Monster Levels and CR

[Yakk]

So I reduced the 5e CR calculator to a single equation.

(HP/8 + DPR/3 + AC + StatBonus)/4 - 6

It doesn't work well with really low AC, HP under 80, etc. Also, over 20 CR the steps are about 2-3 times larger between CR (a CR 30 is "really" like a CR 40-50 if you continued the sub-20 pattern).

A monster with 80 HP, 12 DPR, 13 AC and 12 in its attack stat in the CR math of the DMG has a CR of 1.

Similarly, (80/8 + 12/3 + 13 + 1)/4 - 6 = 1

We can do the same for a naive Rogue. The Naive Rogue either has advantage on a ranged attack for 1d6+3+sneak attack with extra accuracy, or two short swords and lands sneak attack 40% more often than expected by the two swings.

This means their sneak attack DPR is about 5 points per die (after accounting for the accuracy boost), and their base (non-sneak-attack) damage is 10ish (going up slowly) after accounting for either advantage or two attacks.

So their DPR is roughly 12 + 2.5*level.

Their AC is 14 at level 1, going up to 16 at level 4, 17 at level 8 and up to 20+ at level 20 (9-20 from magic armor). Call this 14 + Level/3 roughly.

Their HP with 12 con starts at 9, and goes up by 6 per level; 3 + level*6.

Their Dex is 16 (+3), and goes up by +1 at level 4 and 8. It seems reasonable to pretend this continues due to magic items or whatever; +3 + Level/4.

Plugging this back into the CR math we get:

((3+L*6)/8 + (12+2.5*L)/3 + 14+L/3 + 3+L/4)/4 - 6 = (52L-63)/96

Or, about CR = L/2 - 2/3.

As mentioned, my equation doesn't work exactly with low HP. But bear with me.

Flipping it we get CR+2/3 = L/2, or Level = 2*CR + 4/3; we can round the 4/3 down and say that the "virtual level" of a CR X monster is 2X+1.

Ie, a CR 1 monster is "roughly equivalent" to a Level 3 naive rogue.

(I suspect we could map 1/2 to Level 2 and 1/4 to Level 1 and 1/8 to level 0.5.)

What I propose is to flip the script on monster CR. Using this equation I'll map monster CR to a monster Level. Then I'll make a monster Level based building system, where monsters very roughly correspond in power to PCs of the same level.

Then building encounters looks a bit more like 4e. An encounter with an equal number of even-level monsters will be the baseline difficulty (which I believe is harder than medium).

[Yakk]

Things the above "naive rogue" math neglects:
1. Subclass abilities
2. Uncanny Dodge (half damage against 1 attack 1/round).
3. Spending HD between combats
4. Fancier rogue techniques (like booming blade, or multiclassing)

But the goal is a simple ballpark. I think I can add 2nd order effects to cover that.

--

A basic 5e monster is the Guard. It has +1 ATK stat, 11 HP, 16 AC and does 4 DPR.

Under my linear CR calculator it has (16+1+1.3+1.4)/4-6 = -1 CR, but my CR calculator doesn't deal with that low HP/damage/etc very well.

As I'm using Level = CR*2+1 as my approximation, if I feed my CR calculator into it I get

Level = HP/16 + DPR/6 + AC/2 + StatBonus/2 - 11

Feeding the Guard into this as a sanity check
11/16 + 4/6 + 16/2 + 1/2 - 11 = Level -1
which agrees with the CR calculator (-1*2+1 is -1).

A level 1 Rogue has 9 HP, +3 ATK stat, 15 AC (studded) and deals 1d6+1d6+3 (10) with 2 chances to land 1d6 (call that 5) or 15 DPR.

Feeding that back into my level calculator I get 9/16 + 15/6 + 15/2 + 3/2 -11, or "Level 1.06". Pretty close. Which makes sense, as I used that Rogue to calibrate my scales.

I'd argue that a Rogue is an average toughness high damage creature.

Suppose we define a L 1 baseline creature:
10 HP
+2 ATK stat
13 AC
9 DPR

This has a level calculation of 10/16 + 9/6 + 13/2 +2/2 -11, or -1.375.

Add on "Skirmisher" for +2 AC and special movement abilities (which the Rogue has) and "Striker" for +1 ATK +6 DPR

10/16 + 15/6 + 15/2 +3/2 -11, or 1.125.

...

Suppose we have 2 base types of major features: "Striker" could be +2 ATK *1.5 DPR and be a "major" feature, while "Tough" should be *1.5 HP and +2 AC.

Base HP*0.5/16 should equal DPR*0.5/6 for this to work. But if we make "Tough" be *2 HP instead of *1.5 then HP/16 would have to equal DPR*.5/6.

I could have 2 units of Defensive/Offensive. So you can be Defensive, Balanced or Offensive. That allows for a wider variety of base stats. Base would be X, and Defensive would be 2HP/1DPR, Offensive be 1HP/2DPR and balanced would be 1.5HP/1.5DPR.

For this to work, the base ends up being HP/16 = DPR/6 at each level.

If we have ATK stat scaling from 12 (+1) to 22 (+6) from level 1 to 20, that is +1 StatBonus/4 levels. Similarly, if AC scales from 13 up to 23, that is +1 AC/2 levels.

