D&D 5E Monster Math: CR1 vs CR½ - Quantifying the differences

[surfarcher]

Thanks [MENTION=6695890]ccooke[/MENTION] everything you are saying about the Imp and Quasit makes pretty good sense, on the surface. Now let's see how I go about enumerating it all, lol.

Yes, I'm aware of some of the situational issues between CR½ and CR1 Sometimes it's just properly understanding and then enumerating

Thanks for the quick response bro!

 

[surfarcher]

Basically, the Imp and quasit look weak, but they have a lot of abilities that can cause havoc in a party. There's nothing like them among the CR½ creatures

I'd draw this general rule out:

CR1 creatures often have the same basic combat statistics as CR½ creatures, but those that do will have situational abilities that make them tactically a much greater threat. Being situational, those abilities will not help them in every situation, but where they apply the threat level is much greater than a similar CR½ creature could provide. Every CR1 creature I've looked at has one (and not usually more than one) of:

• Better survivability than a CR½ creature
• Better pure mathematical offensive ability than a CR½ creature
• A much higher threat level when used in ambush than a CR½ creature
• A much higher threat level when paired with similar allies than a CR½ creature

OK so I'd assessed all the offensive capabilities correctly but had scaled up the significance of resistances at level 1.

The problem with that becomes the Shadow, of course. The main difference in practice between the Shadow and the Imp/Quasit is that the Shadow doesn't have a remove-from-play part of it's attack. But it is an ambusher and it's almost guaranteed to have at least one party member making death saves with 4 lost Strength by the end of it's second turn. All while it hides on the other side of a solid wall with a 1" opening. There's a very good chance it's Radiant vulnerability isn't even a problem for it since a god deal of level 1 parties don't have a radiant attacker.

Thoughts?

 

[ccooke]

OK so I'd assessed all the offensive capabilities correctly but had scaled up the significance of resistances at level 1.

The problem with that becomes the Shadow, of course. The main difference in practice between the Shadow and the Imp/Quasit is that the Shadow doesn't have a remove-from-play part of it's attack. But it is an ambusher and it's almost guaranteed to have at least one party member making death saves with 4 lost Strength by the end of it's second turn. All while it hides on the other side of a solid wall with a 1" opening. There's a very good chance it's Radiant vulnerability isn't even a problem for it since a god deal of level 1 parties don't have a radiant attacker.

Thoughts?

(Warning: Went overboard with maths. Apologies in advance)

The Shadow is definitely a strong CR½ creature. Obviously it's not unthinkable that it's too strong, but I'm going to assume for now that there's a sensible reason.

I think it's clear that we can compare the Shadow directly with both the Imp and the Quasit. They have a similar broad flavour - resistances, stealth, dangerous attacks. So is there any way to see that the Shadow is obviously less dangerous to a party than the CR1 creatures.

They all have similar resistances, and the Shadow has extra condition immunities
They have similar AC, and the Shadow has more hit points.

Thus far, it looks like the Shadow is stronger.

The shadow's base attack (pure damage) is a little stronger than the Imp or the Quasit.

Again, looks stronger.

Let's look at the special abilities.
The Imp has a decent chance of doing 3d6 poison damage. On a hit, it has a 6.6% (15% chance that a creature with proficiency and Con 20 will fail the save. 43.95% chance that the hit and poison damage will be enough to drop the PC to 0hp) chance of taking down the toughest (in terms of hit points) 1st level character it's possible to create¹. Against an average, non-front-line fighter - anyone with d8 hit dice, CON 12 and no proficiency with CON saves - the Imp will take them down in one hit 44.2% of the time.

The Quasit does less damage, but has a chance to impose disadvantage which is a huge penalty. It can't take down the toughest 1st level character in one hit, but it has a 27.5% chance of taking down an average non-front-line fighter. If that average character doesn't go down, they still have a 40% chance of disadvantage.

The shadow has a 41.67% chance of dropping an average 1st level character with its upfront damage alone. The Strength damage can be effectively discounted - yes, three lucky hits will kill a character with average strength instantly (3d4 will roll 10 or higher 15.62% of the time (or 5 times in 32)). However, at level 1 a single lucky hit from any of these will down any character short of a Barbarian or Fighter with a good Constitution; two hits are likely to down anyone. The Strength damage is only truly worrying if the Shadow rolls unusually poorly for damage, or when the party are at a high enough level to be able to survive three average hits without dropping. By that time, the shadow will be dropping in one or two hits from the party, which makes it most likely used as an ambush, or to make an already bad situation worse.

