5E Encounter difficulty: how to fix it.

Gobelure

Visitor
First, I would like to stress that I love the way 5E is going up to now. A lot of effort was put to provide a game that is both rich in possibilities and at the same time simple to run. Well done ! However, when it comes to encounter building, there is a huge level of complexity which gets added and it is almost impossible to handle it without a computer. Even if there are really usefull apps already available, I want to be able to run a game offline, just with pencil and paper. The game is easy to run, and encounter building should be as easy. Fortunately, after some thought I came with a simple way to implement this.


But first, an important disclaimer : already with previous versions, encounter balancing was more an art than a science. My impression is that with 5E it is even more true: depending on the PCs tactics and on the monster synergies, a single number representing the encounter challenge can at best be indicative. CR is not the ultimate truth, so please don't complain if on a given encounter for a given group you find it way too easy or too hard. That's just 5E life !


In the following, I will assume that the DMG Basic rules for encounter building are providing the best guess, and I only will tweak the math to achieve two goals. The first one is to make it simpler. The second is to cure the "3 rats and a lich" bug, which basically says that a CR21 lich in company of 3 rats is as tough as a CR24-25 monster. So, for pack of monsters of almost the same level, my system will retrieve the difficulty rating of official rules, where it will improve it for wildly different CR mix. Plus: you forget forever about encounter XP mutipliers.


The simple way to compute encounters challenge


Philosophy of the method is :
1. Forget XP for encounter building, only use power equivalent levels (or PELs)
2. Compare PELs for PCs and PELs for monsters and deduce the lethality of the enounter.


Player Characters PEL :
PC equivalent level is almost player level, with only a few exceptions. Use the table below


Player levelPEL
11
21.5
32.5
43
55
66
77
88
99
1010
1111
1212
1313
1414
1516
1618
1720
1822
1924
2026


Monsters PEL :


Convert each individual monster CR to it's EL using the following table




Monster CRPEL
01/3
1/82/3
1/41
1/21.5
12
24
36
48
511
613
715
818
921
1024
1128
1232
1336
1440
1544
1648
1752
1856
1960
2064
2176
2288
23104
24120
25136
26152
27168
28184
29200
30216

Encounter challenge :


a. Sum up all PCs PELs get the Total Party Equivalent Levels (TPEL)
b. Sum up all monsters PELs to get the Total Monster Equivalent Levels (TMEL)


Encounter is easy(*) if TMEL ~ 40% to TPEL
Encounter is medium if TMEL ~ 60% to TPEL
Encounter is difficult if TMEL ~ 80% to TPEL
Encounter is deadly if TMEL ~ 100% to TPEL


(*) Assuming Easy is 25% of XP with respect to deadly… The table provided in the DMG preview has however an inconsistent definition of easy across levels. Not a big deal, you can just ignore it. What matters is to have a TML lower than the TPL. The lowest, the easiest.

Summary PDF

Dnddungeoneer made an awesome PDF out of these table. Check it out !
Player Level Charts.pdf


Example :

A CR21 lich and 3 rats is PEL 76 + (1/3)*3 = 77, so basically… a lich !



The math behind the scene :

This section is only meant for math-oriented people.
[sblock]
What did I do here ?


First, I realized that the Encounter XP scales as the number of monsters to the power 3/2.
Indeed, XP for 4 monsters is 4 times the base XP, times 2 for 4 monsters. Total : 8 times the XP, which is 4^3/2. It also works approximatively for other numbers of monsters.


Second, I checked that the strength of a PC group scales with the number of PCs to the power 3/2.
If I have a deadly encounter opposing 4 PCs and 4 monsters, it means than the individual monster XP is half that of the PC deadly scale (4 times deadly scale divided by 8, see above).
Then, a deadly encounter for 2 PCs will be 2 such monsters. It seems just logical, but let's check : 2 monsters is twice individual monster XP, and the multiplier is 2 as I have only 2 PCs : total multiplier is x4, which makes the encounter deadly for 2 PCs. Hurrah, the system is consistent.
As PCs strengh with number scales as monster strength, it is fair to assume that the power of PCs scale as their number to the power 3/2.


