The perception check involves the senses (sight, hearing, smell...) to determine is someone is in hiding.
The investigation check involves the analysis of some details to determine something that is not clear at a first look. Investigation is usually used to find hidden doors or the like.
I agree with filcat. It may help for you to visualize different scenarios using each. Perception is noticing/observing your surroundings. Do you hear someone walking, smell an odor, notice what's happening around you. Inspection/Investigation is actively looking for "clues" or reason for something, ex. footprints in the mud, markings/triggers on a wall, etc - something that may not be plainly visible at first glace.
Think openly noticeable or if they have to actively search.
As an example, a character enters a room that has a secret door. If they have a passive Perception of 15 or higher, they notice the secret door whilst in the room, without actively looking for it. Their perception is sufficiently high that they are able to spot the edge of the door etc. If their passive perception wasn't high enough and they announced they were actively searching the room, they could roll the check.
A different character, with worse Perception, enters the same room instead and has a look around - the DM gets them to roll an active perception check, as they're searching the room. They generate a total of 9 and don't spot the secret door. The player concerned says that he thinks there must be another way out of this room, a hidden trapdoor, door etc, so is searching for that. Now the DM asks for an Investigation check, as the character is now trying to locate something specific - they note that there is grain on the floor of the room, except for the Southern corner, deducing that the only reason why someone would sweep the floor, but only sweep one corner, is to hide any tracks that might be left. Checking the floor further in that corner, there are some scratches on the wooden floor in an arc, indicating a door opening and scraping the floor. Following that back, they locate the edge of the door.
Tl;dr - there are many circumstances where both/either check would be suitable, but it changes the way the character sets about finding something.
Personally I think of it this way: Perception is always passive. It's used to spot or notice things without active involvement. Once someone starts active interaction with the environment it becomes Investigation.
PC's traveling down the road, Enemies hidden in the scrub at the side.
Perception vs enemies Stealth to determine if they notice.
If they do not and an enemy with Skulker feat fires and misses. His position isn't revealed but now the PC's know something is up.
Investigation check to see what's going on around them.
Not agree on the Perception skill being only passive. If there an invisible monster nearby, a player can call for a Perceptioncheck to determine his position, if the result of a contest with the monster Stealth check is in your favour.
Not agree on the Perception skill being only passive. If there an invisible monster nearby, a player can call for a Perceptioncheck to determine his position, if the result of a contest with the monster Stealth check is in your favour.
Though for what it's worth, I'd probably (personally) allow a player to use Investigation if they were more methodical about it... Perception would be trying to notice dust, hear breathing, while Investigation would be walking about swinging your arms to feel for the creature, or tossing dust to see how it's disturbed.
In that case, though, it's also a matter of the timescale you have available, and become inconvenient to do in combat.
Agreed with Filcat - Perception very definitely can be (and should be) used actively.
The classic times you're actively using Perception:
You're expecting an ambush - so keeping an eye out for hidden attackers.
Moving slowly through a dungeon area, looking for traps.
There *IS* overlap between the two skills and that is ok - the way a wise & perceptive cleric looks for things is very different to the intelligent Wizard would investigate.
I just got back from a long run so I had a little time to think about this (and other things). I came to essentially the same conclusion you stated above. I think for myself, going forward I will utilize it this way.
Passive Perception will be for what do players notice with their senses without effort.
Active Perception will be for what do players notice with their senses with active effort.
I will likely rarely use Investigation. Investigation is a trained Intelligence check. It's essentially a Sherlock check. They take all of the clues they have found through Perception and figure out how they fit together or what they mean.
So for me it becomes Roleplay vs Roll Play. Are the players making a roll to learn something and I'm handing it to them with a successful roll? By giving them something as a roll result am I denying them the opportunity to figure it out themselves? Sure they might need a boost or a hint every now and then but I personally gain more satisfaction as a player when I figure it out and I'm happiest as a DM when my players genuinely outsmart me.
Again all of this is not what is right or wrong just how it feels to me and how I am going to play with it. Ultimately so long as game play isn't negatively affected playing either way will work.
