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So, I figured out why 5e's encounter building is broken(and how to fix it)
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<blockquote data-quote="NotAYakk" data-source="post: 8917264" data-attributes="member: 72555"><p>The DMG mulpliers are reasonable if you assume PCs are decent at AOE.</p><p></p><p>The basic model of a monster's power is (effective HP)*(effective damage output), where effective takes into account accuracy.</p><p></p><p>If we assume monsters fight PCs "near" their CR, you can convert accuracy and defence to a simple multiplier on HP and DPR. Once you've done this, if you imagine a "fake party" with roughly expected accuracy making 1 HP damage per turn attacks who in turn has infinite HP, the monster power I mention above gives you how much damage the monster does before it dies.</p><p></p><p>As you scale up this fake party damage to X HP per turn, the damage the fake party takes is ... roughly divided by X.</p><p></p><p>(For regeneration cases you have to be a bit less abstract).</p><p></p><p>The XP value of a monster is pretty close to this product; I think there is a factor of 3ish?</p><p></p><p>For multiple monsters when you add up their XP, you model the congo-line situation. Imagine the fake party fighting monster 1, then monster 2, then monster 3. This is "add up the XP of the monsters".</p><p></p><p>Now, as you can imagine, monsters don't fight in congo lines usually. If we assume all of the monsters are roughly equal and they all swarm at once, when 3 monsters attack the fake party will take 6x one monster's damage, not 3x. If 4 monsters attack, it is 10x not 4x. And if 5 monsters attack, 15x instead of 5x.</p><p></p><p>The number here is called a triangular number -- it is 1+2+3+4+5+6+... etc. It isn't quite the square, but it grows faster than linearly.</p><p></p><p>If you divide the triangular number by the linear number, you get 1, 1.5, 2, 2.5, 3, 3.5, 4 -- you get (N+1)/2.</p><p></p><p>So if we assume foes swarm the party, and the party focus fires down one monster at a time, the proper XP value for N monsters is N*1 monster * (N+1)/2.</p><p></p><p>This is lower than the DMG, as you have observed. But there are two assumptions here.</p><p></p><p>First, the party does perfect focus fire and has no AOE.</p><p>Second, the monsters can engage the party with perfect efficiency.</p><p></p><p>When you have many foes, often the foes get in each others way. Second, AOE massively increases the capabilities of the party against large numbers of foes.</p><p></p><p>Between the two of them, we get closer to N^0.4 as the "encounter size multiplier" instead of the naive "N+1".</p><p></p><p>None of this cares about action economy. It cares about (a) the expectation that you'll be eliminating monsters, or (b) you'll be using AOEs to deal efficiently with multiple monsters.</p><p></p><p>Finally, we can model what happens if the fake party spreads damage out. Then all N of the monsters deal damage each round, and they last N times longer than a single monster. This corresponds to a multiplier of N, instead of (N+1)/2.</p><p></p><p>...</p><p></p><p>Your model, where you scale team monster's XP by its side size, reflects players not doing any AOE or any focus fire at all.</p><p></p><p>...</p><p></p><p>On the other hand, the model assumes <em>PCs are not being eliminated</em>. That between healing and tactics and abilities, team PC avoids being taken out, so their damage flux doesn't drop.</p><p></p><p>This is why the fake party has one basket of HP and steady damage output.</p><p></p><p>A real party also does spike damage. This can help eliminate foes when there are more than 1 of them early in the fight, which has high value, and another reason why N or (N+1)/2 is not a great model.</p><p></p><p>A smart party will burn more resources in the earlier, more dangerous parts of a fight with N foes than they will at the tail end. Meanwhile, the simple model I described had flat damage output.</p></blockquote><p></p>
[QUOTE="NotAYakk, post: 8917264, member: 72555"] The DMG mulpliers are reasonable if you assume PCs are decent at AOE. The basic model of a monster's power is (effective HP)*(effective damage output), where effective takes into account accuracy. If we assume monsters fight PCs "near" their CR, you can convert accuracy and defence to a simple multiplier on HP and DPR. Once you've done this, if you imagine a "fake party" with roughly expected accuracy making 1 HP damage per turn attacks who in turn has infinite HP, the monster power I mention above gives you how much damage the monster does before it dies. As you scale up this fake party damage to X HP per turn, the damage the fake party takes is ... roughly divided by X. (For regeneration cases you have to be a bit less abstract). The XP value of a monster is pretty close to this product; I think there is a factor of 3ish? For multiple monsters when you add up their XP, you model the congo-line situation. Imagine the fake party fighting monster 1, then monster 2, then monster 3. This is "add up the XP of the monsters". Now, as you can imagine, monsters don't fight in congo lines usually. If we assume all of the monsters are roughly equal and they all swarm at once, when 3 monsters attack the fake party will take 6x one monster's damage, not 3x. If 4 monsters attack, it is 10x not 4x. And if 5 monsters attack, 15x instead of 5x. The number here is called a triangular number -- it is 1+2+3+4+5+6+... etc. It isn't quite the square, but it grows faster than linearly. If you divide the triangular number by the linear number, you get 1, 1.5, 2, 2.5, 3, 3.5, 4 -- you get (N+1)/2. So if we assume foes swarm the party, and the party focus fires down one monster at a time, the proper XP value for N monsters is N*1 monster * (N+1)/2. This is lower than the DMG, as you have observed. But there are two assumptions here. First, the party does perfect focus fire and has no AOE. Second, the monsters can engage the party with perfect efficiency. When you have many foes, often the foes get in each others way. Second, AOE massively increases the capabilities of the party against large numbers of foes. Between the two of them, we get closer to N^0.4 as the "encounter size multiplier" instead of the naive "N+1". None of this cares about action economy. It cares about (a) the expectation that you'll be eliminating monsters, or (b) you'll be using AOEs to deal efficiently with multiple monsters. Finally, we can model what happens if the fake party spreads damage out. Then all N of the monsters deal damage each round, and they last N times longer than a single monster. This corresponds to a multiplier of N, instead of (N+1)/2. ... Your model, where you scale team monster's XP by its side size, reflects players not doing any AOE or any focus fire at all. ... On the other hand, the model assumes [I]PCs are not being eliminated[/I]. That between healing and tactics and abilities, team PC avoids being taken out, so their damage flux doesn't drop. This is why the fake party has one basket of HP and steady damage output. A real party also does spike damage. This can help eliminate foes when there are more than 1 of them early in the fight, which has high value, and another reason why N or (N+1)/2 is not a great model. A smart party will burn more resources in the earlier, more dangerous parts of a fight with N foes than they will at the tail end. Meanwhile, the simple model I described had flat damage output. [/QUOTE]
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So, I figured out why 5e's encounter building is broken(and how to fix it)
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