Mathmuse |
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This post grew out of a side topic around the 1600th comment in the Pathfinder Second Edition Remaster Project discussion thread. Some people suggested moving the discussion to its own thread, which I started to do. But several errands yesterday and today delayed me. In the meanwhile, the side discussion was erased. I am trying to write this thread as a tutorial to avoid further controversy. And I begin with math and history because I like math and history.
When Pathfinder 1st Edition was published in 2009, it was largely based on the Open Gaming License parts of Dungeons & Dragons 3.5 but it has several improvements. And the most mathematically elegant of those improvements was exponential leveling.
Dungeons & Dragons 3rd Edition has quadratic leveling: 0 xp to start at 1st level, 1000 xp to reach 2nd level, 3000 xp for 3rd level, 6000 xp for 4th level, 10000 for 5th level, and so on, following the formula that 500n(n-1) xp would reach nth level. This meant that the gap between (n-1)st level and nth level was 1000n xp, a linear progression. Matching this, earning a new level progresses linearly, too. A 1st-level party defeating a CR 1 monster earns 75 xp, a 2nd-level party defeating a 2nd-level monster earns 150 xp, a 3rd-level party defeating a CR 3 monster earns 225 xp, a 4th-level party defeating a CR 4 monster earns 300 xp, etc. Or the 1st-level party could face one CR 1 monster for 75 xp, a 2nd-level party could face two CR 1 monsters for 150 xp, a 3rd-level party could face three CR 1 monsters for 225 xp, and a 4th-level party could face four CR 1 monsters for 300 xp.
Alas, the difference between a 6th-level party fighting six CR 1 wolves or seven CR 1 wolves does not feel significant. Because it isn't significant, it is only a 16% difference in difficulty. Encounter design did not have to care about the difference. At higher levels, the percentage difference between consecutive Challenge Ratings got smaller. And since the challenges did not grow much, Dungeons & Dragons did not have to offer much to new levels. Dungeons & Dragons 3.5 character classes have a few levels in which no new special features were added and only a tiny set of bonuses improved. We call them "dead levels."
With Pathfinder's exponential leveling, each new level is 41.4% more powerful than the previous level. Therefore, every new level feels powerful. This is much more exciting! I even started a thread about it in the PF2 playtest, The Mind-Boggling Math of Exponential Leveling. 41.4% means that the next level is 141.4% as strong, the level after that is 200% as strong (because 1.414 is the square root of 2), the level after that is 282.8% as strong, and continues in exponential growth of power.
The flip side of that exponential growth in power is that the foes of the party have the same growth. A creature of level N+2 will be twice as dangerous as a creature of level N. A single creature four levels above the party's level will be as powerful as the entire party of four adventurers. This makes encounters with higher-level creatures very risky for the party. A GM with linear progression of risk can afford to be sloppy, but a GM with exponential progression of risk has to be careful to avoid a Total Party Kill.
Thus, Pathfinder 2nd Edition explains five different categories of risk in the Core Rulebook's Building Encounters section: Trivial Threat, Low Threat, Moderate Threat, Severe Threat, and Extreme Threat.
Trivial Threat means the party will win. The threat is one-quarter the power of the party or even weaker, so one party member could face the brunt of the threat and still win due to minor support from teammates.
Low Threat is stronger than a single party member but weaker than two party members. Thus, abysmal tactics or the dice acting hatefully could risk one party member being knocked unconscious. Reasonable tactics with average dice rolls will be victorious will little loss of resources. A party could face a dozen Low Threat encounters in a row and have to stop only due to eventual bad luck on the dice rolls.
Moderate Threat is half as strong as the party. The party is well favored to win, but they will take their bruises in the effort and have to spend resources such as spell slots. A GM should provide a safe opportunity to rest after one or two Moderate Threat encounters.
Severe Threat means 75% as strong as the party. This will be a tough fight. The party is still favored to win, but they will be so worn out from the fight that they can face only Low and Trivial Threats afterwards.
Extreme Threat is the mirror match where the enemy is exactly as strong as the party. If both sides use good tactics, then the dice will decide who wins.
Beyond-Extreme Threat is not an official threat category, but sometimes the enemy is stronger than the party. My players have defeated enemies this strong, but they had a method of dividing the enemy into smaller, manageable pieces. And they planned an exit strategy in case the tide of battle let the enemy regroup at full strength.
To illustrate the separation between threat catagories, let's count wolves. To a 3rd-level party, a 1st-level wolf is worth 20 xp. Two wolves at 40 xp total are a trivial threat. Three wolves at 60 xp are a low threat. Four wolves at 80 xp are a moderate threat. Six wolves at 120 xp are a severe threat. And eight wolves at 160 xp are an extreme threat. Next, consider how a classic party of fighter, cleric, rogue, and wizard would deal with three wolves. The fighter and the cleric would stand as a front line to protect the wizard and the rogue would circle around to flank. The two frontliners could prevent a Pack Attack that requires three wolves next to one target by splitting the three wolves between them. The wolves would advance and attempt a jaws attack with Knockdown, followed by another jaws attack if successful. Since the wolves have 24 hp each, the combat will last long enough for some successful knockdowns. But the fighter and cleric can get back up. The fighter and the rogue with the wizard throwing cantrips from a safe distance focus on one wolf and take it down. Then the wolves are less of a problem and they can focus on another. The frontliners will lose a few hp, but a fighter with about 30 hp is just down a little and maybe they can take 10 minutes for Treat Wounds. Add a fourth wolf, and the knockdowns become more frequent or maybe the fourth wolf bypasses the front line to harass the wizard. That makes the fight more difficult, up to moderate threat. Add a fifth and sixth wolf, and we guarantee frequent knockdowns and a wolf attacking the wizard. The wizard won't throw mere cantrips at that Moderate Threat risk. He will use 2nd-level spells. But with eight wolves, the cleric and wizard might run out of hit points before the battle is over, so two PCs will have to finish off the remaining wolves alone. Each wolf gives the pack more of an edge, though to overwhelm the party the GM has to add pairs of wolves. Remember, one pair of wolves is as strong as any single 3rd-level party member.
However, imagine that the wolves were not balanced precisely, say we had a homebrew Deepforest Wolf that was 33% stronger than a plain Wolf, but the GM mistook it for 1st-level creature regardless. Three Deepforest Wolves would be a Moderate Threat rather than a Low Threat. Four Deepforest Wolves would be between a Moderate Threat and a Severe Threat. Five Deepforest Wolves would be a Severe Threat. Six Deepforest Wolves would be an Extreme Threat rather than a Severe Threat. A series of encounters with Deepforest Wolves designed to give a fairly safe Low Threat impression of a dangerous forest would really be a gauntlet of Moderate Threat encounters that would wear down and destroy the party.
The threat system lets the GM design appropriate encounters, easy or tough as the GM chooses, that avoid Total Party Kills despite the inherent risk in exponential leveling. However, the threat system requires being able to judge the threat accurately. Fortunately, the so-called tight math in Pathfinder 2nd Edition gives such accuracy that the monster designers are not going to make a terrible 33% error. And the Building Creatures guidelines and the Building Hazards guidelines lets the GMs themselves create homebrew creatures and hazards with accurate danger ratings, too. A 1st-level creature is close (10% accuracy) to as strong as a 1st-level creature ought to be. A 2nd-level creature is 41.4% stronger than 1st level, and a 3rd-level creature is twice as strong as 1st level, accurately.
Mathmuse |
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Choosing the different threat categories--trivial threat, low threat, moderate threat, severe threat, or extreme threat--is about the GM's world-building narration and dramatic tension.
If a GM has been warning about an impressive Big Bad Evil Guy (BBEG) and the party finally reaches that villain, then the players would be disappointed if the BBEG put up a weak battle. A BBEG along with their surrounding minions ought to be a severe threat.
To handle a severe threat, the party needs to be in good shape with most of their hit points and several solid resources, such as highest-level spell slots, available. But if the BBEG has protective guards around his stronghold, then fighting past moderate-threat guards would wear down the party, reducing their hit points and resources. The PF2 ten-minute break for Treat Wounds and Refocus can restore hit points and focus points to restore readiness, but that requires being able to actually take a ten-minute break in an undisturbed location. That requires advance planning, such as, "Old Man McGregor told us of a secret room behind the kitchen fireplace. Yes, here is the fake brick that opens it." Or the guards in the inner keep have no view of the outer wall, so once the moderate-threat outer guards are dealt with, the party can rest before proceeding to the inner keep. More commonly, the party will have no good place to rest. In that case, the guard patrols ought to be mostly low threat with one moderate threat veteran patrol for spice. That will leave the party ready to handle the BBEG.
Sometimes, the current mission has no BBEG. For example, the party could be traveling along a forest road to the next city. But they encounter bandits waiting in ambush for travelers. The bandits and other one-shot encounters should be a moderate threat to feel like a real challenge. A severe-threat encounter would leave a mystery to solve--how did the bandits get so dangerous? A low-threat encounter leaves a mystery for the opposite reason--are bumbling peasants being forced into banditry? A moderate-threat encounter is the right level of challenge for game challenge's sake. Two moderate encounters with a break in between are fine, too.
Trivial threats are trivial. They are so easy that they don't feel victorious. But they are great for flavor. Perhaps the party is climbing a castle wall, but they have to worry about a sentry on patrol. They climb the wall when the sentry is elsewhere on his rounds, but the party will have to get past the sentry to reach the main rooms. The story has no reason for the sentry to be a tough battle; in fact, a quick battle where the party can defeat the sentry and run before anyone else shows up would be the most exciting. Thus, the sentry ought to be trivial threat.