Yes, Sherlock skill is a decent analogy - you can use it as a great skill to feed the players' roleplay though.
Consider the following:
A character uses Perception (either passive or active) and finds there are some tracks leading through the cellar, up to a wall. Seems they have spotted a hidden door.
The character rolls a successful investigate check and you say, "The footprint tracks are boots and left with a clay-based mud."
Player, "Has it rained recently?"
GM, "Not since yesterday morning, so the ground is mostly dry"
Player (looking over the map of the village), "Oh, there's a village pond and a small stream, so we have a clue whereabouts in the village they came from .... let's go check those areas for boot prints...."
It's up to the DM to compliment the play-style of the players - if they love solving puzzles, then feed them clues via various skills. If they don't really like solving puzzles, then allow the skill checks to give them the answer.
Investigation is still useful in intrigue-based games or during puzzles. Keep in mind that the player may be playing someone with an Intelligence of, say, 15+ even if they aren't all that smart themselves. Denying them the ability to apply their character's smarts by denying Investigation rolls (saying "you should roleplay the deduction instead") is doing such players a disservice. I see a use for both roleplay as well as making a roll, no matter what the skill being rolled is. I think Stormknight gave a good example of how you can roll Investigation and still enable players to think on their own as well. You don't always have to give out the answer with a successful roll, maybe it just reveals a clue or two instead.
Perception is a much more broad skill, however, covering both just noticing things passively as you're going by, or actively searching for things using your senses.
I think the easy way to view the difference is that a Perception check comes into play when you are quickly glancing at something and lack the time to investigate it further. In other words if you aren't going to be spending 10 min. or so on the activity it probably requires a perception check. If you can spend a good amount of time on the activity then Investigation becomes more accurate.
The key is that Perception is used when you can't make deductions and wisdom is more appropriate. Investigation is more important when you can make logical deductions. So they aren't really interchangeable, though they may overlap.
So you could have a Perception check to determine if you see the Wizards secret door (maybe DC 20?) while the Investigation check to see if you can locate the door might be (DC 15) if you are actively searching for it and looking for clues.
I would say investigation can not be used in combat as it would require longer than 6 seconds, and so in combat perception is the more appropriate activity.
Part of how I look at Perception, Investigation, and Insight a bit as a balancing component.
In 3.5 editions there was just Spot (Wis) and Sense Motive (Wis).
Now we have Perception (Wis), Investigation (Int), and Insight (Wis).
To me the idea is to open up more way for players to solve puzzles. Any particular player is only going to have so may skills (2 for backgrounds, 2-4 for class, 0-2 for race) out of 18 possible skills. To me Investigation was an attempt to give high Int players a possible way to solve such problems through deductive reasoning.
Especially, if your description allow for players to build upon each other. I'm personally a fan giving players clues based on their states without necessarily having to roll if it's a plot critical.
Lets say a Wizard, Rogue, and a Ranger are chasing after an NPC, down alleys and suddenly he disappears and the PCs lose sight of him. Now, I as the GM want the PCs to follow the NPC's trail, but I want this to be a chase so time is of the essence.
I might tell the Rogue and Ranger they are *sure* (high Wis and Perception trained) they heard a door slam before they lost track of the NPC, but they don't know which building. I might prompt the Ranger to roll Survival, if she does well then I'd say "you notice fresh grooves in mud under a particular door." If she rolls poorly, I'll tell her that "there is a lot of foot traffic, it's taking you a while to figure out who's prints are who's, but there is fresh grooves in the mud under a particular door" (They still solve the puzzle, but the NPC has a bigger lead).
Now they have entered a room of the building, but it's a dead end and the NPC isn't anywhere to be found. Maybe the rogue rolls well on perception and notices (sees it or feel a breeze) the hidden door, but hasn't found the mechanism yet. I might give the Wizard (who has Investigation) a roll to solve that to open the hidden door, obviously they need to turn the wall sconce! If he Rogue also has Investigation maybe she solves it by using her Thieves Tools to unlock the mechanism, sliding a peice of metal into the crack.