Ultimately, I'd say that the Shadow is about on par with the Imp and Quasit, there.

Which puts the Shadow ahead on survivability and roughly tied for offence.

So let's look at the tactical abilities.

The shadow is a decent Ambush attacker and, with its ability to hide in darkness or dim light, it has some ability to prolong a fight be continuing to attack from hiding. Using this, it could possibly gain advantage every round (using a Bonus action to hide). However, the party are extremely likely to be able to negate this ability. The chances that even a level 1 party has no sources of light at all - especially the light spell - are extremely low, and as soon as there is light the Shadow is unable to make use of its ability to hide well. Yes, it can skulk at the edges of the light's area, but it has no ranged attacks and would need to close to melee range to attack. Thus, while it may get one good ambush round in, it is unlikely to be able to gain advantage on any subsequent round unless there is a highly unusual conflux of circumstances

Both the Imp and the Quasit can become invisible at will. This allows them to draw out combats to a much greater extent. In addition to their surprise round, they will be able to attack with advantage every other round. It is entirely possible that a 1st level party will have no clear way to counter invisibility at all.

I think that's the clear cutoff. The Shadow can be a terrifying ambush, but even a 1st-level party will almost always be able to counter its tactical advantages, whereas countering invisibility cannot be guaranteed in even a higher level party, so the threat of the Imp and Quasit is multiplied.

I'm discounting the Shadow's vulnerability to daylight here - yes, it's a factor against the Shadow, but the DM will simply not use them in daylight. If the party has and casts daylight, that's fine, but it's a situational ability that does not detract from the Shadow's power. Ditto the vulnerability to radiant.


¹ The toughest (in terms of hit points) possible 1st level character² is a Barbarian with rolled 18 Constitution and either the Hill Dwarf (+2 CON, +1hp/level) or Human(Variant) with the Tough feat (+2hp/level). That character would have 17 hit points at level 1.
² Yes, this is a challenge. I'm curious to see if I missed anything

 

[surfarcher]

Thanks again for your response [MENTION=6695890]ccooke[/MENTION] !

(Warning: Went overboard with maths. Apologies in advance)

No you didn't. There's no such thing in this thread! Well... I probably won't get bogged down in 4e-style DPR calculations. But the level of math you posted is perfectly fine ;-)

A while ago (pre-PHB release) on a WotC community thread a number of us worked through various stats on PCs. We came up with average L1 PC hitpoints at 10.25. For "removed from play" effects I have been using that value, however it may be more compelling to use it with a 1.5 multiplier, to take into account tougher PCs. I'm going to trial that today.

The way I currently view the three monsters in question...

Defensively...

• Imp overall score 30
  Defensively: 14.71. This includes it's HP, AC, saves, resistances, immunities, invisibility and shapechanging. Plus an assumption that it gets about 50% Advantage on defensive thanks to Magic Resistance.
  Offensively: 15.38. It has a NAD of 13.38 and a slightly above average to-hit. Devil's Sight should be used to give it a tactical edge, which I've factored in as equivalent to another +2 to hit.
• Quasit overall score 24
  Defensively: 10.46. Includes HP, etc in the same way as the Imp. It's asumed to get about 75% Advantage on defence because of Magic Resistance and the assumption that it's poisoned an attacker about half the time. Because of it's low hitpoints the Advantage boost to defences doesn't cause so much swing.
  Offensively: 13.13. NAD of 13.13 is decent thanks to Scare basically doing a 50% removed from play. To-hit is average for CR.
• Shadow overall score 34
  Defensively: 23.8. It's got more in the way of immunities/resistances than the other two above and many more HP. That's even without Invisibility/Shapchanger.
  Offensively: 10.00. It has a NAD of 9 and also has an average to hit against a L1 PC. I have factored a +1 to actual damage to reflect the Str damage but removing this doesn't significantly change it's overall ranking.

So let's look at the tactical abilities.

Very important! We definately need to understand these critters to do them service in play... and in analysis.

I think you may be undervaluing the Shadow's trait Amorphous. This should be used with appropriate terrain to make it skirmshy. However, I don't disagree with what you are saying about the three overall.

I have another idea though. It's not fully formed, but it's about factoring in alpha type damage. Basically if a monster has either standard or spike damage that exceeds say 1.25x the average HP of a same-level PC then we should give their offensive index an additional bump. As I said the idea is rough and I haven't worked through the details, but it does seem as though it may provide the appropriate differentiation.

 

[ccooke]

Very important! We definately need to understand these critters to do them service in play... and in analysis.