Trivial threats are also good for a sample of a bigger problem elsewhere. A single wolf attacking the goats on a farm could be an alert to a bigger wolf pack in the area.
Extreme threats are threats that the party should avoid until they figure out an advantage by scouting, information gathering, and advance planning. And the advance planning should include an exit strategy in case the combat goes sour and the party has to escape. If a group of players hates to plan in advance, then avoid throwing extreme threats at them, except as the direct consequence of extreme stupidity. "Why did you stab the king! He was our employer."
Mathmuse |
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I have been extolling the virtues of accuracy in measuring the threat of an encounter by the levels of the monsters involved, but four circumstances can throw off that accuracy. GMs need to keep an eye out for these to realize that the calculations might be off. Those circumstances are luck, terrain, readiness, and tactics.
Combat in Pathfinder is ruled by dice. In the long run the effect of the dice averages out to a predictable average. But probability also allows short runs of bad rolls and good rolls, and those short runs can last through an entire encounter. Luck can change a moderate-threat encounter into a severe-threat encounter because no PCs could roll well enough to hit during the first two rounds. It could also convert a moderate-threat encounter into a low-threat encounter when the same thing happens to the enemies. The GM needs to keep in mind that their intent might be overcome by plain luck.
Terrain is a circumstance that the GM can control. Nevertheless, the GM has to factor it into the true threat category of an encounter. A blatant case is that a bunch of weak archers can overwhelm a stronger party when the archers are on a castle wall protected by Taking Cover behind battlements and the party is in an open field without cover. Or imagine a 3rd-level party walking down a 5-foot wide straight corridor and at the end of the corridor is a 5th-level enemy wizard who has prepared Lighning Bolt. Ordinarily, a wizard is lucky to hit three targets with one bolt, but the terrain here guarantees that the party will be lined up like sitting ducks. The 5th-level wizard on paper looks like a moderate threat, but on that terrain he is much more dangerous.
Readiness and tactics are similar, but a GM should know the difference. Imagine the party tracks down a goblin camp in which the goblins are busy drinking the wine that they stole from a caravan with loud hoots and hollers. The party rushes forward--and finds the goblins with all their weapons in hand and arranged in a solid defensive formation. If the GM had given the goblins a lookout who had spotted the party and the goblins had planned a counterdefense while pretending to be drunk, then that is tactics. If the goblins had been truly caught by surprise, but they were already ready for combat, that is unearned readiness by GM fiat. If the goblins are caught by surprise, let the situation show that surprise: they will be grouped for comfort by warm fires and have bottles in their hands instead of weapons. Dropping the bottles and drawing their weapons will be a free action and an action, but that will use up one action per goblin and reduce their threat for that first round. One side being ready and the other side not being ready is what makes ambushes so effective. The GM knows what is going on, but the foes that the GM runs do not, so the GM should not metagame their readiness. I often have my hostile NPCs lose an action that would be the Perception checks and Recall Knowledge checks necessary to understand what is happening.
Lack of readiness is often funny, too. In my last game session, the party entered the enemy stronghold from an unexpected direction. They opened the doors to a new room--and the room was the mess hall where some enemy soldiers had sat down for a meal. The monk rushed forward toward one of the more dangerous foes and provoked an Attack of Opportunity from a soldier eating a pie with his sword still in his scabbard. So the soldier hit the monk with the pie. The pie dealt only 2 bludgeoning damage, and the monk had to make an easy Fortitude save to avoid having his vision obscured (with a +10 circumstance bonus because he was wearing Goggles of the Night).
Tactics requires a very long explanation. I am going to take a nap before writing about it.
magnuskn |
Thank you for this thread, this is very helpful already.
Now, I haven't GM'ed Pathfinder 2nd edition yet and if things go well, I won't do it for another year at least (i.e. if the 1E Strange Aeons campaign we just started doesn't implode, given that the current GM has never GM'ed Pathfinder at all, only Shadowrun). However, I am very much looking forward to it. Hence, I have been prepping a lot over the last weeks already.
One thing which I don't really get yet that well is how the math is so tight, that just going up one or two levels on an encounter can have so severe consequences, when one level up amounts to only 10% better saves and to-hits (looking at the elite template, which add +2 to everything)?
So upping a moderate encounter into an extreme one on a single opponent is just is adding 20% on the stats on top? I get that due to the degrees of success it's more like those 20% are doubled (i.e. the +4 to hit is also an increased 20% chance to crit), but since player characters still have only to roll four higher than normal to hit their opponent, the hitpoint pool is increased by about 40 points and damage by only +4 for the opponent, it is difficult for me to process how that translates into an encounter where a TPK is 50% expected. Maybe you can make it explain this a bit, math very appreciated.
Also a topic of interest is how many moderate encounters you can trust a regular party of four to do if you plan to add a climactic severe encounter at the end, before they need to retreat and recuperate, so that they don't enter a death spiral due to depleted ressources. I presume, though, that this is a very variable equation, depending on at which level the party is at.
Unicore |
Thank you Mathmuse for starting this thread. I appreciate your thoughts here and your analysis of the math is always something I learn from. I think a lot of GMs could learn from your ideas here.
One thing I try to play with as a GM for really exciting encounters is the beyond-extreme encounter that is over a sprawlingly large map, with enemies spread out across in different locations, close enough to trigger when appropriate, but far enough away to have that be a visible factor in the party tactics. I think that one of the reasons why some tables experience "weak casters" is when durations of encounters are never longer than 3 to 5 rounds and the map is so small that the longer range of many powerful spells is an irrelevant feature of the spell. My players have responded very well to encounters that are several trivial, low and moderate encounters, with one severe hidden in there somewhere, that can be fought in waves by moving around a central courtyard or on a boat that is pulling out of dock.
NECR0G1ANT |
Do note that the encounter-building guidelines only account for 1) the number of foes and 2) their respective level(s) compared to the PCs.
It does not mathematically account for any resource expenditure such as hit points, expended spells, persistent conditions, etc. There is no explicit rule on how to adjust encounters for a party that has expended resources. Be aware of that as both a player and GM.
IME, this kind of bites full casters in the ass compared to martials, and incentivizes a twenty-minute adventuring day.
Mathmuse |
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Pathfinder 2nd Edition adventures feel very much like Pathfinder 1st Edition adventures. They have the same classes and the same monsters (though the upcoming Remastering will remove some classic D&D monsters). Many players were surprised that PF2 has different tactics.
The primary difference is the three-action system. In PF1 standing in one spot to gain a full-round action is an effective combat strategy. It enables more attacks, even though the second attack has a -5 penalty and the third attack has a -10 penalty. In contrast, PF2 allows three attacks, one per Strike action, with a -5 multiple attack penalty on the second attack and a -10 multiple attack penalty on the third attack. And all those three attacks is usually bad tactics.
Two factors cause this difference. First, ACs are lower in PF1, so a -10 penalty to a third attack still leaves a reasonable chance to hit. Second, if a PF1 fighter with base attack bonus +11 or higher uses a full-round action to make a second attack, the third attack is free. The PF2 fighter, in contrast, has to spend his third action on the 3rd attack, giving up using that third action for something else, such as Demoralize or Raise a Shield.
For a few characters three attacks make sense. The high-level Flurry-Edge ranger in my campaign makes four longbow attacks per turn. His Masterful Hunter class ability changes the third and fourth attack penalties from -10 to -4. For most martial characters, their class gives them something better than an attack with a -10 penalty.
Characters who have not yet learned how PF2 tactics work have more trouble with threat levels than expected. And on the other side of the coin, some players master PF2 tactics so well that moderate-threat encounters barely cost them any resources, severe-threat encounters simply wear them down so that they need a rest, and extreme-threat encounters regularly end in a hard-earned victory.
In addition, the enemy can use tactics, too. Goblins are typically played chaotic, without organization or tactics. Hobgoblins, in contrast, organize into militias and use tactics. So a patrol of four 1st-level Hobgoblin Soldiers will often be harder to tackle than a war band of four 1st-level Goblin Pyros.
Mathmuse |
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In the other thread, GM DarkLightHitomi had brought up Tucker's kobolds as an example where a low-level monster could threaten a mid-level party. They are a classic example of using terrain, readiness, and tactics to make an encounter much more dangerous than the standard threat calculations suggests. The story was told [i]Dragon]/i] magazine issue issue 127 in 1987, before the internet. Nowadays the story can be found on the internet, such as at DnDWiki:Tucker's kobolds. In Tucker's campaign, kobolds lived on the 1st level of a multilevel dungeon. They put up little resistance when the adventuring party entered the dungeon, mostly retreating into small tunnels. But when the party was departing after a successful raid on the deeper levels, out of their strongest spells but loaded with treasure, the kobold tribe emerged to assault the party much stronger than before. They had bolt holes to shoot the party from, giving them terrain advantage. They had set up traps--hidden and deactivated earlier but now fully activated--to hurt the party more than the kobolds' own strength of arms could. And they had attacked when the party was no longer ready.
I could recreate this using negative-1st-level PF2 PF2 Kobold Warriors. The Kobold Warrior has training, "Crafting +2 (+4 traps)," to explain how they had make traps. For appropriate traps I find Hidden Pit simple hazard 0, Spear Launcher simple hazard 2, Drowning Pit complex hazard 3, and Scythe Blades simple hazard 4. PF2's threat math breaks down if the difference between the creatures' level and the party level is more that four, so let me assume a 3rd-level party.