I guess I see it as a way to reward players in different ways. Instead of just making having a good Wisdom and training in Perception & Insight the uber stats.
I would agree with filcat and FullMetalBunny. Perception is Wisdom based, Investigation is Intelligence based. Especially about the skill checks being basically a short-cut for actual character actions. Using the character roles is a general assumption about how smart or perceptive the character is. Instead of having a player tell you that they are searching for a secret bottom in a drawer, they can roll an investigation check and it's assumed that they think to look for that. With perception, because the player isn't physically there to hear a person sneaking around a room, the check is a short cut to determine whether they're paying attention for it. I always treated 'passive perception' as a metric of how oblivious a character is. A high passive means a person's always alert, a low passive means they aren't. However just because a person's paying attention to their surroundings doesn't mean they would think to search a bookshelf for secret doorway for example. But if the player specifically asks so search all the bookshelves then a check may not be needed.
Since a lot of people bring up hidden/secret doors and traps, I want to point out that it very clearly says in the Player's Basic Rules, under "Using Ability Scores > Ability Checks > Perception"
FINDING A HIDDEN OBJECT When your character searches for a hidden object such as a secret door or a trap, the DM typically asks you to make a Wisdom (Perception) check. Such a check can be used to find hidden details or other information and clues that you might otherwise overlook.
In most cases, you need to describe where you are looking in order for the DM to determine your chance of success. For example, a key is hidden beneath a set of folded clothes in the top drawer of a bureau. If you tell the DM that you pace around the room, looking at the walls and furniture for clues, you have no chance of finding the key, regardless of your Wisdom (Perception) check result. You would have to specify that you were opening the drawers or searching the bureau in order to have any chance of success.
So the basic rules say Perception is used to spot hidden doors or traps.
However, a player/class that is stronger at Investigation than they are at Perception, could likely use Investigation to deduce where a trap or secret door would be placed, if one existed (as opposed to just flat out spotting it). And then roll Investigation to see if they are right. So in game, both could work, as different classes would use their different strengths to accomplish the same thing (when it's appropriate).
There seems to be a bit of a misunderstanding about the meaning of "passive" in the context of skill checks.
Passive is NOT something that is always on or that happens when the character isn't doing anything.Passive has NOTHING to do with the actions of the character. Passive has only one meaning in the context of the D&D 5e rules ... the player does NOT roll dice. That's it. Unfortunately, a lot of people read passive and immediately assume it has something to do with the character.
PHB pg 175
PASSIVE CHECKS A passive check is a special kind of ability check that doesn't involve any die rolls. Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster.
Passive checks can be used to find secret doors or other items but ONLY if the character is actually doing something that would allow them to find the secret door. If they are searching for example or paying attention to their surroundings (which almost everyone does when traveling or in a dungeon) then a passive check could be used to discover or observe whatever is hidden.
This is emphasized in the traveling rules PHB 182 and 183
NOTICING THREATS Use the passive Wisdom (Perception) scores of the characters to determine whether anyone in the group notices a hidden threat.
OTHER ACTIVITIES Characters who turn their attention to other tasks as the group travels are not focused on watching for danger. These characters don't contribute their passive Wisdom (Perception) scores to the group's chance of noticing hidden threats.
So ... if you aren't watching you don't get to use passive perception to discover threats.
This approach is used in the adventures built for 5e. From Lost Mines of Phandelver p7. (small spoiler)
"Snare. About 10 minutes after heading down the trail, a party on the path encounters a hidden snare. If the characters are searching for traps, the character in the lead spots the trap automatically if his or her passive Wisdom (Perception) score is 12 or higher. Otherwise, the character must succeed on a DC 12 Wisdom (Perception) check to notice the trap."
If the party is ACTIVELY searching for traps then their PASSIVE perception can be used to find the trap. If they aren't searching OR if their passive perception is too low they make an ACTIVE check by rolling the dice. The characters have to be taking an appropriate action in order for their passive score to be used.
----------------
As for the difference between perception and investigation, these are also pretty well defined in the PHB.
