D&D 5E Understanding the maths behind 5e

[Charlaquin]

I have read these. Unfortunately his monster building table, that arguably is pretty simple, is not very well suited for varying party sizes. As far as I can tell.

I think it works fine as long as you keep in mind the numbers are balanced around the assumption of a 4-person party. That means “solo” monsters should be outnumbered by PCs 4:1, “pair” monsters should be outnumbered 2:1, “party” monsters should match the PC party size 1:1, “gang” monsters should outnumber the party 2:1, and “mob” monsters should outnumber the party 4:1. Roughly. So, like, if you have a 7-person party, a solo monster should probably be accompanied by a party monster and a gang monster, or by 3 gang monsters (or 6 mob monsters, or 2 gangs and 2 mobs, etc. etc.) If you have a 2-person party, a single pair monster (or two party monsters, or 4 gang monsters or 8 mobs, mix-and match as you like) should give them an equivalent challenge to a 4-person party fighting a single solo, etc.

 

[miggyG777]

I think it works fine as long as you keep in mind the numbers are balanced around the assumption of a 4-person party. That means “solo” monsters should be outnumbered by PCs 4:1, “pair” monsters should be outnumbered 2:1, “party” monsters should match the PC party size 1:1, “gang” monsters should outnumber the party 2:1, and “mob” monsters should outnumber the party 4:1. Roughly. So, like, if you have a 7-person party, a solo monster should probably be accompanied by a party monster and a gang monster, or by 3 gang monsters (or 6 mob monsters, or 2 gangs and 2 mobs, etc. etc.) If you have a 2-person party, a single pair monster (or two party monsters, or 4 gang monsters or 8 mobs, mix-and match as you like) should give them an equivalent challenge to a 4-person party fighting a single solo, etc.

I tested this workaround and it works reasonably well for party sizes <4. But sometimes you just want to build a solo monster for a >4 player party and then it doesn't work anymore.

 

[Charlaquin]

I tested this workaround and it works reasonably well for party sizes <4. But sometimes you just want to build a solo monster for a >4 player party and then it doesn't work anymore.

Gotcha. Yeah, that table doesn’t really equip you to easily design monsters to be fought on their own by groups larger than 4 or 5.

 

[miggyG777]

While playing around with the numbers I noticed that there are some inconsistencies with the rule:

A CR X monster is a medium challenge for 4 * lvl X PCs​

I am not sure if that rule is actually stated somewhere in the DMG or if it's just in my imagination.

Example:

A level 15 PCs XP Threshold for a medium encounter is @ 2800XP
So 4 level 15 PCs have a Threshold of 11200XP.
However 11200XP is slightly lower than a CR 14 monster according to the DMG.

Where does this discrepancy come from? What am I missing here.

 

[NotAYakk]

That math I did just makes it easier to use existing monsters to build encounters.

I still want to run the numbers on PCs and see if I can model them similarly to be able to generate updated EBP for a more optimized PC.

I mean, take the featless itemless fighter.
L1 16 14 con str, longsword, shield, chain. 18 AC, 1d8+5 damage. 12+1d10+2 daily HP, +2d10+2 from short rests.
L2 3 action surge/day
L3 19-20 crit range, 19 AC
L4 18 str
L5 2 attacks
L6 20 str
L7 20 AC
L8 16 con
L11 3 attacks
L12 18 con
L14 20 con
L15 18-20 crit
L17 6 action surge/day
L18 regen
L20 4 attacks

Second wind gives 3HP/day/level. HD grant 11.5+con*2 HP/day/level.

A spreadsheet with total HP budget, per "day" damage, and base DPR would give some interesting numbers. And be pretry accurate up to L 18 (where regen messes it up).

 

[miggyG777]

That math I did just makes it easier to use existing monsters to build encounters.

I still want to run the numbers on PCs and see if I can model them similarly to be able to generate updated EBP for a more optimized PC.

I mean, take the featless itemless fighter.
L1 16 14 con str, longsword, shield, chain. 18 AC, 1d8+5 damage. 12+1d10+2 daily HP, +2d10+2 from short rests.
L2 3 action surge/day
L3 19-20 crit range, 19 AC
L4 18 str
L5 2 attacks
L6 20 str
L7 20 AC
L8 16 con
L11 3 attacks
L12 18 con
L14 20 con
L15 18-20 crit
L17 6 action surge/day
L18 regen
L20 4 attacks

Second wind gives 3HP/day/level. HD grant 11.5+con*2 HP/day/level.

A spreadsheet with total HP budget, per "day" damage, and base DPR would give some interesting numbers. And be pretry accurate up to L 18 (where regen messes it up).

Wouldn't you have to model every class / build to get an accurate picture though? Or is there an underlying pattern that can be used?

Couldn't one just model the "XP Thresholds by Character Level" on DMG p. 82 to get a more accurate player EBP? WotC must have based that table on something.
Since "A CR X monster is a medium challenge for 4 * lvl X PCs" seems to be a rather rough guideline and doesn't hold up with the numbers.

 

[Coroc]

That math I did just makes it easier to use existing monsters to build encounters.

I still want to run the numbers on PCs and see if I can model them similarly to be able to generate updated EBP for a more optimized PC.

