as their passive score for the run.
This means that for some sequences the rogue will have the highest passive Perception score and in other sequences it will be the barbarian or the wizard. It will move around the table, creating variable outcomes over time.
VARIANT: TAKE 0
To lessen the importance of passive Perception without completely eliminating it, base passive Perception scores on Take 0 instead of Take 10. In other words, a character’s passive Perception score is simply equal to their Wisdom (Perception) modifier.
Particularly at Tier 1, this will mean that passive Perception may not even succeed at Easy tasks. That’s okay, because in surprise situations you’ll be calling for a rolled Wisdom (Perception) check in these cases. It will also encourage the players to make active Perception checks, engaging with the environment to find stuff instead of just relying on their passive scores to take care of it.
In practice, when using this variant, you’re really just keeping a list of the lowest possible Wisdom (Perception) check possible, so you know the threshold at which it becomes pointless to roll the dice and you should just tell the PCs what they see.
Remember, of course, that this also applies to the NPCs.
Alternative: Base passive Perception on Take 5, so the score is 5 + the character’s modifier. Combined with consistently applying disadvantage for distraction, this will often create a baseline similar to Take 0, but with passive Perception still having a bit more of a meaningful role in the system.