PHB p178
Investigation. When you look around for clues and make deductions based on those clues, you make an Intelligence (Investigation) check.
Perception. Your Wisdom (Perception) check lets you spot, hear, or otherwise detect the presence of something. It measures your general awareness of your surroundings and the keenness of your senses.
Perception is the ability to SENSE your environment while Investigation is the ability to DEDUCE or figure out something based on what has been perceived.
For example, finding a secret door might be a perception check (which is the check outlined in the PHB) but figuring it out how to open it could be an Investigation check (or deducing the presence based on the draft in the room ... or some other observation). Either or both of these could use a PASSIVE check in which the player doesn't roll dice. "Such a check can represent the average result for a task done repeatedly" ... if the character has sufficient time to thoroughly search a room then first making a passive check to see if that succeeds make sense since a passive check represents the AVERAGE result.
------------------
Finally, passive checks can be used for any check that the DM wishes and they make sense for any situation where
1) There is sufficient time for the character to try repeatedly
2) The action taken has no significant consequences.
For example, if a character is looking through books to do magical research to find magical information for a quest with a DC15 then a passive check against arcana might be in order before anyone rolls dice. This has several advantages. It stops everyone in the party from rolling and wasting time. It also means that the wizard with 16 int and proficiency in arcana is more likely to find the clue than the 8 int barbarian without proficiency and no interest in magic who happens to roll a 20. If no one has a high enough passive score then the task is up to completion by the luck of the dice. The same can apply to forcing a door open (strength check), picking a lock (thieves tools, dex check), history check or any other ability check performed when given enough time and for which failure doesn't have a consequence.
On the other hand, disarming a trap that could go off if failed would likely require a roll. Similarly, picking a lock where the lock could break might require a roll.
All of this is up to the DM, but passive checks are massively under utilized compared to the way the rules are written and the way the examples in both modules and the rule books seem to lay them out. (for example, the observant feat gives +5 to both passive perception and passive investigation ... but I have met very few DMs who use passive investigation since many seem to wonder how investigation can be passive :) ... when it isn't the investigation that is passive ... it is the player that is passive because he doesn't roll dice).
From a role playing perspective, using passive checks when appropriate gives a much smoother narration and plays to the strengths of the characters. If the DC is low enough then the ones who are proficient in the skill with good relevant attribute are the ones who are more likely to notice or make the connection. From a player perspective, the player would never know that there was a task requiring a check, they just hear the narrated result that their character discovered something or figured something out (assuming that they were taking an action that would allow an application of the skill check).
tonight a player and i got into an argument over using perception vs. investigation.
the player walked into a room and asked for a perception check, his roll was too low to notice anything. Therefore he starts walking around the room asking for more perception checks.
I saw this as him searching the room for a hidden creature he assumed (as a player, not his character) was there, so after a few checks i told him he would need to make an investigation check.
He got upset because his character has a low intelligence score and tried arguing that he was trying to perceive the room, even though from his initial perception check he could perceive the whole room.
i would appreciate insight from more experienced DM's on how they would have ruled this.
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Can someone clarify the difference in use between perception checks and inspection checks? I've pretty much had DMs use them interchangeably
The perception check involves the senses (sight, hearing, smell...) to determine is someone is in hiding.
The investigation check involves the analysis of some details to determine something that is not clear at a first look. Investigation is usually used to find hidden doors or the like.
I agree with filcat. It may help for you to visualize different scenarios using each. Perception is noticing/observing your surroundings. Do you hear someone walking, smell an odor, notice what's happening around you. Inspection/Investigation is actively looking for "clues" or reason for something, ex. footprints in the mud, markings/triggers on a wall, etc - something that may not be plainly visible at first glace.
Think openly noticeable or if they have to actively search.
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There's certainly some overlap.
As an example, a character enters a room that has a secret door. If they have a passive Perception of 15 or higher, they notice the secret door whilst in the room, without actively looking for it. Their perception is sufficiently high that they are able to spot the edge of the door etc. If their passive perception wasn't high enough and they announced they were actively searching the room, they could roll the check.
