ezo
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D&D 5E Monster damage realization - DPR per CR diminishes across the game
So, calculate "monster threat volume". It is (damage done per round) times (damage it takes to defeat it). You can do it either ignoring accuracy/defence or factoring it in.
In a 1:1 fight with only damage being done (no conditions), two monsters with the same threat volume do the same damage before being defeated.
If you double damage and HP, you get 4x the threat volume. This monster takes twice as long to kill, and does twice the damage per round while not yet killed.
Now, in the DMG CR calculator, each CR from 1 to 20 adds 15 HP and 6 DPR. Average HP/DPR at CR 1 is 80 HP and 12 DPR.
So Threat =~ 30*(1+L)(13+3L) = (L^2+5.3 L+4.3)*90
We can round it to basically 100 times L^2+5 L+4
Past 20, monster threat grows faster than this - in effect, above CR 20 monsters gain 18 damage and 45 HP per CR, 3x as much as before CR 20. The easiest way to do this is to just scale the input - the mapping from CR to the L variable.
Trying this on a random brute monster - a triceratops. It gets a gore (24) every turn, and 1 stomp (22) every 3 turns. It has 95 HP. DPR is 31.33 giving it a threat volume of 2976 (about 3000).
A CR 1 monster "should" have a threat volume of 1000
A CR 2 monster "should" have a threat volume of 1800
A CR 3 monster "should" have a threat volume of 2800
A CR 4 monster "should" have a threat volume of 4000
A CR 5 monster "should" have a threat volume of 5400.
A CR 6 monster "should" have a threat volume of 7000.
A CR 7 monster "should" have a threat volume of 8800.
A CR 8 monster "should" have a threat volume of 10800.
A CR 9 monster "should" have a threat volume of 13000.
A CR 10 monster "should" have a threat volume of 15400.
A CR 15: 30400
CR 20: 50400.
That Triceratops maps out to a CR 3 not 5. To get CR 5, you need to assume the stomp happens every round and give it credit for its above-average accuracy (both from its +9 attack bonus, and the fact the stomp has advantage).
Lets try a T-Rex. Base threat volume is 53 * 136 or 7208, lining up with a CR 6. It again is unusually accurate (from its high strength) and has a auto-grapple/restrain, but poor AC.
The Giant Ape has a threat volume of 44*157 = 6908, CR 6. It has low AC (12) and a decent attack bonus (+6 strength). You'll note that most people find the Giant Ape competitive to the TRex when polymorphing allies (you just lose the restrain).
You can take the DMG target accuracy values and apply +/-10% per extra accuracy, and +/-10% per lost AC on the end threat value. A CR 6 monster "should" have an accuracy of 6; triceritops and giant ape and t-rex have +9. A CR 3 monster "should" have an accuracy of +4 (so +50%). Their AC's "should" be like 13-15.
...
Higher level monsters might be having lower DPR in comparison because they are being used as bosses for low level PCs?
In a 1:1 fight with only damage being done (no conditions), two monsters with the same threat volume do the same damage before being defeated.
If you double damage and HP, you get 4x the threat volume. This monster takes twice as long to kill, and does twice the damage per round while not yet killed.
If you replace the 1:1 fight with a 1:2 fight (1 PC, 2 foes), the damage the PC takes goes up by 3x, despite there being 2x as many HP and 2x as much damage on the table. This is because half way through the fight, one of the foes drop.
In general, N monsters have (N+1)N/2 the threat volume of 1 monster. In the range N from 1 to 5 this is:
1
3
6
10
15
If you then divide this by the number of monsters, you get:
1
1.5
2
2.5
3
this is the degree to which "adding up total threat" failed to scale; 3 100 threat monsters add up to 300 threat, but are actually as dangerous as a 600 threat monster.
Now, what we can do is have the budget points for encounters not be threat, but something so that when you add up monster budget points, you get a value that corresponds to what a single monster budget would have the same threat.