To force the party to cross the traps, make a long corridor with two Hidden Pits (3xp each), Spear Launcher (6xp), Drowning Pit (40xp), and Scythe Blades (12xp). The hazard rules give the same xp for a complex hazard as for a creature of the same level, but simple hazards have one fifth the xp. That sums to 64 xp. Then throw in six Kobold Warriors (10 xp each) to make a total of 121 xp. If we viewed each trap and the group of kobolds as each an isolated encounter, then we would have four Trivial encounters and one Low-Threat encounter. But the kobolds will use tactics that merge them all into one 124xp encounter.
Ordinarily, 124xp would be a Severe Threat. However, as NECR0G1ANT pointed out,
Do note that the encounter-building guidelines only account for 1) the number of foes and 2) their respective level(s) compared to the PCs.
It does not mathematically account for any resource expenditure such as hit points, expended spells, persistent conditions, etc. There is no explicit rule on how to adjust encounters for a party that has expended resources. Be aware of that as both a player and GM.
IME, this kind of bites full casters in the ass compared to martials, and incentivizes a twenty-minute adventuring day.
The spellcasters have used up their best spells. PF2 casters are more resilient with cantrips and focus spells; nevertheless, we can assume that the offensive spellcaster in the party, say a wizard, is down to nothing but cantrips and focus spells. Likewise, the cleric has used up all his healing spells. I view this as a readiness issue. The party is not ready for a Severe threat. With the wizard and cleric at half effectiveness, the party will function more like a three-member party than a four-member party. And a 124xp challenge is an Exreme Threat to a three-member party.
Let's me run this encounter. The rogue with Trap Sense detects both Hidden Pits, their Stealth DC is only 18. So the party members Leap over them. The Stealth DC of Spear Launcher is 20, so let me pretend that they trigger that one. The spear hits the fighter with AC 20 on a roll of 6 or higher. Then four kobolds spring out of their boltholes behind the party, separated from them by the Hidden Pits that the party already leapt over. They attack with sling stones, Ranged sling +5 (propulsive, range increment 50 feet, reload 1), Damage 1d4 bludgeoning. The damage is pathetic, but it does hurt. The party leaps back over the Hidden Pits to try to confront the kobolds, but the pair of leaps gives the kobolds time to crawl back into their boltholes. And then they see a fifth kobold reloading the Spear Launcher! They rush toward him, scaring him back into his bolthole before he finishes resetting the Spear Launcher. The party takes the time to smash the Spear Launcher, but the four kobolds return to pelt them with stones again while they do so.
The party proceeds, making Seek checks to look for more traps, so they are not moving at full speed. The fighter, instead of Seeking, has pulled out his shortbow and pierced two kobolds badly enough that they retreated out of sight permanently, one dragged away unconscious. Since they are being careful, they spot the Drowning Pit and Leap over it instead of falling over it. And they spot the Scythe Blades, but the rogue fumbles his attempt to disarm it and gets hit by a blade for 2d12+4 slashing damage, rolled as 14 damage. A hidden sixth kobold shoots an arrow at the rogue, finally dealing enough damage to knock him out. The cleric stabilizes him and the wizard angrily throws a focus spell at that kobold, killing the enemy. But now the party has an unconscious rogue to carry.
Time for an exit strategy. The players don't know whether any more traps lie ahead. The kobolds slinging stones yell, "Drop your treasure into a pit and we will turn off the traps and let you live." The party obliges with tossing the rogue's bag of treasure, one quarter of their loot, into the Drowning Pit. Both sides stop attacking and the party limps away carrying the rogue. They survive, but they have been humbled by Kobold Warriors, creature -1.
Mathmuse |
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One thing which I don't really get yet that well is how the math is so tight, that just going up one or two levels on an encounter can have so severe consequences, when one level up amounts to only 10% better saves and to-hits (looking at the elite template, which add +2 to everything)?
So upping a moderate encounter into an extreme one on a single opponent is just is adding 20% on the stats on top? I get that due to the degrees of success it's more like those 20% are doubled (i.e. the +4 to hit is also an increased 20% chance to crit), but since player characters still have only to roll four higher than normal to hit their opponent, the hitpoint pool is increased by about 40 points and damage by only +4 for the opponent, it is difficult for me to process how that translates into an encounter where a TPK is 50% expected. Maybe you can make it explain this a bit, math very appreciated.
My mathematics tells me that a +1 to an attack bonus is about a 14% improvement. Suppose that a Strike has a 60% chance of hitting. That breaks down to 50% chance of a regular hit and a 10% chance of a critical hit. I view a critical hit as equivalent to two regular hits, since it deals double damage, so I see those 0.5 regular hits + 0.1 critical hits = 0.7 hits. With a +1 increase, that changes to 0.5 regular hits + 0.15 critical hits = 0.8 hits. 0.8/0.7 = 1.14, so it is a 14% improvement.
The +1 to AC is equivalent, a 14% improvement to survivability. The extra hit points are hard to describe as a percentage, since they vary from a 50% improvement at 2nd level to a 5% improvement at 20th level, so let's call it a 10% improvement. All three are aiding the character at the same time, so the combined effect is (1.14)(1.14)(1.10) = 1.43, a 43% improvement.
The improvement to saving throws is not multiplied in. Instead, when a martial character makes a save against a damaging spell, saving throw replaces the AC in the formula (1.14)(1.14)(1.10) = 1.43, because saving throw is substituting for AC in the protective role. It says the improvement is still 43%.
We can also factor in class features, feats, ability score bonuses, and improved gear to show that the increase in power by leveling up is actually higher than 43%. How do I reconcile this with saying that the character gets 41.4% stronger with a level up? The answer is that I am measuring the wrong scale.
The xp value of creatures improves 41.4% per level. But xp does not truly measure danger. Consider the difference between a 40xp encounter and an 80xp encounter, for example, a 3rd-level party fighting four Goblin Warriors, creature -1, versus fighting eight Goblin Warriors. If we simplify the combat down to every party member fighting one goblin independently in the first case and two goblins in the second case, the second case takes three times as much damage as the first case. This is because for the first half of the battle, the PC is taking damage from two goblins. The PC kills one, and then has a full battle against the one remaining goblin. 2 + 1 = 3.
And that is for an oversimplified view of combat. In real gameplay, one party member wades right into the goblins, relying on high AC and a raised shield and another one hangs back, throwing spells from a safe distance and possibly targeting multiple goblins with each spell. Modeling all the complexities of combat would also require different models for different party compositions and against different kinds of monsters. I would be essentially playtesting multiple combats to see how the numbers work out. And that is what Paizo did. Two monsters of level N test to be about as dangerous as one monster of level N+2. That is the only fact necessary to make the math of exponential leveling work.
Mathmuse |
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Also a topic of interest is how many moderate encounters you can trust a regular party of four to do if you plan to add a climactic severe encounter at the end, before they need to retreat and recuperate, so that they don't enter a death spiral due to depleted ressources. I presume, though, that this is a very variable equation, depending on at which level the party is at.
It actually depends on the party's playing style, and the party's playing style depends on the GM's encounter building style. In general, if a party is good at losing mostly renewable reasources, such as focus spells and hit points, during moderate-threat encounters, then designing opportunities for renewal with Refocus and Treat Wounds means that they can handle about ten moderate-threat encounters. If the party instead consumes valuable daily resources, such as highest spell slots and once-per-day Battle Medicine, during moderate-threat encounters, then they can handle about one moderate-threat encounter before the final boss battle.
I did not figure out encounter balance on my own. I learned it by watching how my players dealt with encounters. And players are complicated.
Right now in my PF2-converted Vault of the Onyx Citadel module, the party is storming the Onyx Citadel with a Low Threat or Moderate Threat in every room. The 19th-level druid is throwing Fireball and Chain Lightning frequently against the troops, some of those spells heightened. But those are her spells for dealing with lower-level troops. She is saving her strongest spells for the upcoming boss battles. And the party is going for speed, because if they pause, then the troops from other rooms will unite into Extreme-Threat encounters. Therefore, the druid is burning herself out early so that the rest of the party will be in good shape to confront the final boss. It is elegant teamwork, but it prevents me from generalizing basic principles of resource consevation from their battles.
Ascalaphus |
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It's my experience that the encounter building guidelines try to compress a complex problem down to a simpler one. You have the individual power of each enemy, which you're trying to sum up to a single quantity that you can compare to the PCs. The method, just add the value of each enemy, is simple and practical to use.
But it does make a major assumption: that the whole is exactly equal to the sum of the parts. That there's no significant synergy or anti-synergy between the enemies in the encounter.
Also, there's a kind of linearity assumption: 16 X-4 creatures are assumed to be equally threatening as 8 X-2 creatures, 4 level X creatures, 2 X+2 creatures or 1 X+4 creature. They do kinda tell you that going beyond +/-4 is getting ridiculous. But I think the linearity breaks down earlier than that.
So, I think the encounter design system is a pretty good model for guesstimating the actual difficulty of an encounter when you're close to the middle of the table, but I think it breaks down more and more towards the top and bottom.
16 L-4 creatures are on paper just as hard as a single L+4 creature. In practice I think nobody feels that's true. Almost all the time, the L-4s are quickly roasted by some area effect while they have difficulty even hitting the PCs. While the L+4 might have such strong defenses that the PCs struggle to land any hits; that the creature tends to crit save against attempts to debuff it; and that it's own attacks put PCs out of the fight so quickly that the party quickly collapses.