A different character, with worse Perception, enters the same room instead and has a look around - the DM gets them to roll an active perception check, as they're searching the room. They generate a total of 9 and don't spot the secret door. The player concerned says that he thinks there must be another way out of this room, a hidden trapdoor, door etc, so is searching for that. Now the DM asks for an Investigation check, as the character is now trying to locate something specific - they note that there is grain on the floor of the room, except for the Southern corner, deducing that the only reason why someone would sweep the floor, but only sweep one corner, is to hide any tracks that might be left. Checking the floor further in that corner, there are some scratches on the wooden floor in an arc, indicating a door opening and scraping the floor. Following that back, they locate the edge of the door.
Tl;dr - there are many circumstances where both/either check would be suitable, but it changes the way the character sets about finding something.
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Personally I think of it this way: Perception is always passive. It's used to spot or notice things without active involvement. Once someone starts active interaction with the environment it becomes Investigation.
Not agree on the Perception skill being only passive. If there an invisible monster nearby, a player can call for a Perceptioncheck to determine his position, if the result of a contest with the monster Stealth check is in your favour.
Agreed with Filcat - Perception very definitely can be (and should be) used actively.
The classic times you're actively using Perception:
There *IS* overlap between the two skills and that is ok - the way a wise & perceptive cleric looks for things is very different to the intelligent Wizard would investigate.
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Yes there is overlap somehow.
one more way to distinguish the two skills:
Perception is about feeling and intuition.
Investigation is about deduction.
Yes, Sherlock skill is a decent analogy - you can use it as a great skill to feed the players' roleplay though.
Consider the following:
A character uses Perception (either passive or active) and finds there are some tracks leading through the cellar, up to a wall. Seems they have spotted a hidden door.
The character rolls a successful investigate check and you say, "The footprint tracks are boots and left with a clay-based mud."
Player, "Has it rained recently?"
GM, "Not since yesterday morning, so the ground is mostly dry"
Player (looking over the map of the village), "Oh, there's a village pond and a small stream, so we have a clue whereabouts in the village they came from .... let's go check those areas for boot prints...."
It's up to the DM to compliment the play-style of the players - if they love solving puzzles, then feed them clues via various skills. If they don't really like solving puzzles, then allow the skill checks to give them the answer.
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Investigation is still useful in intrigue-based games or during puzzles. Keep in mind that the player may be playing someone with an Intelligence of, say, 15+ even if they aren't all that smart themselves. Denying them the ability to apply their character's smarts by denying Investigation rolls (saying "you should roleplay the deduction instead") is doing such players a disservice. I see a use for both roleplay as well as making a roll, no matter what the skill being rolled is. I think Stormknight gave a good example of how you can roll Investigation and still enable players to think on their own as well. You don't always have to give out the answer with a successful roll, maybe it just reveals a clue or two instead.
Perception is a much more broad skill, however, covering both just noticing things passively as you're going by, or actively searching for things using your senses.
Perception is detection.
Investigation is understanding the nature or purpose of something.
I think the easy way to view the difference is that a Perception check comes into play when you are quickly glancing at something and lack the time to investigate it further. In other words if you aren't going to be spending 10 min. or so on the activity it probably requires a perception check. If you can spend a good amount of time on the activity then Investigation becomes more accurate.
The key is that Perception is used when you can't make deductions and wisdom is more appropriate. Investigation is more important when you can make logical deductions. So they aren't really interchangeable, though they may overlap.
So you could have a Perception check to determine if you see the Wizards secret door (maybe DC 20?) while the Investigation check to see if you can locate the door might be (DC 15) if you are actively searching for it and looking for clues.
I would say investigation can not be used in combat as it would require longer than 6 seconds, and so in combat perception is the more appropriate activity.
Part of how I look at Perception, Investigation, and Insight a bit as a balancing component.
In 3.5 editions there was just Spot (Wis) and Sense Motive (Wis).
Now we have Perception (Wis), Investigation (Int), and Insight (Wis).
