Thinking about this in game design terms rather than realism:
Oddly, hiding and moving silently are much much different in this edition than they were in previous editions
AD&D
Move silently was explicitly part of movement, but reduced movement speed to 1/3 normal. AD&D lacked a defined perception skill.
Hide required the character to remain "virtually motionless", but had no defined action cost.
Hide required concealment (apparently equivalent to lightly obscured in 5e).
3.x
Both Hide and Move Silently were explicitly part of movement, but the roll was a -5 if you moved more than half your speed, -20 if you ran or engaged in combat.
Hide was resisted (no action required) by Spot, Move Silently was resisted (no action required) by Listen.
A character could attempt to retry a failed Spot or Listen as a Move action.
Hide required cover or concealment, and no-one currently watching you, even casually, so you generally needed either a distraction, or total cover/concealment.
4e
Hide and Move Silently were merged into Stealth.
Stealth was at -5 if you moved more than 10', -10 if you ran, impossible in combat. Stealth was resisted (no action required) by Perception.
No search action that I could find.
Hide required cover or concealment, both to become hidden and remain hidden, unless the creature was distracted.
So in every prior edition, hiding was part of movement, and perception was mostly passive. That doesn't mean the 5th edition way of doing things is bad, just different, but it might be bad.
What do players and DMs actually expect?
My experience is that people do not expect perception checks to require an action for normal hazards, but something that does require an action is usually impossible without an action -- the DM won't even give you a roll unless you say "I'm searching the bookshelf" or whatever. I think the actual expected behavior of perception checks is something like:
Perception Checks: Perception checks are normally done as part of another action, and cover finding things that the DM thinks would reasonably be found when performing that action. For example, a DM might use a perception check to determine whether a character walking down a dungeon passage notices that one of the pebbles is actually a gemstone. Characters may choose to move slowly (granting advantage) or swiftly (granting disadvantage) if they choose.
A character may also take time to actively search, in which case the DM should set difficulty based on what they're doing. This might make previously difficult or impossible tests straightforward or even automatic (for example, if there's a key on the top of a doorframe, someone passing through the room will never spot it because they have no reason to look there, whereas someone who actually says they're searching that location finds it automatically, and someone searching the room should get a roll to decide if they check) but generally takes quite a bit of extra time.
Of course, that's about outside of combat. In combat, it really comes down to plausibility and balance. I think the expected behavior is something like
Stealth: stealth is normally rolled as part of another action; it may make that other action slower or more difficult but is not its own action. However, if you are trying to hide from someone who has already spotted you and is paying attention to you, you typically must use an action to throw their attention off. The DM may relax this rule if you become heavily obscured or move behind total cover, then exit your hiding place in an unexpected way.
Is this "common practice" actually written in the rule books anywhere?
That's not the best way to think about it in this case. Instead, what I've described is just the only possible conclusion that can be drawn from the rules that actually are written. The books emphasize brevity so when this sort of thing occurs, they tend not to actually write the conclusion into the text.
The reason why it works this way is because passive perception is explicitly used to determine what a creature notices within the environment through general awareness without actually consciously searching.
Passive Perception
Passive Perception is a score that reflects a creature’s general awareness of its surroundings. The DM uses this score when determining whether a creature notices something without consciously making a Wisdom (Perception) check.
So, by the time that you are ready to declare an action to search for something either you've already passively noticed it, or you haven't. So, any value for your active roll that is lower than your Passive score simply has no meaning other than as a failure state. For example, if your Passive Score is 13 and you actively roll a 6, that does NOT mean that you are perceiving something "even worse" than you could have passively. That's not a correct interpretation. Instead, this simply means that the thing that you are searching for was too well hidden to notice passively and that with this particular active roll you still cannot find it. The actual number doesn't matter except as a pass/fail mechanism. Therefore, as a way to explain what the rules actually say in a simplified manner, we can consider that any value for the active check below your Passive score can just be rounded up to your Passive score which therefore acts as a "floor" for your active check numerically.
Example: Your Passive score is 13. You are walking down a hallway. A secret door on one wall is defined to be impossible to detect unless a creature is 10 feet away or closer. When within that distance the DC = 10. Well, if you happen to be walking close enough to that wall during your walk you will automatically "notice" the secret door without actively searching for it (no action required). If you never got close enough to that portion of the wall while walking down this hallway then you will not "notice" it. Now, if instead you do walk close enough but the DC = 15 then you will not notice it and will likely walk on by without ever finding it. However, if instead for whatever reason you are actually searching this wall for secret doors, then since your Passive check has already failed (no action required) then the DM will now ask you to roll a Perception check (action required). This active roll has a 45% chance of success. The actual value of the roll is meaningless beyond the fact that it either represents succeeding (45% of the time) or failing (55% of the time).
"I duck behind a pillar and suddenly they've lost track of me" doesn't actually work.
By the RAW, this technically does work although it's not as good of a hiding place as most other places.