Also, the model doesn't seem to be quite as accurate at each level. On paper, an 80XP encounter is Moderate no matter what level the PCs are. In practice, a level 1 party finds a Moderate encounter to be pretty spicy, while a level 18 party might not spend any real resources on it. And this is actually in the game by design; the GM advise sections tell you that you need harder encounters to really challenge high level parties. Because actually the PCs get comparatively more powerful compared to enemies of the same relative level. (In numbers, barely, and in having just the right option for the situation, a lot.)
Another place where the 16/4/1 thing breaks down is when the mooks do more than just single target melee attacks. Suberbidi gives an example of how a lot of mooks with just the right area attacks can do disproportionate damage. I've also run into this in a PFS scenario where due to the party size, we fought against a LOT of enemies that caused Frightened and cast Paranoia. Although individually we could handle them okay, they just cast it so many times that eventually the champion succumbed. The champion no longer treating us as allies meant that he couldn't use his reaction to protect us, which became a big difference in how hard the encounter was.
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My point in this is: encounter design is still an art more than a science. The tables are extremely useful, just like someone going to art school is going to learn techniques like how to draw realistic perspective or how to mix paint. But not many people become great artists just by reading their handbook at art school.
The guidelines in the book are a model for difficulty. The model is very useful, but all models contain less information than the real thing they're modeling.
GM DarkLightHitomi |
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The two frontliners could prevent a Pack Attack that requires three wolves next to one target by splitting the three wolves between them. The wolves would advance and attempt a jaws attack with Knockdown, followed by another jaws attack if successful.
Why would wolves ever attack like this? They wouldn't. Neither if basing tactics on slim knowledge of real wolf tactics nor on just logical tactics based on the wolves' goals.
Wolves won't be attacking seeking a tpk, nor will they be acting like idiot bots in an mmo.
The wolves are going to attack for either, desperate hunger, to defend territory, or feeling cornered/defending pups.
If hungry, they aren't going to go for the whole party, they'll harrass and provoke until they can get a chance to isolate one member (by pack members hiding if possible) then trip and drag off the one member, likely expecting the rest of the group to leave. If pressed too hard, they'll retreat, and that would probably happen after the first or second solid hit the party gets on any of the wolves.
Otherwise, they'll be defensive, trying to scare away the intruders, not kill them. Not even tripping because a tripped opponent can't run away.
And if pushed so far they have nowhere to run, they'll be fighting to escape unless they can't see a way out or have pups they are defending.
This fight you described with wolves is completely ridiculous as anything but a cosmetically altered mmo fight. It completely ignores the wolves' reason for being in the fight and how that impacts tactics and decision making for them.
GM DarkLightHitomi |
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Thank you Mathmuse for starting this thread. I appreciate your thoughts here and your analysis of the math is always something I learn from. I think a lot of GMs could learn from your ideas here.
One thing I try to play with as a GM for really exciting encounters is the beyond-extreme encounter that is over a sprawlingly large map, with enemies spread out across in different locations, close enough to trigger when appropriate, but far enough away to have that be a visible factor in the party tactics. I think that one of the reasons why some tables experience "weak casters" is when durations of encounters are never longer than 3 to 5 rounds and the map is so small that the longer range of many powerful spells is an irrelevant feature of the spell. My players have responded very well to encounters that are several trivial, low and moderate encounters, with one severe hidden in there somewhere, that can be fought in waves by moving around a central courtyard or on a boat that is pulling out of dock.
In the old days, encounters started when opponents were sighted, or understood to be enemies, which could happen at hundreds of feet away. There would be the question of how to approach an enemy. Archers and mages could be attacking multiple rounds before the martials ever get close enough to attack.
Further, in the older days, you could not assume hostility unless clearly marked as an enemy faction currently at war. Even bands of savages aren't always out to slaughter everything. Sometimes you could just evade the enemy instead, either because they didn't notice you or they let you avoid contact.
GM DarkLightHitomi |
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"Tucker's Kobolds" ... They put up little resistance when the adventuring party entered the dungeon, mostly retreating into small tunnels. But when the party was departing after a successful raid on the deeper levels, out of their strongest spells but loaded with treasure, the kobold tribe emerged to assault the party much stronger than before.
This is incorrect. It was on the way into the dungeon. They escaped down to level 10 (much less scary), and they dreaded when it would be time to leave. So they were facing the kobolds full and fresh.
Of course, spell limits mattered more back then. For example, the wizard could not cast fireball because in the tight confines the area affected would spread further and hit the party too.
GM DarkLightHitomi |
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Fun idea, run a special campaign in which each player gets twelve standard npc characters and a party of four pcs. Then have them face off tourny style, npcs vs pcs. Do it repeatedly with difficulty kinds of npc races. Let the players get creative in tactics and consumables use.
Npcs live in a world of magic, I think it's only logical to assume that even goblins would learn to avoid being bunched up for a fireball when it can be avoided. Doing this exercise will help everyone develop better tactics, and the gm can include more sensible tactics that account for the quirks of the world.
That said, doing this should stick to the levels commonly found in the world. 9th level spells are basically legendary and thus no warriors have significant experience facing such magic and so unlikely to gave tactics adapted to them.
magnuskn |
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So, what I'm understanding so far is that despite the encounter system being far more accurate than it was in 1E, encounters of the same nominal difficulty are still likely to be harder at low levels and easier at high levels. However, since the math is tighter (no more bonus stacking to an absurd degree, for example), this is much easier remedied than in 1E, where at a certain point a GM could only put fantasy numbers on the enemies to remotely challenge a well-built party and it still wouldn't work out too well. Adding an Elite template to one or two enemies in a moderate encounter should probably make it feel more like a challenging moderate encounter if the party is doing too well at high levels, correct?
And many thanks to Mathmuse for mathing out encounter statistics. It still went mostly over my head, I fear, but it makes a bit more sense now than before. ^^
The Raven Black |
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Unicore wrote:Thank you Mathmuse for starting this thread. I appreciate your thoughts here and your analysis of the math is always something I learn from. I think a lot of GMs could learn from your ideas here.
One thing I try to play with as a GM for really exciting encounters is the beyond-extreme encounter that is over a sprawlingly large map, with enemies spread out across in different locations, close enough to trigger when appropriate, but far enough away to have that be a visible factor in the party tactics. I think that one of the reasons why some tables experience "weak casters" is when durations of encounters are never longer than 3 to 5 rounds and the map is so small that the longer range of many powerful spells is an irrelevant feature of the spell. My players have responded very well to encounters that are several trivial, low and moderate encounters, with one severe hidden in there somewhere, that can be fought in waves by moving around a central courtyard or on a boat that is pulling out of dock.
In the old days, encounters started when opponents were sighted, or understood to be enemies, which could happen at hundreds of feet away. There would be the question of how to approach an enemy. Archers and mages could be attacking multiple rounds before the martials ever get close enough to attack.
Further, in the older days, you could not assume hostility unless clearly marked as an enemy faction currently at war. Even bands of savages aren't always out to slaughter everything. Sometimes you could just evade the enemy instead, either because they didn't notice you or they let you avoid contact.
All of this holds as true now as it did "in the older days".
Unicore |
One thing I have noticed is that the effect of critical hits on the game changes from low level to high level. PCs end up at high level with all kinds of crit riders and extra damage on crits that ends up doing way more than half damage. The party also gets more access to buffs and debuffed that shift accuracy by a bigger margin than at lower levels, meaning that they have more ways to shift the math and a bigger effect for having done so.
In my experience this is what stretches things out at higher levels the most and is why more enemies instead of stronger enemies is a bigger challenge at higher level than lower level. Party tactics designed for fighting one enemy at early level can trivialize solo bosses at higher level, but using them against multiple foes can make encounters much more severe. Tanking, for example, against multiple foes becomes a much worse idea than kiting and battlefield control against 8 enemies.
SuperBidi |
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Also, the model doesn't seem to be quite as accurate at each level. On paper, an 80XP encounter is Moderate no matter what level the PCs are. In practice, a level 1 party finds a Moderate encounter to be pretty spicy, while a level 18 party might not spend any real resources on it.
I disagree on that. There are differences in the game dynamic between low and high level but it's not as simple as saying that low level fights are harder than high level fights.
Lower level fights are more swingy. That's certainly the biggest difference: A few high or low rolls turn any fight into a nightmare or a breeze. That's why it's more dangerous to put hard fights at low level as a bit of bad luck turn them into TPKs.
And the biggest difference is that level difference is more impactful at low level than at higher level. A level +2 creature is stronger at low level than a level +2 creature at higher level but at the same time a level -2 creature is much easier at low level than it is at high level. That's why everyone discourages fights against level +2 and +3 creature at low level.
There's a last difference: Party synergies are bigger at high level than at low level, due to the sheer number of abilities. So a well organized party can end up stronger at higher level when a badly organized party will suffer more at higher level.
My experience, that may not be everyone's, is that the game is the easiest at mid level. At low level, it's swingy and some characters may not be fully functional yet, creating bigger differences in party efficiency. At high level, a few failed saves can turn any fight into a nightmare considering how awful the effects of spells/abilities are. At mid level, the game is quite solid in every way, making it overall quite easy (well, easier, as PF2 is hardly easy).
One thing which I don't really get yet that well is how the math is so tight, that just going up one or two levels on an encounter can have so severe consequences, when one level up amounts to only 10% better saves and to-hits (looking at the elite template, which add +2 to everything)?