To me the idea is to open up more way for players to solve puzzles. Any particular player is only going to have so may skills (2 for backgrounds, 2-4 for class, 0-2 for race) out of 18 possible skills. To me Investigation was an attempt to give high Int players a possible way to solve such problems through deductive reasoning.
Especially, if your description allow for players to build upon each other. I'm personally a fan giving players clues based on their states without necessarily having to roll if it's a plot critical.
Lets say a Wizard, Rogue, and a Ranger are chasing after an NPC, down alleys and suddenly he disappears and the PCs lose sight of him. Now, I as the GM want the PCs to follow the NPC's trail, but I want this to be a chase so time is of the essence.
I might tell the Rogue and Ranger they are *sure* (high Wis and Perception trained) they heard a door slam before they lost track of the NPC, but they don't know which building. I might prompt the Ranger to roll Survival, if she does well then I'd say "you notice fresh grooves in mud under a particular door." If she rolls poorly, I'll tell her that "there is a lot of foot traffic, it's taking you a while to figure out who's prints are who's, but there is fresh grooves in the mud under a particular door" (They still solve the puzzle, but the NPC has a bigger lead).
Now they have entered a room of the building, but it's a dead end and the NPC isn't anywhere to be found. Maybe the rogue rolls well on perception and notices (sees it or feel a breeze) the hidden door, but hasn't found the mechanism yet. I might give the Wizard (who has Investigation) a roll to solve that to open the hidden door, obviously they need to turn the wall sconce! If he Rogue also has Investigation maybe she solves it by using her Thieves Tools to unlock the mechanism, sliding a peice of metal into the crack.
I guess I see it as a way to reward players in different ways. Instead of just making having a good Wisdom and training in Perception & Insight the uber stats.
I would agree with filcat and FullMetalBunny. Perception is Wisdom based, Investigation is Intelligence based. Especially about the skill checks being basically a short-cut for actual character actions. Using the character roles is a general assumption about how smart or perceptive the character is. Instead of having a player tell you that they are searching for a secret bottom in a drawer, they can roll an investigation check and it's assumed that they think to look for that. With perception, because the player isn't physically there to hear a person sneaking around a room, the check is a short cut to determine whether they're paying attention for it. I always treated 'passive perception' as a metric of how oblivious a character is. A high passive means a person's always alert, a low passive means they aren't. However just because a person's paying attention to their surroundings doesn't mean they would think to search a bookshelf for secret doorway for example. But if the player specifically asks so search all the bookshelves then a check may not be needed.
Since a lot of people bring up hidden/secret doors and traps, I want to point out that it very clearly says in the Player's Basic Rules, under "Using Ability Scores > Ability Checks > Perception"
So the basic rules say Perception is used to spot hidden doors or traps.
However, a player/class that is stronger at Investigation than they are at Perception, could likely use Investigation to deduce where a trap or secret door would be placed, if one existed (as opposed to just flat out spotting it). And then roll Investigation to see if they are right. So in game, both could work, as different classes would use their different strengths to accomplish the same thing (when it's appropriate).
There seems to be a bit of a misunderstanding about the meaning of "passive" in the context of skill checks.
Passive is NOT something that is always on or that happens when the character isn't doing anything.Passive has NOTHING to do with the actions of the character. Passive has only one meaning in the context of the D&D 5e rules ... the player does NOT roll dice. That's it. Unfortunately, a lot of people read passive and immediately assume it has something to do with the character.
PHB pg 175
PASSIVE CHECKS
A passive check is a special kind of ability check that doesn't involve any die rolls. Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster.
Passive checks can be used to find secret doors or other items but ONLY if the character is actually doing something that would allow them to find the secret door. If they are searching for example or paying attention to their surroundings (which almost everyone does when traveling or in a dungeon) then a passive check could be used to discover or observe whatever is hidden.
This is emphasized in the traveling rules PHB 182 and 183
NOTICING THREATS
Use the passive Wisdom (Perception) scores of the characters to determine whether anyone in the group notices a hidden threat.