At the same time, it means that the XP value for a PC is the half the deadly encounter XP !


Now, is is just a matter of rescaling: saying that A N^3/2 = B M^3/2, is equivalent to state that A^2/3 N = B^2/3 M. In other words : instead of taking some crazy math according to monster numbers relative to PCs numbers, just do simple addition, and precompute the corrected XP scale to make it fit.


The formula I used for my tables above is thus PEL = (XP/49)^(2/3), approximated up to 10% to get numbers easy to remember.
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Elric

Visitor
Great analysis. The key is that in your new tables PC and monster power scales more slowly with CR/levels, so that you don't need the "fudge factor" of a multiplier. You don't explain that as directly as you could. Here's how I put it in another thread, feel free to use any of the wording.

Elric said:
It seems to me that PC and monster power doesn't scale as fast in general as the XP numbers alone would imply (e.g., a CR 5 Hill Giant worth 1,800 XP is not as deadly as 4 CR 2 Ogres worth 450 XP each). So large numbers of lower CR monsters would be too strong relative to what the XP total suggests.

The encounter XP multiplier (basic DM guide, p. 57) helps to address that design flaw. However, the XP multiplier is itself flawed (as an encounter with an Adult Red Dragon and 3 Kobolds demonstrates).

My take is that some monsters are particularly dangerous in groups (e.g., with their own kind, like Intellect Devourers, or with any melee combatant, like Hobgoblins). Those should have been handled with special guidelines in their stat blocks (CR varies based on group composition), and XP should have simply scaled more slowly as CR increased (with the corresponding decrease in the XP budget encounter guidelines), thus obviating the need for a multiplier.
Also, one unfortunate typo:
Encounter is easy if TMEL ~ 100% to TPEL
Should be "deadly."
 
I will look this over and perhaps give it a try. I like it because it doesn't assume a party of a given size OR that everyone in the party will be the same level. :)
 

DM Howard

Explorer
Encounter is easy(*) if TMEL ~ 40% to TPEL
Encounter is medium if TMEL ~ 60% to TPEL
Encounter is difficult if TMEL ~ 80% to TPEL
Encounter is easy if TMEL ~ 100% to TPEL


(*) Assuming Easy is 25% of XP with respect to deadly… The table provided in the DMG preview has however an inconsistent definition of easy across levels. Not a big deal, you can just ignore it. What matters is to have a TML lower than the TPL. The lowest, the easiest.
I think I like this, however ~100% of TPEL means it would be very hard (right?) not easy?
 
Nice analysis.

I think your PEL for NPCs is way off(assuming NPC=PEL, if not ignore since we dont know true NPC equivalents). Even looking at some of the NPCs in the MM or supplements, they are not close to the same as your PEL. Heck, I think a 8th level caster is like a CR3.

Dont see how this is any easier or quicker than adding up the monster XP and referring to a chart?
 

Skyscraper

Visitor
Interesting stuff.

Back in the old AD&D days, where monsters had a level scaling from I to X (in roman numbering, mind you!), there were no encounter building rules. You had to follow your gut feeling.

I plan on trying to do just that in a conscious effort to move away from a math-oriented approach. Use intuition. This will of course yield some easy fights and some tough fights. And some of those will be unexpectedly easy or difficult. I think this is desirable.

I think that CR and hit dice are valuable, albeit very general, indicators of a monster's difficulty level. This allows a DM to sieve through the list of monsters more quickly. But otherwise, back with good ol' DM intuition. This is what D&D is all about baby! :)
 

Elric

Visitor
I also made a quick PDF for those who prefer landscape like I do since I have the Customizable GM Screen.
This chart is missing the guide to determining what's an easy vs. hard encounter, which seems like it would be useful to have in the same place

Encounter is easy if TMEL ~ 40% to TPEL
Encounter is medium if TMEL ~ 60% to TPEL
Encounter is difficult if TMEL ~ 80% to TPEL
Encounter is deadly if TMEL ~ 100% to TPEL
I think your PEL for NPCs is way off(assuming NPC=PEL, if not ignore since we dont know true NPC equivalents). Even looking at some of the NPCs in the MM or supplements, they are not close to the same as your PEL. Heck, I think a 8th level caster is like a CR3.
NPCs in this system should be treated based on their CR, not based on the PC table.
 