The reason why this works is because I cannot see or hear this creature and therefore I do not actually know it's location. I can make a pretty decent educated guess. But you might have used Subtle Spell to cast Dimension Door. Or you may have dropped down into a hole. I don't actually have any way of knowing this if my sense of sight and/or my sense of hearing cannot currently detect your location. What I CAN do is guess the square. And in this scenario, I'd be correct most of the time. But not necessarily every time.
__________
One final point I'd like to make here is somewhat of an appeal to common sense. Why do you all think that the game designers went through all of the trouble to define, include and print a Passive Perception score into just about every single published monster stat block in the game?
One final point I'd like to make here is somewhat of an appeal to common sense. Why do you all think that the game designers went through all of the trouble to define, include and print a Passive Perception score into just about every single published monster stat block in the game?
Unfortunately, "failure of internal communication" is a reasonably plausible answer, because it was definitely important in 2014.
Instead of making Passive Perception lower, the Devs opted to increase the Hide DC.
A DC 15+ requires a high Wisdom and/or Proficiency Bonus in Perception. Many low-mid CR creatures don't have a Passive Perception of 15+
More player characters tend to eventually have Passive Perception of 15+ because Perception is a popular skill proficiency and Wisdom is a primary ability of some classes.
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Thinking about this in game design terms rather than realism:
Oddly, hiding and moving silently are much much different in this edition than they were in previous editions
AD&D
3.x
4e
So in every prior edition, hiding was part of movement, and perception was mostly passive. That doesn't mean the 5th edition way of doing things is bad, just different, but it might be bad.
What do players and DMs actually expect?
My experience is that people do not expect perception checks to require an action for normal hazards, but something that does require an action is usually impossible without an action -- the DM won't even give you a roll unless you say "I'm searching the bookshelf" or whatever. I think the actual expected behavior of perception checks is something like:
Of course, that's about outside of combat. In combat, it really comes down to plausibility and balance. I think the expected behavior is something like
That's not the best way to think about it in this case. Instead, what I've described is just the only possible conclusion that can be drawn from the rules that actually are written. The books emphasize brevity so when this sort of thing occurs, they tend not to actually write the conclusion into the text.
The reason why it works this way is because passive perception is explicitly used to determine what a creature notices within the environment through general awareness without actually consciously searching.
So, by the time that you are ready to declare an action to search for something either you've already passively noticed it, or you haven't. So, any value for your active roll that is lower than your Passive score simply has no meaning other than as a failure state. For example, if your Passive Score is 13 and you actively roll a 6, that does NOT mean that you are perceiving something "even worse" than you could have passively. That's not a correct interpretation. Instead, this simply means that the thing that you are searching for was too well hidden to notice passively and that with this particular active roll you still cannot find it. The actual number doesn't matter except as a pass/fail mechanism. Therefore, as a way to explain what the rules actually say in a simplified manner, we can consider that any value for the active check below your Passive score can just be rounded up to your Passive score which therefore acts as a "floor" for your active check numerically.
Example: Your Passive score is 13. You are walking down a hallway. A secret door on one wall is defined to be impossible to detect unless a creature is 10 feet away or closer. When within that distance the DC = 10. Well, if you happen to be walking close enough to that wall during your walk you will automatically "notice" the secret door without actively searching for it (no action required). If you never got close enough to that portion of the wall while walking down this hallway then you will not "notice" it. Now, if instead you do walk close enough but the DC = 15 then you will not notice it and will likely walk on by without ever finding it. However, if instead for whatever reason you are actually searching this wall for secret doors, then since your Passive check has already failed (no action required) then the DM will now ask you to roll a Perception check (action required). This active roll has a 45% chance of success. The actual value of the roll is meaningless beyond the fact that it either represents succeeding (45% of the time) or failing (55% of the time).
Nope. I've quoted the rule above.
I've quoted the rule above.
By the RAW, this technically does work although it's not as good of a hiding place as most other places.
The reason why this works is because I cannot see or hear this creature and therefore I do not actually know it's location. I can make a pretty decent educated guess. But you might have used Subtle Spell to cast Dimension Door. Or you may have dropped down into a hole. I don't actually have any way of knowing this if my sense of sight and/or my sense of hearing cannot currently detect your location. What I CAN do is guess the square. And in this scenario, I'd be correct most of the time. But not necessarily every time.
__________
One final point I'd like to make here is somewhat of an appeal to common sense. Why do you all think that the game designers went through all of the trouble to define, include and print a Passive Perception score into just about every single published monster stat block in the game?
Unfortunately, "failure of internal communication" is a reasonably plausible answer, because it was definitely important in 2014.
Instead of making Passive Perception lower, the Devs opted to increase the Hide DC.
A DC 15+ requires a high Wisdom and/or Proficiency Bonus in Perception. Many low-mid CR creatures don't have a Passive Perception of 15+
More player characters tend to eventually have Passive Perception of 15+ because Perception is a popular skill proficiency and Wisdom is a primary ability of some classes.