OTHER ACTIVITIES
Characters who turn their attention to other tasks as the group travels are not focused on watching for danger. These characters don't contribute their passive Wisdom (Perception) scores to the group's chance of noticing hidden threats.
So ... if you aren't watching you don't get to use passive perception to discover threats.
This approach is used in the adventures built for 5e. From Lost Mines of Phandelver p7. (small spoiler)
"Snare. About 10 minutes after heading down the trail, a party on the path encounters a hidden snare. If the characters are searching for traps, the character in the lead spots the trap automatically if his or her passive Wisdom (Perception) score is 12 or higher. Otherwise, the character must succeed on a DC 12 Wisdom (Perception) check to notice the trap."
If the party is ACTIVELY searching for traps then their PASSIVE perception can be used to find the trap. If they aren't searching OR if their passive perception is too low they make an ACTIVE check by rolling the dice. The characters have to be taking an appropriate action in order for their passive score to be used.
----------------
As for the difference between perception and investigation, these are also pretty well defined in the PHB.
PHB p178
Investigation. When you look around for clues and make deductions based on those clues, you make an Intelligence (Investigation) check.
Perception. Your Wisdom (Perception) check lets you spot, hear, or otherwise detect the presence of something. It measures your general awareness of your surroundings and the keenness of your senses.
Perception is the ability to SENSE your environment while Investigation is the ability to DEDUCE or figure out something based on what has been perceived.
For example, finding a secret door might be a perception check (which is the check outlined in the PHB) but figuring it out how to open it could be an Investigation check (or deducing the presence based on the draft in the room ... or some other observation). Either or both of these could use a PASSIVE check in which the player doesn't roll dice. "Such a check can represent the average result for a task done repeatedly" ... if the character has sufficient time to thoroughly search a room then first making a passive check to see if that succeeds make sense since a passive check represents the AVERAGE result.
------------------
Finally, passive checks can be used for any check that the DM wishes and they make sense for any situation where
1) There is sufficient time for the character to try repeatedly
2) The action taken has no significant consequences.
For example, if a character is looking through books to do magical research to find magical information for a quest with a DC15 then a passive check against arcana might be in order before anyone rolls dice. This has several advantages. It stops everyone in the party from rolling and wasting time. It also means that the wizard with 16 int and proficiency in arcana is more likely to find the clue than the 8 int barbarian without proficiency and no interest in magic who happens to roll a 20. If no one has a high enough passive score then the task is up to completion by the luck of the dice. The same can apply to forcing a door open (strength check), picking a lock (thieves tools, dex check), history check or any other ability check performed when given enough time and for which failure doesn't have a consequence.
On the other hand, disarming a trap that could go off if failed would likely require a roll. Similarly, picking a lock where the lock could break might require a roll.
All of this is up to the DM, but passive checks are massively under utilized compared to the way the rules are written and the way the examples in both modules and the rule books seem to lay them out. (for example, the observant feat gives +5 to both passive perception and passive investigation ... but I have met very few DMs who use passive investigation since many seem to wonder how investigation can be passive :) ... when it isn't the investigation that is passive ... it is the player that is passive because he doesn't roll dice).
From a role playing perspective, using passive checks when appropriate gives a much smoother narration and plays to the strengths of the characters. If the DC is low enough then the ones who are proficient in the skill with good relevant attribute are the ones who are more likely to notice or make the connection. From a player perspective, the player would never know that there was a task requiring a check, they just hear the narrated result that their character discovered something or figured something out (assuming that they were taking an action that would allow an application of the skill check).
tonight a player and i got into an argument over using perception vs. investigation.
the player walked into a room and asked for a perception check, his roll was too low to notice anything. Therefore he starts walking around the room asking for more perception checks.
I saw this as him searching the room for a hidden creature he assumed (as a player, not his character) was there, so after a few checks i told him he would need to make an investigation check.
He got upset because his character has a low intelligence score and tried arguing that he was trying to perceive the room, even though from his initial perception check he could perceive the whole room.
i would appreciate insight from more experienced DM's on how they would have ruled this.