I think you may be undervaluing the Shadow's trait Amorphous. This should be used with appropriate terrain to make it skirmshy. However, I don't disagree with what you are saying about the three overall.

I don't think so. Yes, it's situational just like the ability to hide or turn invisible, but it's something that provides more flavour than tactical ability.

Think about it this way: The situationality (abuse of language is a fun game) of an ability falls into several categories and there's a lot of subtlety involved, but I think there's a reasonable way to rank them:

1. Abilities which are negated only by extreme misfortune or planning
2. Abilities which may be negated by reasonable tactical choices
3. Abilities which will only be useful in extremely fortunate or planned-for ambushes.

Against a level 1 party, invisibility is rank 1.
Being able to hide on a bonus action is rank 2.
Amorphous is a rank 3 ability - in order for it to be tactically useful in a fight, the Shadow needs some place to squeeze through that provides it with an advantage. How often does that come up in real games? At the point where an ability is only truly tactically useful when the DM designs an encounter to facilitate it, I believe it's safe to call that ability weakly situational.

This of course does not mean that such an encounter would be bad, or should be discouraged, or anything of the sort - it's merely a reason why I believe the Shadow actually is CR½.

This is the inverse of the reasoning I discounted the Shadow's weakness to sunlight as a detriment to its danger. It's a rank 3 weakness - powerful if it comes up, but the party will generally not be able to take advantage of it. Shadows simply won't be used much during the day, or near the open sun.

I have another idea though. It's not fully formed, but it's about factoring in alpha type damage. Basically if a monster has either standard or spike damage that exceeds say 1.25x the average HP of a same-level PC then we should give their offensive index an additional bump. As I said the idea is rough and I haven't worked through the details, but it does seem as though it may provide the appropriate differentiation.

Yes, that sounds like a useful thing.

How are you ranking creatures according to their more situational abilities?

 

[surfarcher]

I don't think so. Yes, it's situational just like the ability to hide or turn invisible, but it's something that provides more flavour than tactical ability.

Think about it this way: The situationality (abuse of language is a fun game) of an ability falls into several categories and there's a lot of subtlety involved, but I think there's a reasonable way to rank them:
...snip...

Sure and I agree with your ranking. I'm also happy to consider Amorphous trivial. Now if I can find some compelling reason to dock the Shadow some freaking HP... lol.

Yes, that sounds like a useful thing.

With that and the "removed from play" multiplier tweaked the vast majority of CR1 and CR½ monsters are separated. There are only a few with some overlap, which I'd be happy to live with.

The damn Shadow standing out in the graphs offends my sensibilities though, lol.

How are you ranking creatures according to their more situational abilities?

There are a number of ways, it's up to the person doing the assessment. They can factor it into the NAD calculation (like with the attack-save-attack pattern). There are four adjustment pools that roughly correspond to base HP pool, AC/save, damage and To-hit/accuracy. And finally there are the offensive/defensive Advantage/Disadvantage percentages.

 

[ccooke]

Sure and I agree with your ranking. I'm also happy to consider Amorphous trivial. Now if I can find some compelling reason to dock the Shadow some freaking HP... lol.


With that and the "removed from play" multiplier tweaked the vast majority of CR1 and CR½ monsters are separated. There are only a few with some overlap, which I'd be happy to live with.

The damn Shadow standing out in the graphs offends my sensibilities though, lol.

So, again, let's compare two creatures - this time the Shadow with the Thug.

The Thug has 32 hit points. The Shadow has 16, but with its resistances you can call it 32. So, that's basically the same.
The Thug is AC 11, the Shadow AC 12 - slight advantage to the Shadow, there.
They're both at +4 to hit. The Thug gets two attacks at +4, doing 1d6+2 each. The Shadow gets one attack doing 2d6+2 and some strength damage. I'm discounting the strength damage again for the reasons in my previous post - it's there to be scary, not to actually kill people (nice design there, actually).

The thug isn't stealthy. A pair of thugs are probably going to go straight for someone they want to lynch and have at it. However, they get pack tactics... which means they're going to be attacking with advantage. Most of a level 1 party is going to have an AC of 15 or so, and with advantage the thug will hit that 75% of the time. I hesitate to go for DPR calculations, but in this case it does make sense. Assuming an AC of 15 and the ability to use advantage every round, the thug is going to do about 8.25 damage every round. The shadow does 4.5, or 6.75 when it has advantage. The shadow can be expected to get a surprise round with advantage, but is unlikely to get be able to hide once the party brings out some light sources. Maybe two rounds with advantage, but almost certainly not three.