I've personally used the encounter guidelines a lot (and Elite/Weak templates, and creature building guidelines, too). They are extremely solid. I've faced/created a few problematic situations, but honestly you can apply them blindly, and should if you're not used to the game too much.
dirtypool |
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Why would wolves ever attack like this? They wouldn't. Neither if basing tactics on slim knowledge of real wolf tactics nor on just logical tactics based on the wolves' goals.
Firstly, because this is a game and the Pack Attack is one of their pre-statted actions that appears in their Bestiary entry.
Secondly, because surrounding opponents is a documented tactic of real life wolf packs.
thejeff |
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Unicore wrote:Thank you Mathmuse for starting this thread. I appreciate your thoughts here and your analysis of the math is always something I learn from. I think a lot of GMs could learn from your ideas here.
One thing I try to play with as a GM for really exciting encounters is the beyond-extreme encounter that is over a sprawlingly large map, with enemies spread out across in different locations, close enough to trigger when appropriate, but far enough away to have that be a visible factor in the party tactics. I think that one of the reasons why some tables experience "weak casters" is when durations of encounters are never longer than 3 to 5 rounds and the map is so small that the longer range of many powerful spells is an irrelevant feature of the spell. My players have responded very well to encounters that are several trivial, low and moderate encounters, with one severe hidden in there somewhere, that can be fought in waves by moving around a central courtyard or on a boat that is pulling out of dock.
In the old days, encounters started when opponents were sighted, or understood to be enemies, which could happen at hundreds of feet away. There would be the question of how to approach an enemy. Archers and mages could be attacking multiple rounds before the martials ever get close enough to attack.
Further, in the older days, you could not assume hostility unless clearly marked as an enemy faction currently at war. Even bands of savages aren't always out to slaughter everything. Sometimes you could just evade the enemy instead, either because they didn't notice you or they let you avoid contact.
The olden days were full of "you open the door to this room in the dungeon and the monster inside attacks".
Sure, sometimes you could spot enemies outside from long distance, but it was hardly the common rule. And "clearly marked as an enemy faction currently at war" has nothing to do with anything from the olden days. Olden gaming was about exploring dangerous places in search of loot.If anything, modern gamers are far likely to treat the little green creatures living in the dungeons as people rather than sacks of hp that might have gold.
thejeff |
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Sometimes, the current mission has no BBEG. For example, the party could be traveling along a forest road to the next city. But they encounter bandits waiting in ambush for travelers. The bandits and other one-shot encounters should be a moderate threat to feel like a real challenge. A severe-threat encounter would leave a mystery to solve--how did the bandits get so dangerous? A low-threat encounter leaves a mystery for the opposite reason--are bumbling peasants being forced into banditry? A moderate-threat encounter is the right level of challenge for game challenge's sake. Two moderate encounters with a break in between are fine, too.
The mechanics make sense, but doesn't the mystery depend on the level of the party? Why the assumption that the party is just the right level for a moderate encounter to be appropriate for the area?
Bandits should be tough enough to be a severe threat to average travelers on the road. If the PCs are low level and people only travel this route in large well armed groups, that could be even worse for the PCs. If the PCs are high level, even a low threat encounter could be well above "bumbling peasants".
Unless traveling in exceptionally dangerous places, high level PCs probably shouldn't face random encounters or just handle them narratively. Assume most area appropriate creatures avoid the obvious threat of the party or just describe them thwarting the attack without risk.
And that would include "Tucker's kobolds" type situations. If they're clever enough to pose a threat, then play it out, but that also means that the route is highly dangerous, even if it's theoretically weak creatures. Not a case where normal travellers pass without problems, but the PCs get slaughtered.
Castilliano |
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GM DarkLightHitomi wrote:All of this holds as true now as it did "in the older days".Unicore wrote:Thank you Mathmuse for starting this thread. I appreciate your thoughts here and your analysis of the math is always something I learn from. I think a lot of GMs could learn from your ideas here.
One thing I try to play with as a GM for really exciting encounters is the beyond-extreme encounter that is over a sprawlingly large map, with enemies spread out across in different locations, close enough to trigger when appropriate, but far enough away to have that be a visible factor in the party tactics. I think that one of the reasons why some tables experience "weak casters" is when durations of encounters are never longer than 3 to 5 rounds and the map is so small that the longer range of many powerful spells is an irrelevant feature of the spell. My players have responded very well to encounters that are several trivial, low and moderate encounters, with one severe hidden in there somewhere, that can be fought in waves by moving around a central courtyard or on a boat that is pulling out of dock.
In the old days, encounters started when opponents were sighted, or understood to be enemies, which could happen at hundreds of feet away. There would be the question of how to approach an enemy. Archers and mages could be attacking multiple rounds before the martials ever get close enough to attack.
Further, in the older days, you could not assume hostility unless clearly marked as an enemy faction currently at war. Even bands of savages aren't always out to slaughter everything. Sometimes you could just evade the enemy instead, either because they didn't notice you or they let you avoid contact.
Yeah, I agree. There's nothing about PF2's better tuned challenge system that delineates how one must GM. If anything, PF2 makes it easier for the GM to whatever option they're aiming for. And if talking about published adventures, thejeff rightly points out how "the olden days" had subpar encounters. No edition has a monopoly on superior encounter design in their published adventures, but PF2 does have a leg up on superior encounter design tools.
And I'm talking as a GM whose personal campaigns have a broader, war-like scope where you don't go fight "the dragon you just heard about" simply because it must therefore be level-appropriate...because it's not. If you've heard about it, in a major city full of more powerful NPCs, then it's likely famous yet alive for a reason. And that's an actual "encounters must be balanced for PCs, right?" example from a player from 3.0, so it's not like PF2's tuning spawned such notions of game balance. Nor does PF2 require balance. And since 3.X/PF1 encounters were generally swifter, I'd say PF2 gives more leeway for PCs to escape when outmatched.
Complaining about PF2's game balance is like complaining about a finely tuned musical instrument. Just because one can play popular genres with it doesn't prevent another musician from riffing some jazz, scat, or whatever freeform style one prefers.
Unicore |
A hack I use when designing smallish dungeons designed to probably result in one collapsing wave encounter that will take 12 to 14 rounds of combat and end up being around 250 to 350 xp (although one time I hit 400 with a small story award for having a puzzle to unravel in the middle of it all), is to have a couple of the minions that I switch up tokens or minis for and will give the elite template plus one skill or ability that is visually broadcast and a part of describing them as they enter the room. So the end up being level -1 or -2 instead of level -3ish and will have a chain for tripping instead of a scimitar. I find this a fun way to keep “lots of enemies” from getting stale, but also keeping my mental load as GM manageable as they really are the same enemy with just a very minor tweak.
Another fun twist to having a bag full of minions to toss around a large map encounter is to have the one or two of them that don’t really want to be there and who are more than happy to abscond with some loot at a point where they think they can get away with it. I will often keep this in my bag of tricks for the “party raid” type dungeon where I know that the players could seriously get themselves in over their head if the push in to far after raising the alarm, and I might need a reason to lighten the encounter load if things really start going badly for the party. I find both players and the boss enemy will suddenly both not want to let the thieves get away and it can really dynamically flip the script on the encounter. There are a lot of ways to vary this up too, but it is very faction/creature dependent and not something to over use. But it is usually much more interesting than a TPK. Doing it once can also get PCs thinking about ways to engage in encounters other than just rushing into combat., and create fun opportunities for splitting the enemy up, creating future problems and antagonists to return later and even be a way to lead PCs to a secret door they missed or to a room they overlooked earlier.
thejeff |
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In the other thread, GM DarkLightHitomi had brought up Tucker's kobolds as an example where a low-level monster could threaten a mid-level party. They are a classic example of using terrain, readiness, and tactics to make an encounter much more dangerous than the standard threat calculations suggests.
They survive, but they have been humbled by Kobold Warriors, creature -1.
Or really they've been humbled by some level appropriate traps. With just terrain and tactics, it's a lot harder to make even clever weak enemies nearly that effective. And I think the original version was using even stronger traps/hazards.
What I'd argue they really did was to expose a flaw in old school D&D (or in a particular mindset?) that didn't account for the dangers of such traps in considering balance. When 3rd edition introduced CR as a way of calculating encounter balance, flawed as it was it at least tried to account for such things. Once you see that the encounter math turns the "weak kobolds" into a severe or beyond encounter, it no longer looks like the GM was just playing them smart and beating the PCs with weak enemies.
There may still be something of a flaw in that non-hazard terrain elements can boost the threat of an encounter in ways that aren't really accounted for in the CR system, but exploiting that to boost the difficulty of an encounter without treating it as a harder encounter is a GM problem. If you want to have the kobolds attacking through slits and murder holes in tunnels the PCs don't fit in, that can be an interesting and fun challenge, but don't pretend that it's just the same difficulty as fighting them in the open.
breithauptclan |
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One thing which I don't really get yet that well is how the math is so tight, that just going up one or two levels on an encounter can have so severe consequences, when one level up amounts to only 10% better saves and to-hits (looking at the elite template, which add +2 to everything)?
I only have actual play experience at reasonably low levels - up to level 7. It seems that the experience may change at higher levels, but only slightly - if I am reading the comments from the others in this thread correctly.
But disclaimer out of the way, how I think about this is that level is the big knob. It is like the master volume control on a sound board. And it only has a few discrete values and they are large jumps.
The reason for that is because it affects everything. For player characters, a bit less so because things like damage don't go up every level. Moving from one level up to the next level will increase offense (attack and spell accuracy, and damage), and defense (AC, saves, Hit Points). And the +1 to each of those has the +/-10 effect of affecting both the hit/miss and the regular/crit boundaries of the d20 roll.
