# How do I account for attack distribution when calculating CR?

When calculating a monster's CR, how do I account for whether the monster deals all its damage in one attack or via several attacks?

Based on the DMG, it doesn't matter how the damage is distributed, in a single attack or multiple. Yet I find that a CR2 creature is far more threatening if it does 20 damage per hit, than two hits for 10 damage each.

Analyzing this over 3 rounds, let's say at 50% chance of hit, there's a 12.5% of the worst case scenario (hitting thrice for 60 damage) for the single attack, while for two attacks it's merely 1.6% (and 3% for 5 or 6 hits). In other words, the max damage per round for 97% of the cases would be 40.

Of course the average is balanced by the higher chance of not hitting at all, but it feels that the maximum is more indicative of the difficulty of an encounter.

It also seems that as the CR goes up, creatures generally have multiattack. Of course, this provides the flexibility to attack more creatures, but it also provides a more uniform distribution of damage.

How do I account for attack distribution when calculating CR?

I'd say that having one instead of two attacks is roughly equivalent to 20-50% damage increase (possibly reduced if the monster is meant to be encountered in groups and depending on the to hit and expected AC); but I haven't actually tried using this as a rule of thumb.

• It would be useful, in framing this question, if you offered an example AC that the monster is trying to hit. DPR is sensitive to armor class. (The comparisons between GWM and Two Weapon Fighting here at RPG.SE have an answer or two that shed some light on that) – KorvinStarmast Nov 29 '18 at 22:45
• This seems like a XY Problem, but I'm not sure cuz it's still unclear what exactly is your problem or your question. – HellSaint Nov 29 '18 at 22:55
• Or are you actually trying to figure out why your lazors-firing scorpion seems to have TPK'd the party? :P - try to focus on your actual problem and what you are trying to understand, not on a problem you might have faced because of the solution you thought for the first problem. (if that makes sense) – HellSaint Nov 29 '18 at 22:58
• @HellSaint the first one; whether it's advisable to consider the distribution of attacks when calculating CR (even if the DMG says no), and if people have come up with a formula/rule of thumb. – falsedot Nov 29 '18 at 23:05
• This seems like an excellent question to me. Potentially changing it to "How do I account for attack distribution when calculating CR?" Would make it more of an RPG.se style question. But the premise is good. – linksassin Nov 29 '18 at 23:53

By the DMG guidelines, no, the probability of damage does not change the CR of a monster, only the average does.

Now, for more experience-based stuff.

# First, a caveat

Actually, the more attacks you have, the more Gaussian the probability is, not uniform - an uniform distribution is actually quite the opposite, one which has equal probability of doing any amount of damage. What you probably mean is that the distribution has a lower variance.

Also, the actual PMF (probability mass function) of the damage depends on the damage dice. For example, an attack that deals 10d4 has a variance smaller than five attacks dealing 1d8. I will assume that for some reason you are using the average damage instead of actually rolling for it.

# The actual question

Okay, so, about your question. Less attacks do not make the combat easier or harder, it makes the combat more swingy. Yes, there is a higher probability that you will deal max damage, but there is also a higher probability that you will deal no damage, which would be an incredibly easy combat. That means concentrating the damage on one attack makes good rolls really good and bad rolls really bad.

In D&D, and in particular for 5e, higher variance compromises low level parties and is indifferent at higher levels. As you mentioned, in early levels (CR2 for example) a creature dealing 60 damage in 3 rounds could potentially kill one member of the party or force the party to spend a huge amount of resources. On the other hand, since the damage does not increase as fast as the PC's HP does and the party has more recovery resources at higher levels, three rounds of hitting damage is not that threatening to a 10th+ level party.

For really low CRs (1-), monsters don't have multi-attack because their damage output is already low (1d8 or less).

For higher CRs, a good reason for multi-attack is exactly to provide a lower variance in the attack hits. It wouldn't be too fun for me, as a DM, if my CR 10 creature did one thing in its entire round and it failed, doing virtually nothing. On the other hand, "The dragon tries to bite you and misses, but then he quickly uses his claws while you were still dodging the bite and gets you" at least gives me something to narrate.

So, if you are looking for a rule of thumb, mine is: Swingy dice are bad. Save or suck features are not good when put against the PCs, because one "suck" for a PC might be really, really bad and unfun for that player. For more on why I think swingy dice are bad, read about Goblin Dice.

As others have said, single strong attacks can make combats swingy. However, there's one more thing to keep in mind.

# A single attack roll is much easier to interfere with

There are many examples of this, such as rogue's Uncanny Dodge, the Protection fighting style, a Divination Wizard's Portent, the Lucky feature, the Mirror Image spell, and so on.

So depending on what the party has, enemies with high damage single attacks can either be completely trivial as their one attack roll is sabotaged even when they do hit, or extremely swingy and lethal if the party doesn't have the tools and gets unlucky. The CR of such a creature might be deceptive.

There are more things to consider than "did I hit 3 times" and that is why CR can not take the attack distribution into account.

• In the same way that the chances of hitting all 3 are increased, so are the chances of missing all 3.
• Having 6 attacks instead of 3 attacks doubles the chance of getting a critical hit, though the reduced damage per hit halves the impact of getting a critical hit.
• Hitting a Character who has 10 HP left for 20 HP is no more deadly than hitting them for 10 HP. 6 characters with 10 HP left would much prefer to face a monster with 3 x 20 HP attacks than 6 x 10 HP attacks.

As you can see, all these comparisons are situational. 20 HP in one hit is not always better than 10 HP in two hits.

As for the maths on chances to hit.
Damage by attempts by chance to hit

\begin{align} 20 \cdot 3 \cdot 0.5 = 30 &\hspace{20pt}\text{vs.}&10 \cdot 6 \cdot 0.5 = 30 \\[5pt] 20 \cdot 3 \cdot 0.15 = 9&\hspace{20pt}\text{vs.}&10 \cdot 6 \cdot 0.15 = 9 \end{align} The damage per round is the same for the same AC (chance to hit)

• Your math is saying one thing but your examples are saying another. The third point shows why distribution should be considered. – linksassin Nov 30 '18 at 5:45
• "Having 6 attacks instead of 3 attacks doubles the chance of getting a critical hit" isn't true – kviiri Nov 30 '18 at 7:16
• @kviiri I think Luke was trying to say that it doubles your chance of getting a crit in a single round, which is true. – illustro Nov 30 '18 at 10:22
• @illustro No it's not. It doubles the expected number of crits but less-than-doubles the chance of getting at least a single crit. – kviiri Nov 30 '18 at 10:54
• @kviiri while not totally mathematically precise it's approximately true. Chance of at least one crit with 3 attacks is 14.3%. Chance of at least one crit with 6 attacks is 26.5%. That's close enough that to say it "doubles" your chance of getting a crit is approximately true. – illustro Nov 30 '18 at 11:01