Nice analysis.

I think your PEL for NPCs is way off(assuming NPC=PEL, if not ignore since we dont know true NPC equivalents). Even looking at some of the NPCs in the MM or supplements, they are not close to the same as your PEL. Heck, I think a 8th level caster is like a CR3.

Dont see how this is any easier or quicker than adding up the monster XP and referring to a chart?
I think the intent was that NPCs would be using the monster CR chart. The PEL chart is for PCs only (if I am reading it correctly).

The advantages I see are for mixed level parties. In the standard system, figuring out an encounter for 3 3rd level, 3 2nd level, and 1 1st level party members is quite the chore.
 

Joe Liker

Visitor
Do I understand correctly that this system ignores the number of monsters and computes only their total "threat level"?

If so, that's a dramatic flaw. With bounded accuracy, the number of combatants on either side is a hugely important consideration in estimating the difficulty of the encounter. A single giant is much, much easier to take down than an equivalent number of goblins, and is far less likely to KO one or more party members.
 

drjones

Visitor
Yeah I appreciate the effort to simplify things but to prove that it 'works' reliably in a wide variety of encounters vs. a wide variety of parties will take significant testing.

If the goal is to have portable, paper only DM tools, why not make a generic set of 10, 20 'standard' encounters for your expected party size with generic monsters by CR level while you have the tools available and note them on a sheet. Then plop in monsters that fit your encounter idea and tweak it till it matches one of the templates that you know approximately works. Like if you have 4 level 5 pcs you know 1 CR 5 or 4 CR 1 should be Med difficulty. It will be limiting on how complex things can get but if it's not enough, sites like http://kobold.club/enc/#/encounter-builder are there to help get complicated.
 

Tormyr

Adventurer
Someone at Wizards are going: "doh" now, like in, "why didn't we think of this". :D
They probably did come up with something similar. They question is: "Why did they not use it?"

Do I understand correctly that this system ignores the number of monsters and computes only their total "threat level"?

If so, that's a dramatic flaw. With bounded accuracy, the number of combatants on either side is a hugely important consideration in estimating the difficulty of the encounter. A single giant is much, much easier to take down than an equivalent number of goblins, and is far less likely to KO one or more party members.
The PEL scales both with number of PCs or monsters by a factor of 3/2. The end result is that it gives estimations of encounter difficulty that are similar to WotC's method, but it has a bias toward encounters being easier than WotC's method. Most of that is probably in rounding errors as both the WotC's XP budget and the PEL round a bit.

I don't see how this is all that much easier though. In either case, you have your Easy, Moderate, Hard and Deadly thresholds pre-calculated. Adding the numbers isn't really more or less difficult either way (as my Calculus teacher said, "anything above 4 is a big number"), but the pre-calc of XP budgets will take 4 times as long unless you calculate only the deadly and go for 25%, 50%, and 75% for the other thresholds. In the PEL method, you have to multiply by 40%, 60% and 80% for the other thresholds. There is a small time savings for PEL.

The total monster XP versus PEL is a wash.

Scaling the monster XP is a matter of looking at a table based on # of PCs and monsters and multiplying the XP by the number. Small time advantage for the PEL again.

Now the question comes as to is it fundamentally more or less accurate (hard to discern about guidelines, but what the heck). The PEL has a bias toward labeling encounters as slightly easier than the XP budget. For ease of calculation, I made the cutoffs for the difficulty thresholds right at 40%, 60% and 80%. 41%,61% and 81% read as the next difficulty up. This makes things read a little more difficult than the ~40%, ~60% and ~80% of the OP. Even with that, the assessment of encounter difficulty was coming out at the same or easier difficulty to the XP budget. This even happened with a standard 4 person party versus equivalent CR monster at CRs 3, 8, 9, and 10, where it labeled the encounter as 1 difficulty less than the XP budget. While these are probably accentuated by rounding differences at those particular levels and the fact that XP budgets for creatures are right around the moderate threshold for a standard 4 PC party, it might show a general bias toward labeling the encounter easier than it is.