Plugging that back in

dLevel/dLevel = dHP/dLevel/16 + dDPR/dLevel/6 + dAC/dLevel/2 + dStatBonus/dLevel/2

1 = 1.5*dHP/dLevel/16 + 1.5*dDPR/dLevel/6 + 1/4 + 1/8
5/8 = dHP/dLevel/16 + dDPR/dLevel/6

dHP/dLevel/16 = dDPR/dLevel/6, so

5/8 = 1.5*dHP/dLevel/8
5 = dHP/dLevel
Base HP goes up 3.333 points per level, and DPR by ... 1.25. Ick.
Balanced gets *1.5 or 5 and 1.875. Call that 5 and 2 (making monsters a bit tougher), which is equivalent to dividing HP by 17 and DPR by 6.

If we make a defensive monster get +3 HP/level, that is "worth" roughly 1 DPR, and vice versa.

First iteration of Monster Stats by Level:
HP: (5 or 10 or 15)+(2 or 5 or 8)*Level
DPR: (6 or 4 or 2)+(3 or 2 or 1)*Level
AC: 12+Level/2
Max Stat: 12+Level/2

Plugging the "balanced" monster back in to the level calculator:

HP/17 + DPR/6 + AC/2 + StatBonus/2 - 11
= (10+5L)/17 + (4+2L)/6 + (12+L/2)/2 + (1+L/4)/2 - 11
= 10/17+5/17L + 2/3 + 1/3L + 6 + 1/4 L + 1/2 + 1/8 L - 11
= 10/17 + 2/3 + 6 - 11 + 1/2 +5/17L+ 1/3L+ 1/4 L+ 1/8 L
= -3.75 + L

which means we have 3.75 "bonus points" to spend, worth +7.5 ATK, +7.5 AC, 64 HP or 22.5 DPR.

+1 ATK (0.5) +1 AC (0.5) +2 DPR (1/3) +5 HP (1/3) sums to 1.7, leaving about 2 bonus points:

I'll distribute a point of HP and DPR:

HP: (10 or 23 or 37)+(2 or 5 or 8)*Level
DPR: (14 or 9 or 4)+(3 or 2 or 1)*Level
AC: 13+Level/2
Max Stat: 14+Level/2

Bonus Packages (pick 1):
+4 primary stat
+2 AC
+6 DPR
+17 HP



Type
HP
DPR
AC
Stat


Balanced
23+5*Level
9+2*Level
13+Level/2
14+Level/2


Fragile
10+2*Level
14+3*Level
13+Level/2
14+Level/2


Tough
37+8*Level
4+Level
13+Level/2
14+Level/2


Then add in one of +2 AC, +4 Stat, +6 DPR or +18 HP.

You can trade +/-1 AC for +/- 2 stat, +/-3 DPR, or +/- 9 HP.

Now, the Tough/Fragile might be "too extreme". I'll play with it.

[Yakk]

At level 21 (CR 10) a Fragile foe we get:

52 HP
DPR 77
AC 23
Stat 24

That is off. I think I need to drop AC, especially on Fragiles, and boost HP.

Balanced is:
128 HP
DPR 51
AC 23
Stat 24

Suppose I drop AC to +1/4 for Fragile, and put that into HP (adding 17/8 or 2 HP/level). That is worth 2 HP/level.

96 HP
DPR 77
AC 18
Stat 24

that is far better.

Tough is
205 HP
DPR 25
AC 23
Stat 24

That DPR is way too low. I think I have to shave off some HP; shave off 28 HP for 10 DPR?

Tough (adjusted) is:
177 HP
DPR 35
AC 23
Stat 24

This does make me want to do a Soldier/Brute split (like in 4e), where one has AC the other has HP.

+HP, -AC - Brute
+AC, -DPR - Soldier
++DPR, -AC, -HP - Fragile (which includes Artillery and Controllers)
+DPR, -HP - Skirmisher

[Yakk]

The next thing to think about is Elite.

Elites are intended to take up more than 1 creatures "slot" in combat. In 5e, they are just higher CR (and often legendary).

In this model I don't want to up their level.

An Elite(N) monster is "N times wider" than a normal monster. It should have N times the HP and (N+1)/2 times the damage output -- each level of Elite adds 1/2 a monster's damage output.

We'll also need some defence against save-or-lose. Unlike baseline 5e, I'll combo the two.

Elite(N) adds (20+5*Level)*(N-1) HP.

Elite(N) adds +N to all saving throws.

Elite(N) adds (N-1) Elite Actions. Elite Actions act like legendary actions. When you take an Elite Action, you can make a save against an effect that normally gives a save at the end of your turn, with no penalty if you fail. Against effects that have a fixed duration, you can still make a save against the original DC with disadvantage, nullifying future effects if you pass. If you are blocked from taking actions, Elite Actions can still be taken to do nothing but make a saving throw.

An Elite Action has a damage budget of (4+Level). (Double Elite Actions can be a thing).

So a level 25 Elite(5) creature has 580 extra HP, and 4 Elite Actions each with a damage budget of 29 (each).