It is inaccurate to see that +1 as being a 5% or even a 10% increase in effectiveness. It is a 'death by a thousand cuts' type of effect. A +1 may only be 5% to any one thing, but the total effect of having that applied to every aspect of the enemy character really adds up. It is like adding 5% to the radius of a sphere and thinking that the volume isn't going to change all that much. Or that moving from the 32-bit IPv4 address space to the 64-bit IPv6 address space is only a 2x increase in the number of addresses. Math is weirder than that.
What this does in practical terms is that it changes the time to kill. Higher level enemies hit harder. And more accurately. And they get hit less frequently. And they have more HP. So they will live for more rounds, and they will kill PCs in fewer rounds.
What I have experienced from my level 5-7 play is that a level +2 enemy is a fun, though challenging, boss fight. A level +3 enemy is a frustrating slog of a battle of attrition - can we do enough chip damage to this enemy to bring it down before it kills the last of our party.
And that level +3 enemy will kill player characters. A level +3 enemy does enough damage that a one round attack routine of ◆Stride, ◆Strike (crit), ◆Strike(hit) will drop a PC from full health to Dying 1. And with their accuracy, they will crit on that first hit with a 13 roll and hit on their second with a 8 - so that particular combat routine is rather frequent.
And when that happens, the best thing to do is to ignore the dropped character and have everyone else continue doing their chip damage to the best of their ability. Because any character that spends a round on bringing up one of the fallen is one less character round contributing to taking down the enemy. Which will in turn mean that the enemy will get that much more time to continue living and dropping more party members.
Battles in PF2 snowball rather quickly.
The Raven Black |
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Mathmuse wrote:The two frontliners could prevent a Pack Attack that requires three wolves next to one target by splitting the three wolves between them. The wolves would advance and attempt a jaws attack with Knockdown, followed by another jaws attack if successful.
Why would wolves ever attack like this? They wouldn't. Neither if basing tactics on slim knowledge of real wolf tactics nor on just logical tactics based on the wolves' goals.
Wolves won't be attacking seeking a tpk, nor will they be acting like idiot bots in an mmo.
The wolves are going to attack for either, desperate hunger, to defend territory, or feeling cornered/defending pups.
If hungry, they aren't going to go for the whole party, they'll harrass and provoke until they can get a chance to isolate one member (by pack members hiding if possible) then trip and drag off the one member, likely expecting the rest of the group to leave. If pressed too hard, they'll retreat, and that would probably happen after the first or second solid hit the party gets on any of the wolves.
Otherwise, they'll be defensive, trying to scare away the intruders, not kill them. Not even tripping because a tripped opponent can't run away.
And if pushed so far they have nowhere to run, they'll be fighting to escape unless they can't see a way out or have pups they are defending.
This fight you described with wolves is completely ridiculous as anything but a cosmetically altered mmo fight. It completely ignores the wolves' reason for being in the fight and how that impacts tactics and decision making for them.
I get that you really dislike maths in encounter design. But this thread is all about the underlying math in PF2's encounter design.
Its purpose is to help GMs new to the game to avoid TPKing their party without meaning to.
And that is IMO a very worthy goal.
The example given was used to better explain this based on the stats. Not on the behaviour of actual wolves.
Use "idiot bots with the stats of wolves" if you prefer.
magnuskn |
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What I have experienced from my level 5-7 play is that a level +2 enemy is a fun, though challenging, boss fight. A level +3 enemy is a frustrating slog of a battle of attrition - can we do enough chip damage to this enemy to bring it down before it kills the last of our party.
And that level +3 enemy will kill player characters. A level +3 enemy does enough damage that a one round attack routine of ◆Stride, ◆Strike (crit), ◆Strike(hit) will drop a PC from full health to Dying 1. And with their accuracy, they will crit on that first hit with a 13 roll and hit on their second with a 8 - so that particular combat routine is rather frequent.
And when that happens, the best thing to do is to ignore the dropped character and have everyone else continue doing their chip damage to the best of their ability. Because any character that spends a round on bringing up one of the fallen is one less character round contributing to taking down the enemy. Which will in turn mean that the enemy will get that much more time to continue living and dropping more party members.
Battles in PF2 snowball rather quickly.
Yeah, I just did a test encounter at level 1 of a 5 people party against a CR 1 challenge... the opponent critted with his first hit and immediately dropped a character to Dying 2. I can see how combats are very swingy in PF2E. ^^
I'll have to see how a severe encounter plays like when I get the time. I hope it's not as frustrating as you say, because I can't imagine that many players would like to do those kind of encounters too often.
breithauptclan |
Level 1 is a bit swingier than normal. But even that, a level 1 party against a couple level 1 enemies - it isn't standard for enemies to be dropping characters in one round. That only happens on nat-20 crits with really high damage rolls. Which is a pretty rare event.
A level 1 party against a level 4 boss enemy - yeah, that's no fun.
magnuskn |
Ah, that'd be an Extreme encounter, not a Severe one. Of course that would be very bad and probably not winnable. I'm more looking into working out for myself how Severe encounters feel and work.
breithauptclan |
For a 4 character level 1 party, a lone level 4 enemy is a level +3 enemy that costs 120 XP. Which is a Severe encounter.
For a 4 character level 1 party, a level 3 enemy and two level -1 enemies is also 120 XP (80 XP for the +2 and 20 XP each for the -2) and therefore is also a Severe encounter.
The main point that I am trying to make is that the fight against the one level +3 enemy is going to be a lot harder than the fight against a level 3 enemy and two level -1 enemies.
A level 3 enemy is much less likely to be one-round-KO'ing level 1 party members than a level 4 enemy is. And that pattern continues up to at least level 6 where our 7-character party got absolutely wrecked by a level 9 Vrock. 4 PCs down and the other 3 had to retreat.
magnuskn |
For a 4 character level 1 party, a lone level 4 enemy is a level +3 enemy that costs 120 XP. Which is a Severe encounter.
For a 4 character level 1 party, a level 3 enemy and two level -1 enemies is also 120 XP (80 XP for the +2 and 20 XP each for the -2) and therefore is also a Severe encounter.
The main point that I am trying to make is that the fight against the one level +3 enemy is going to be a lot harder than the fight against a level 3 enemy and two level -1 enemies.
A level 3 enemy is much less likely to be one-round-KO'ing level 1 party members than a level 4 enemy is.
Yeah, you're correct, I remembered the table on page 489 of the CRB wrong. Sorry, still very new at this.
Thanks for the further explanation, that makes quite a lot of sense.
Unicore |
Mathmuse,
Were you imagining this Advice thread as trying to be specific and just about the encounter balance of math in PF2 and how monsters work? Or were you open to having other folks add their tips and ideas and discussion about Balancing different kinds of encounters to be fun? I realized a few of my posts might be more in that direction than discussing the math specifically, so I just wanted to check before posting more.
Unicore |
The biggest math problem that GMs homebrewing and modding existing encounter will find (and even running early APs that were trying to figure this stuff out with not many lower level enemies) is that you just don't have a lot of lower level monsters to work with, so it is easy to fall into the trap of adding monsters that are higher level, and thus become incredibly dangerous (per Mathmuse's break down of the difficulty types above), if the encounters spill over onto each other or the party presses ahead unprepared.
Especially if you and your players are newer to the System, Using some level 1 solo monsters or 2 level -1 or 0 monsters as a warm up can make a lot sense. This is doubly true if you know that your players are going to feel frustrated if their PCs fall unconscious, and will say "it was an impossible encounter" if 2 or 3 of them end up unconscious at the end of an encounter.
Low level PF1 is swingy and easy to get knocked out in as well, so I don't know that PF2 is particularly unique about it, but it is important to realize just how large an impact critical results have on the game. One of the things I love about the Abomination Vaults AP is that there is a lot of really scary stuff, that is broadcast as scary stuff, all throughout the dungeon and there will be many times where just shutting the door and saying "not today" is a very wise tactic.
But some players hate the scooby-doo style of adventure, where your initial goal is to survive and escape, so that you can learn more about the situation and come back more prepared next time. Players that hate running, and are not comfortable with frequent character death, and who will stand to the last character trying to protect fallen party members rather than cutting their losses occasionally, are going to struggle with a lot of the default encounter difficulty of PF2. It is very easy to adjust encounters down to be more of slow grind encounters (which can still be challenging but hinge less on the feast or famine of a system built around a D20 die that is trying to keep math balanced in the middle of the spectrum rather than around succeeding on 5s or better, you just have to know to do it based upon your party's reaction to things like taking a 24 point critical hit at first level, or even sometimes seeing a character instantly die from massive damage if the character was built to have low HP.
Mathmuse |
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Why would wolves ever attack like this? They wouldn't. Neither if basing tactics on slim knowledge of real wolf tactics nor on just logical tactics based on the wolves' goals.
...
This fight you described with wolves is completely ridiculous as anything but a cosmetically altered mmo fight. It completely ignores the wolves' reason for being in the fight and how that impacts tactics and decision making for them.
GM DarkLightHitomi is right. When I have a wolf pack attack in a real campaign, usually going for one of the party's horses while the party is camped for the night, the wolves flee at the first counterattack. Wolves seek food rather than combat. A wolf pack would fight like computer-game opponents only if they were controlled by an evil huntsman or intelligent dire wolf.