So: The Shadow is fractionally more durable than a Thug. However, it can expect to get about 75% the damage output of a Thug during one or if it's lucky two surprise rounds, after which it will be doing 50% of the thug's damage. The condition immunities, strength damage and situational abilities are the only thing that rescue it from looking underpowered in this analysis.

So, if the shadow is still an outlier... are you overestimating its power, or am I missing something?

There are a number of ways, it's up to the person doing the assessment. They can factor it into the NAD calculation (like with the attack-save-attack pattern). There are four adjustment pools that roughly correspond to base HP pool, AC/save, damage and To-hit/accuracy. And finally there are the offensive/defensive Advantage/Disadvantage percentages.

I wonder, how do you treat resistances? As an adjustment to the HP pool?

 

[surfarcher]

...snip...
So, if the shadow is still an outlier... are you overestimating its power, or am I missing something?

In the end I had modified a couple of constants that needed retuning. There's now clear separation, with 3 instances of overlap at index 27. The Thug is at 27, with the Quasit and Sildar Hallwinter. That's not an issue at this stage and a little more tuning might resolve them. Or not. There's enough clear separation to make the method viable.

I wonder, how do you treat resistances? As an adjustment to the HP pool?

Ultimately as adjustments to AC/Saves, although there's a structured way to input and weight them. But these are more significant at lower levels. Assuming that works out at lower and higher CR than we have looked at here I'll have to build a scaling formula to cover the increased multiplier.

 

[ccooke]

In the end I had modified a couple of constants that needed retuning. There's now clear separation, with 3 instances of overlap at index 27. The Thug is at 27, with the Quasit and Sildar Hallwinter. That's not an issue at this stage and a little more tuning might resolve them. Or not. There's enough clear separation to make the method viable.

That's probably about right.
In this case, CR isn't just tracking pure threat level, it's tracking threat-level-by-level. Invisibility is a very powerful ability at low level. Or, to put it another way, imagine adding invisibility to any CR½ creature and still attacking a 1st level party with two of them - serious chance of multiple character deaths. CR1 in this case is telling the GM "Do not use two of these creatures against a 1st level party".

Ultimately as adjustments to AC/Saves, although there's a structured way to input and weight them. But these are more significant at lower levels. Assuming that works out at lower and higher CR than we have looked at here I'll have to build a scaling formula to cover the increased multiplier.

It might be better to look at resistance as a multiplier of hit points. Effectively, they boost the hit points by a multiplier between 1 and 2 depending on how likely a party of the relevant level can cut through the resistance; against a level 1 party, the Shadow, Imp and Quasit all effectively have double their hit points because the average party will not bypass resistance.

 

[surfarcher]

That's probably about right.
In this case, CR isn't just tracking pure threat level, it's tracking threat-level-by-level. Invisibility is a very powerful ability at low level. Or, to put it another way, imagine adding invisibility to any CR½ creature and still attacking a 1st level party with two of them - serious chance of multiple character deaths. CR1 in this case is telling the GM "Do not use two of these creatures against a 1st level party".

Agreed.

It might be better to look at resistance as a multiplier of hit points. Effectively, they boost the hit points by a multiplier between 1 and 2 depending on how likely a party of the relevant level can cut through the resistance; against a level 1 party, the Shadow, Imp and Quasit all effectively have double their hit points because the average party will not bypass resistance.

OK so it's like MM tweeted at the end of August, CR is about defensive (ac,hp,etc) and offensive (damage,to-hit,etc) capability. But how do you break down both aspects? Using statistical indexing you have additive pools and adjustors. In D&D we do this kind of thing in DPR calculations - multiplying average damage by chance to hit, etc. I'm simply doing the same kind of thing with defenses. AC/saves derive to a multiplier that's applied to the HP pool. Currently I am treating resistances/immunities the same. So they act to multiply HP as part of an adjustor... For now.

This way it's easy to enumerate the multiplier at level 1 with weightings by type, something like this...

n=(2×Num_Immunities + Num_Resistances + 0.25×Num_Condition_Immunities) × Level_Multiplier × 0.05​

And the result is added to the HP pool multiplier before it's applied to the HP pool.

So multiple immunities stack up fast, multiplying HP fast... depending on level. Level_Multiplier should decrease as level increases. Right now 3 is working well for level 1.

And yes, you are quite right. This may not hold up in the end. So far it's working perfectly for CR0 through CR1 though. My planned fallback is a multiplier % field for the HP pool that gets applied before adjustors. Not very scientific though.