To do this, when threat doubles the budget needs to go up by a factor of 3, not 2. If you set Budget = (HP*Damage)^0.6, then (2 HP*3 Damage) = 6^0.6 * (HP*Damage) = 2.9 * (HP*Damage).
3 10 DPR 10 round-to-kill monsters deal 3+2+1 = 600 damage.
1 30 DPR 20 round-to-kill monster deals 600 damage.
In short, if we did set XP=Threat^0.6 we'd have linear encounter building. No "multiplier for size of encounter".
In general, N monsters have (N+1)N/2 the threat volume of 1 monster. In the range N from 1 to 5 this is:
1
3
6
10
15
If you then divide this by the number of monsters, you get:
1
1.5
2
2.5
3
this is the degree to which "adding up total threat" failed to scale; 3 100 threat monsters add up to 300 threat, but are actually as dangerous as a 600 threat monster.
Now, what we can do is have the budget points for encounters not be threat, but something so that when you add up monster budget points, you get a value that corresponds to what a single monster budget would have the same threat.
To do this, when threat doubles the budget needs to go up by a factor of 3, not 2. If you set Budget = (HP*Damage)^0.6, then (2 HP*3 Damage) = 6^0.6 * (HP*Damage) = 2.9 * (HP*Damage).
3 10 DPR 10 round-to-kill monsters deal 3+2+1 = 600 damage.
1 30 DPR 20 round-to-kill monster deals 600 damage.
In short, if we did set XP=Threat^0.6 we'd have linear encounter building. No "multiplier for size of encounter".
Now, in the DMG CR calculator, each CR from 1 to 20 adds 15 HP and 6 DPR. Average HP/DPR at CR 1 is 80 HP and 12 DPR.
So Threat =~ 30*(1+L)(13+3L) = (L^2+5.3 L+4.3)*90
We can round it to basically 100 times L^2+5 L+4
Past 20, monster threat grows faster than this - in effect, above CR 20 monsters gain 18 damage and 45 HP per CR, 3x as much as before CR 20. The easiest way to do this is to just scale the input - the mapping from CR to the L variable.
Trying this on a random brute monster - a triceratops. It gets a gore (24) every turn, and 1 stomp (22) every 3 turns. It has 95 HP. DPR is 31.33 giving it a threat volume of 2976 (about 3000).
A CR 1 monster "should" have a threat volume of 1000
A CR 2 monster "should" have a threat volume of 1800
A CR 3 monster "should" have a threat volume of 2800
A CR 4 monster "should" have a threat volume of 4000
A CR 5 monster "should" have a threat volume of 5400.
A CR 6 monster "should" have a threat volume of 7000.
A CR 7 monster "should" have a threat volume of 8800.
A CR 8 monster "should" have a threat volume of 10800.
A CR 9 monster "should" have a threat volume of 13000.
A CR 10 monster "should" have a threat volume of 15400.
A CR 15: 30400
CR 20: 50400.
That Triceratops maps out to a CR 3 not 5. To get CR 5, you need to assume the stomp happens every round and give it credit for its above-average accuracy (both from its +9 attack bonus, and the fact the stomp has advantage).
Lets try a T-Rex. Base threat volume is 53 * 136 or 7208, lining up with a CR 6. It again is unusually accurate (from its high strength) and has a auto-grapple/restrain, but poor AC.
The Giant Ape has a threat volume of 44*157 = 6908, CR 6. It has low AC (12) and a decent attack bonus (+6 strength). You'll note that most people find the Giant Ape competitive to the TRex when polymorphing allies (you just lose the restrain).
You can take the DMG target accuracy values and apply +/-10% per extra accuracy, and +/-10% per lost AC on the end threat value. A CR 6 monster "should" have an accuracy of 6; triceritops and giant ape and t-rex have +9. A CR 3 monster "should" have an accuracy of +4 (so +50%). Their AC's "should" be like 13-15.
...
Higher level monsters might be having lower DPR in comparison because they are being used as bosses for low level PCs?
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