However, here I am writing a tutorial on encounter balance. The motives of the foes are beyond the scope of my simplified examples. Instead I rely on the stereotypes of common monsters. Goblins are chaotic, hobgoblins are militaristic, wolves group into packs. And they are simple, too. If I used an Air Mephit, the first entry in an alphabetical list of 1st-level creatures in Archives of Nethys, then my example would have a more complicated monster with fast healing 2, Fly speed 40 feet, and a breath weapon. The next entry, Akata, is more normal, but it is a rare abberation that no-one has heard of. The fourth entry, Amoeba Swarm, would bring swarm mechanics into the battle, and a group of swarms seems weirdly redundant.
Nevertheless, GM DarkLightHitomi statement about realism and motives in combat provide a nice hook for another encounter balance topic: Designing a hostile encounter to be resolved without combat. These usually require a wider scope than the combat alone. The enemy needs a motive.
For example, in Fangs of War, the 2nd module of the Ironfang Invasion adventure path, the party encountered an Ironfang forest patrol. I made the map too large--I had copied a real forest with clearing and stream off of Google maps onto Roll20--so the party engaged the patrol 180 feet away. The ranger shot his longbow and the 5th-level druid cast her brand new Fireball spell. The rest of the party could do nothing at that range. The forest patrol exchanged shots for two rounds, but by luck the ranger kept hitting, so they ran. No, this is not the encounter I want to describe. The forest patrol ran to the next encounter in the module, an angry CR 6 wood giant named Herge.
The forest here suffered a severe but localized fire. Ash coats an area devoid of undergrowth, while the larger trees are badly scorched. At the center of the devastation is a large oak tree, killed by the fire and standing like a blackened skeleton. Two bodies are lodged in its branches, burned beyond recognition.
... a wood giant named Herge came to the area, drawn by the fire. Herge extinguished the fire with his quench spell-like ability, but he believes—incorrectly—that the arsonists are still nearby.
...
Development: If the PCs surrender or otherwise convince Herge to stand down, they find the giant to be talkative. The PCs should quickly realize that Herge believes the PCs set the fire and killed the Rangers; once they explain their innocence, Herge apologies for his hasty attack and works with the PCs...
Herge was angry at the Ironfang Legion patrols, but ordinarily he would not be able to distinguish an adventuring party from the Ironfang Legion, so he would attack. The party could either fight him or convince him that they were not Ironfang soldiers and had not set the fire that killed two local Chernasardo Rangers.
The party had three advantages for the peaceful resolution. First, the ranger had been in training to become a Chenasardo Ranger and dressed like them. Second, actual Ironfang soldiers were in the area, the ones running away from the previous encounter. Third, the Scoundrel-racket rogue in the party had CHA 18, trained in Diplomacy, and learned the Glad-Hand feat for fast diplomacy. The rogue persuaded Herge to follow them as the ranger tracked the Ironfang patrol, Herge could then compare uniforms, and he helped corral the patrol with his greater speed so that the party could kill them. Then the druid aided Herge in replanting the burnout.
My pointers for setting up a possible peaceful resolution to combat are:
1) The party has to want peace. Some players are playing Pathfinder for the combat.
2) Know the motives behind the fight.
3) Blatantly inform the party of the motives and possibility for peace immediately, before someone gets hurt. For example, Herge's first line could have been, "You burned the forest. You must pay!"
4) Look for hooks to open a tentative discussion, such as the ranger dressing like a Chernasardo Ranger friend of Herge. In the module as written, Herge was not a friend of a Chernasardo Ranger, but I added that to make the hook stronger.
5) This negotiation is still a challenge, so it has to be difficult. The party has to succeed at a Diplomacy or Deception check against the Will DC of an opponent. And then they need to talk to find common ground.
6) Because the diplomatic challenge is not easy, it could fail and combat will resume. The party will be a little unready due to the switch from negotiations back to battle, so combat is best set at Moderate Threat rather than Severe Threat or Extreme Threat.
7) Beyond-Extreme Threat would be okay if the foes want to arrest the party alive and take them to trial. However, some players don't trust their GMs enough to let their characters be arrested. Ask before trying an arrest that they won't fight to the death instead.
Claxon |
Do note that the encounter-building guidelines only account for 1) the number of foes and 2) their respective level(s) compared to the PCs.
It does not mathematically account for any resource expenditure such as hit points, expended spells, persistent conditions, etc. There is no explicit rule on how to adjust encounters for a party that has expended resources. Be aware of that as both a player and GM.
IME, this kind of bites full casters in the ass compared to martials, and incentivizes a twenty-minute adventuring day.
It also doesn't account for terrain or others hazards a GM might add.*
Although terrain is talked about and that it should impact the challenge, here are no hard rules for it. Same for Hazards in combat.
Basically anything and everything affects the true challenge PCs experience, but the only ones the CR system accounts for with explicit math is number of enemies and their relative level.
Mathmuse |
Mathmuse,
Were you imagining this Advice thread as trying to be specific and just about the encounter balance of math in PF2 and how monsters work? Or were you open to having other folks add their tips and ideas and discussion about Balancing different kinds of encounters to be fun? I realized a few of my posts might be more in that direction than discussing the math specifically, so I just wanted to check before posting more.
My main purpose was that magnuskn said that the encounter balance discussion in the Remaster thread was helpful, so I wanted to draw the discussion out of the Remaster thread into a more appropriate location. Thus, people should talk about and ask about whatever encounter-balance topics interest them. Besides, some people will have tips better than mine.
My own interests are that I love the mathematics of game design, including encounter balance, and I also love telling stories about my campaigns.
thejeff |
But some players hate the scooby-doo style of adventure, where your initial goal is to survive and escape, so that you can learn more about the situation and come back more prepared next time. Players that hate running, and are not comfortable with frequent character death, and who will stand to the last character trying to protect fallen party members rather than cutting their losses occasionally, are going to struggle with a lot of the default encounter difficulty of PF2.
I'm often bothered by the logic of the scooby-doo style of adventure. It often seems that the bad guys should also be able to be better prepared and ready for us when we return.
Depends on the scenario of course.
thejeff |
2 people marked this as a favorite. |
NECR0G1ANT wrote:Do note that the encounter-building guidelines only account for 1) the number of foes and 2) their respective level(s) compared to the PCs.
It does not mathematically account for any resource expenditure such as hit points, expended spells, persistent conditions, etc. There is no explicit rule on how to adjust encounters for a party that has expended resources. Be aware of that as both a player and GM.
IME, this kind of bites full casters in the ass compared to martials, and incentivizes a twenty-minute adventuring day.
It also doesn't account for terrain or others hazards a GM might add.*
Although terrain is talked about and that it should impact the challenge, here are no hard rules for it. Same for Hazards in combat.
Basically anything and everything affects the true challenge PCs experience, but the only ones the CR system accounts for with explicit math is number of enemies and their relative level.
Hazards in combat count, right? They've got CRs, just figure them into the encounter math.
dirtypool |
Although terrain is talked about and that it should impact the challenge, here are no hard rules for it. Same for Hazards in combat.
There are hard rules for Environment (including both Terrain and Weather) beginning on page 512 - including the DC's to overcome and damage imposed for those that have specific encounter effects.
Hazards explicit rules, including their levels for inclusion in the Encounter Budget begins on page 520 in the CRB and page 74 in the GMG
krazmuze |
Thank you for this thread, this is very helpful already.
One thing which I don't really get yet that well is how the math is so tight, that just going up one or two levels on an encounter can have so severe consequences, when one level up amounts to only 10% better saves and to-hits (looking at the elite template, which add +2 to everything)?
The math is tight because everything is level is added to proficiency. Which means that having an unbalanced encounter of +/-4 levels is going to have an unbalancing math difference of +/-4 to the dice, which is a +/-20% shift in odds
The other key part of the math that interacts with leveled proficiency is the criticals are DC+/-10 and apply to all checks with four levels of success (including skills - and their combat skill actions). So the leveled proficiency means that +/-1 is no longer a meager bonus overwhelmed by the die but instead is a level shift in difficulty that can be felt. But it is not just an odds shift of hit/miss - it is a odds shift in crit/hit/miss/fumble - your odds of crit or fumble get multiplied/divided. Compound this further with crits doing double all damage including bonus damage. That is what makes the extreme boss a TPK - they can serially murder the entire party without any minions in four rounds one by one by doing crit/crit/hit while the party does miss/fumble/fumble (attack fumble is optional card deck but saves and skills do fumble).
https://2e.aonprd.com/Rules.aspx?ID=497
See how the creature level XP aligns with the encounter XP table aligns with the difficulty level? That means that increasing difficulty steps is as simple as level step up in monster or a level step down in PCs. It is extremely easy for the GM to balance the encounters for the described difficulty level to fit their narrative.
monster are created by numbers and do not use PC build rules unlike prior editions. That means that they will conform to their level rating and can reliable be used in encounter building - be their role is the extreme boss because they are +4 or that trivial lackey because they are -4. The same monster in the bestiary itself serves as the normal, boss and lackey version. This does not mean every monster is the same, they have tactical and class and NPC roadmaps that give guidelines how to vary their build within the level so that they have strengths and weaknesses the party can exploit.
You will hear the phrase +1 matters, and a good GM is one who tracks where the bonuses comes from and rewards those who use skill tactics to change the math balance. If you are facing a +4 boss, and can consistently apply a net -4 to the boss, you are knocking it down to a weak solo boss of your level. That boss will no longer crit constantly doing double damage and just does normal damage. Get more levels and came back and trounce it as a lacky it will do no damage because it misses/fumbles all the time.