I mean, take the featless itemless fighter.
L1 16 14 con str, longsword, shield, chain. 18 AC, 1d8+5 damage. 12+1d10+2 daily HP, +2d10+2 from short rests.
L2 3 action surge/day
L3 19-20 crit range, 19 AC
L4 18 str
L5 2 attacks
L6 20 str
L7 20 AC
L8 16 con
L11 3 attacks
L12 18 con
L14 20 con
L15 18-20 crit
L17 6 action surge/day
L18 regen
L20 4 attacks

Second wind gives 3HP/day/level. HD grant 11.5+con*2 HP/day/level.

A spreadsheet with total HP budget, per "day" damage, and base DPR would give some interesting numbers. And be pretry accurate up to L 18 (where regen messes it up).

Wow, just wow. I often create custom mobs (in not reskinned MM mobs) and in most cases I manage to put up a challenging fight and I roll out in the open. But that kind of analysis ...

So I got a little task for you just out of curiosity:

How many mobs of which CR would it need to create a TPK for a level 20 4-man let us say fighter-rogue- cleric-mage party with a 90% probability?

 

[NotAYakk]

Wouldn't you have to model every class / build to get an accurate picture though? Or is there an underlying pattern that can be used?

At a first iteration, you can assume D&D designers balanced the classes.

So I say we pick one of the easiest classes to model, and work out the characters total HP soak and damage over a "typical adventuring day" (well, "burst damage" and "at-will damage" as two separate values).

Paladin is also easy if we assume they use all their spell slots for smite. They have HP, HD, Lay on Hands, at-will weapon attacks, ASIs that are a bit slower than the fighter, and smites.

The next time I have 20 minutes free with a spreadsheet I'll plot it out.

Wow, just wow. I often create custom mobs (in not reskinned MM mobs) and in most cases I manage to put up a challenging fight and I roll out in the open. But that kind of analysis ...

So I got a little task for you just out of curiosity:

How many mobs of which CR would it need to create a TPK for a level 20 4-man let us say fighter-rogue- cleric-mage party with a 90% probability?

No can do. What I'm doing is analyzing encounter building math. I'm not doing PCs yet.

The point of the encounter building math to me is being able to reliably build encounters with a wide variety of monsters that are reasonably on-target in difficulty, relative to other encounters built differently.

I'm at this point trying to emulate the D&D 5e DMG math, but doing it without having to use their specific awkward system.

So I can build encounters with a Hydra, or a bunch of Barbarians, or some Harpies, or whatever. And they will be in the right ballpark.

I mean, take a published adventure where you fight 10 orcs and an orc chieftan. You drop it into a world where they are no orcs, and want to use a knight and a bunch of guardsmen.

Orc War Chief: CR 4 (36 EBP)
Orcs: CR 1/2 (8 * 10 EPP = 80)

Knight: CR 3 (28 EBP)
Guards: CR 1/8 (3 each)

116 - 28 = 88
88 / 3 =~ 29

So, try using Knight and 29 Guards as a swap in for an Orc War Chief and 10 Orcs. A bit of a pain, but mass Guards can be rolled. (sanity check: Orcs deal almost 2x damage of Guards and are more accurate. They have worse AC, but more HP, which is mostly a wash. Knight is weaker than the War Chief by a reasonable chunk.)

At 116, this is a level 10-11ish medium difficulty encounter.

It isn't the only way to do this, but it is one way. And I find this way really easy, once I get the base math right.

In addition, I can use this to scale an exiting encounter for more/fewer PCs.

---

The largest problem with PCs is that individual character optimization levels vary, and classes/builds vary in how much they can "full burn" for the 5 minute adventuring day style. So you'll have to get an idea of what kind of encounters your party can handle over a day. Once you have that, you can get an idea of what difficulty of encounters they can deal with.

 

[miggyG777]

The largest problem with PCs is that individual character optimization levels vary, and classes/builds vary in how much they can "full burn" for the 5 minute adventuring day style. So you'll have to get an idea of what kind of encounters your party can handle over a day. Once you have that, you can get an idea of what difficulty of encounters they can deal with.

Isn't this reflected in the "XP Thresholds by Character Level" (DMG p. 82) table? This should theoretically be a model of what an average party can handle. If you take that table into consideration when calculating Party EBP with your model, rather than assuming 4x lvl X PCs => 1x CR X is a Medium encounter, what extra benefit does the modeling of the PCs give?

I am repeating myself but I find this an important point to understand.

 

[NotAYakk]

Isn't this reflected in the "XP Thresholds by Character Level" (DMG p. 82) table? This should theoretically be a model of what an average party can handle. If you take that table into consideration when calculating Party EBP with your model, rather than assuming 4x lvl X PCs => 1x CR X is a Medium encounter, what extra benefit does the modeling of the PCs give?

I am repeating myself but I find this an important point to understand.

Sure. We have to take 4 PCs budget, raise it to the 2/3 power and divide it it by 2.8, then divide by 4, to get 1 PC's budget in EBP. You have to do it in clumps of 4, because that is basically what the "zero point" of number of monster scaling is. That'll give the medium budget for medium values.

PC_EBP = ((Party_XP^(2/3))/2.8)/4
4*PC_XP = Party_XP
PC_EBP = (((4*PC_XP)^(2/3))/2.8)/4
PC_EBP = (((PC_XP)^(2/3))* 4^(2/3)/2.8)/4
PC_EBP =~ 2/9 * PC_XP^(2/3)

Level 1 PC easy EBP: 1.9
Level 1 PC medium EBP: 3
Level 1 PC hard EBP: 4
Level 1 PC deadly EBP: 4.8

That is close enough to 2/3/4/5 for my taste.