The next thing is the most contentious. What is done about groups of monsters of varying CR. There are two schools of thought. One is that low CR monsters should not multiply the danger of a high CR monster, and the other is that all the monsters in an encounter should help multiply the total XP budget. I am of the thought that the answer is somewhere in the middle. If a 4 PC 20th-level party is attacking the lich, both systems label the encounter as hard, but if you add anything to the encounter, XP budget changes to say it is deadly, which is the substantial chance of character death.

So the question between either system becomes: "Can a small change like adding a few commoners (or more realistically a couple of CR2 or above creatures to survive fireballs) drastically change the difficulty of an encounter from hard to deadly or beyond deadly. PEL says no; XP budget says yes. The calculation is not really more or less difficult either way, and is no different for me since I use a spreadsheet. Even by hand, you are going to want a calculator for both to speed things up. But if one or the other is more indicative of the difficulty of an encounter more often, that is some real value.

I have several encounters tonight. They were built under the XP budget method. If they come out significantly easier than the XP method indicates, then the PEL method has some real value. Otherwise, it may be easier to calculate, but it does not give as good an indication of encounter difficulty.

My 2cp.
 

Elric

Visitor
Do I understand correctly that this system ignores the number of monsters and computes only their total "threat level"?

If so, that's a dramatic flaw. With bounded accuracy, the number of combatants on either side is a hugely important consideration in estimating the difficulty of the encounter. A single giant is much, much easier to take down than an equivalent number of goblins, and is far less likely to KO one or more party members.
The key is that this system lowers the number of Goblins that a Giant is equivalent to (as opposed to a standard where you compare a Giant to a number of Goblins worth the same XP, and do not consider the "Encounter XP multiplier" in the DM basic guide). That's why it doesn't have to consider the total number of combatants (separately from adding up the total threat level), and still achieves similar results to the original encounter guidelines.

The original post doesn't lay this out that well, which is why I attempted to do that here: http://www.enworld.org/forum/showthread.php?367697-Encounter-difficulty-how-to-fix-it&p=6402241&viewfull=1#post6402241
 
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Tormyr

Adventurer
The key is that this system lowers the number of Goblins that a Giant is equivalent to (as opposed to a standard where you compare a Giant to a number of Goblins worth the same XP). That's why it doesn't have to consider the total number of combatants (separately from adding up the total threat level), and still achieves similar results to the original encounter guidelines.
Actually it doesn't really. 15 goblins is the threshold for both systems for changing the difficulty from medium to hard for a 4 PC 6th-level party. This makes 14 goblins roughly equal to a cyclops in both systems. It does not always hold to be the same, but most of the time it is the same for a group of monsters of the same CR. Where things start varying to a greater degree is when the monsters are made up of different CRs.
 

Elric

Visitor
Actually it doesn't really. 15 goblins is the threshold for both systems for changing the difficulty from medium to hard for a 4 PC 6th-level party. This makes 14 goblins roughly equal to a cyclops in both systems. It does not always hold to be the same, but most of the time it is the same for a group of monsters of the same CR. Where things start varying to a greater degree is when the monsters are made up of different CRs.
Updated my post for clarity. This system does adjust the number of Goblins that a Giant is equivalent to, if you don't use the Encounter XP multiplier rule from DM Basic Guide p. 57, and that's why it can do away with the Encounter XP multiplier rule and achieve similar results.

The key is that this system lowers the number of Goblins that a Giant is equivalent to (as opposed to a standard where you compare a Giant to a number of Goblins worth the same XP, and do not consider the "Encounter XP multiplier" in the DM basic guide).
 

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