One thing to note is the elite/weak template is doing +/-2 rather than +/-1 even though it is said to be a level shift. The reason is the PC/NPC numbers by levels are not perfectly linear - it either jumps by one or two and averages 1.5. For PCs this comes from ability boosts at each tier of play, or when they get weapon runes. So the elite/weak is OP to account for these tier jumps. So beware when you use it at lowest levels - you might want to use half elite/weak because full elite/weak is really to much. See Game Mastering > Creature numbers table is probably better way to adjust monsters. https://2e.aonprd.com/GMScreen.aspx
magnuskn |
magnuskn wrote:Thank you for this thread, this is very helpful already.
One thing which I don't really get yet that well is how the math is so tight, that just going up one or two levels on an encounter can have so severe consequences, when one level up amounts to only 10% better saves and to-hits (looking at the elite template, which add +2 to everything)?The math is tight because everything is level is added to proficiency. Which means that having an unbalanced encounter of +/-4 levels is going to have an unbalancing math difference of +/-4 to the dice, which is a +/-20% shift in odds
The other key part of the math that interacts with leveled proficiency is the criticals are DC+/-10 and apply to all checks with four levels of success (including skills - and their combat skill actions). So the leveled proficiency means that +/-1 is no longer a meager bonus overwhelmed by the die but instead is a level shift in difficulty that can be felt. But it is not just an odds shift of hit/miss - it is a odds shift in crit/hit/miss/fumble - your odds of crit or fumble get multiplied/divided. Compound this further with crits doing double all damage including bonus damage. That is what makes the extreme boss a TPK - they can serially murder the entire party without any minions in four rounds one by one by doing crit/crit/hit while the party does miss/fumble/fumble (attack fumble is optional card deck but saves and skills do fumble).
https://2e.aonprd.com/Rules.aspx?ID=497
See how the creature level XP aligns with the encounter XP table aligns with the difficulty level? That means that increasing difficulty steps is as simple as level step up in monster or a level step down in PCs. It is extremely easy for the GM to balance the encounters for the described difficulty level to fit their narrative.
monster are created by numbers and do not use PC build rules unlike prior editions. That means that they will conform to their level rating and can reliable be used in encounter building -...
Thank you, that was a very thorough explanation.
Temperans |
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An additional thing to consider when looking at the math and encounters. There are 3 basic parts that determine how challenging an encounter might be before adding anything else:
A) How quickly do the base numbers go.
A.1) In a game that has a flat increase, action economy is more important than level. A level 2 character might be slightly stronger than a single level 1 creature, but it cannot do anything versus two level 1 creatures.
A.2) In a game that has a moderate increase (numbers increase about half level) the level matters much more but things can still be overcomed with enough creatures. Here a level 3 creature will be strong enough to deal with 2 level 1 creatures, would struggle versus 3, and would likely fail vs 4.
A.3) In a game that has a steep increase, then level matters more than action eceonomy. Here a level 4 creature would only start to struggle vs 16 level 1 creatures.
B) How critical hits work.
B.1) No critical hits means that there is never the chance to hit a weak spot. This makes it so things are very predictable, but is not fun. There is a reason why games always have some form of critical hit/miss system.
B.2) Critical hit requires a threshold, this means that a weak spot can be hit if you roll high enough. This is more predictable than no crit, but it makes it so whoever has the highest attack has a higher chance to crit. Inversely, it also means that the lower your ability to block the higher your chance to be crit.
B.3) Critical hit requires you roll a specific number, this means that a weak spot can be hit if you are lucky. This is highly unpredictable (assuming no cheating) but it ensures that there is always the change of a hit.
C) How wide is the swing of buff/debuff.
C.1) No swing means that there is no way to become stronger or weaker. Great for predictability, but often seen as boring.
C.2) Small swing (less than 1 or 2 levels) means that you can nudge things slightly.
C.3) Medium swing (2-4 levels) means that assuming the abilities work, a hard fight can become moderate.
C.4) Large swing (5+ levels) means that assuming you are able to apply everything even a very difficult fight can become moderate or even trivial.
*******************
Pathfinder 2 has a steep gradient, with a treshhold crit system, and a small buff/debuff swing. So a party of 4 without buffing will be at a -8 to attack and AC versus a level +4 enemy, but can swing the math to -4 if they successfully apply the max buff/debuff.
To explain the math: The party would have an AC that is ~4 points while the enemy's attack is ~4 points higher, and vice versa. That means a swing of 8. The max buff you can apply is ~2 while the max debuff is ~2, a swing of 4. Potency and resistance runes don't apply because they are built into the enemy's math.
So level +/-2 is consistent because you can apply buff/debuff to make it less bad. But level +/-4 or higher becomes increasingly more difficult. While level +/-11 is actually impossible because the highest roll is equal to AC-10, a critical failure that becomes a failure because you rolled a nat 20.
Claxon |
Claxon wrote:Hazards in combat count, right? They've got CRs, just figure them into the encounter math.NECR0G1ANT wrote:Do note that the encounter-building guidelines only account for 1) the number of foes and 2) their respective level(s) compared to the PCs.
It does not mathematically account for any resource expenditure such as hit points, expended spells, persistent conditions, etc. There is no explicit rule on how to adjust encounters for a party that has expended resources. Be aware of that as both a player and GM.
IME, this kind of bites full casters in the ass compared to martials, and incentivizes a twenty-minute adventuring day.
It also doesn't account for terrain or others hazards a GM might add.*
Although terrain is talked about and that it should impact the challenge, here are no hard rules for it. Same for Hazards in combat.
Basically anything and everything affects the true challenge PCs experience, but the only ones the CR system accounts for with explicit math is number of enemies and their relative level.
But that's my exact point. While they got a CR, you can't actually just add in a random hazard and expect that it all works out. The CR of hazards are when it's encountered in isolation. Same for terrain.*
Perhaps I should have framed it more about the synergistic effect, because what I'm trying to say is that while a CR 5 hazard is that when encountered in isolation, depending on how it's integrated it can be much more of much less of an issue than its CR would indicate.
*Regarding terrain, I haven't seen any "terrain" stuff that isn't framed as a hazard. I'm talking about terrain as in "the GM has created a single choke point that the enemies are set up to exploit".
krazmuze |
I like to illustrate +1 AC from raise shield action this way, it is a 100% chance that you lowered the difficulty of the boss by a level when triple attacked. Much better than nat20 fishing your last attack only to find out that your nat20 is still a miss! That is when you learn that not only is that +4 extreme boss is not just +4 more attack/AC - that monster tables are unfair (strengthen numbers to offset weaker action economy) and they was more powerful than you even if your level!
thejeff |
thejeff wrote:Claxon wrote:Hazards in combat count, right? They've got CRs, just figure them into the encounter math.NECR0G1ANT wrote:Do note that the encounter-building guidelines only account for 1) the number of foes and 2) their respective level(s) compared to the PCs.
It does not mathematically account for any resource expenditure such as hit points, expended spells, persistent conditions, etc. There is no explicit rule on how to adjust encounters for a party that has expended resources. Be aware of that as both a player and GM.
IME, this kind of bites full casters in the ass compared to martials, and incentivizes a twenty-minute adventuring day.
It also doesn't account for terrain or others hazards a GM might add.*
Although terrain is talked about and that it should impact the challenge, here are no hard rules for it. Same for Hazards in combat.
Basically anything and everything affects the true challenge PCs experience, but the only ones the CR system accounts for with explicit math is number of enemies and their relative level.
But that's my exact point. While they got a CR, you can't actually just add in a random hazard and expect that it all works out. The CR of hazards are when it's encountered in isolation. Same for terrain.*
Perhaps I should have framed it more about the synergistic effect, because what I'm trying to say is that while a CR 5 hazard is that when encountered in isolation, depending on how it's integrated it can be much more of much less of an issue than its CR would indicate.
*Regarding terrain, I haven't seen any "terrain" stuff that isn't framed as a hazard. I'm talking about terrain as in "the GM has created a single choke point that the enemies are set up to exploit".
Definitely agreed on terrain.
I don't think that's supposed to be true for hazards though. It's not even strictly true for creatures since some have more synergy than others and it doesn't account for hazards even as well, but I believe the intent is there.
krazmuze |
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Now onto the argument that PF2e is not compatible with simulations or narrative games because level makes it gamist, I have to disagree. Balanced encounter math means that the GM can choose the encounter difficulty that fits the story they want to tell, unlike other editions, they can rely on the built encounter to be the difficulty range that it is labeled and with experience they can judge tactics on PC and GM side to shift difficulty steps as necessary. You want a hex crawl with fixed difficulty where the party needs to run away until they or ready (severe/extreme), or a 5e style attrition (low/trivial warmup encounter before the moderate boss) or an MMO (everything is your level +/- the desired over all difficulty). There is even an alternate rule to remove level proficiency if that is getting your way, but it has the downside that encounter balance is less predictable because lackeys will crit more and bosses will crit less.
The GM guide even gives adventure balances that suggest encounter difficulties that might be proper for different narrative styles.
https://2e.aonprd.com/Rules.aspx?ID=949
Unicore |
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The buffing and debuffing ability in PF2 even at low level is pretty reliably in the 3 to 4 range, not the 1 to 2 range. By higher levels it gets to the 5 or 6 range with consistency. It is the hit point variance that really makes fights against level +3 to +4 dangerous at low levels. High level monsters can hit hard and often have ways to attack multiple PCs at once, but once the debuffing starts, it stacks up fast and players can dish a lot of damage against a prone, frightened 2 creature.
Higher level solo bosses really need speed, terrain advantages or minions to make fights against a party interesting.