# D&D 5EMonster damage realization - DPR per CR diminishes across the game

#### Rabulias

##### the Incomparably Shrewd and Clever
Challenge Rating numbers are just labels, so deriving a value using them is only useful in comparing to other Challenge Ratings. As the lower CRs are fractions, math with them tends to exaggerate differences. If we recalibrate the CR labels so they start at 1 instead of 1/8, we get the following:
ADJUSTED CRDPRDPR PER CR
133.00
252.50
3103.33
4123.00
5173.40
6233.83
7294.14
8354.38
9414.56
10474.70
11534.82
12594.92
13655.00
14715.07
15775.13
16835.19
17895.24
18955.28
191015.32
201075.35
211135.38
221195.41
231325.74

Still a bit wobbly around the lower levels (going down, then up, then down again, then up again), but not so extreme looking, and hovering around 3.00.

#### ezo

##### Where is that Singe?
Challenge Rating numbers are just labels, so deriving a value using them is only useful in comparing to other Challenge Ratings. As the lower CRs are fractions, math with them tends to exaggerate differences. If we recalibrate the CR labels so they start at 1 instead of 1/8, we get the following:
ADJUSTED CRDPRDPR PER CR
133.00
252.50
3103.33
4123.00
5173.40
6233.83
7294.14
8354.38
9414.56
10474.70
11534.82
12594.92
13655.00
14715.07
15775.13
16835.19
17895.24
18955.28
191015.32
201075.35
211135.38
221195.41
231325.74

Still a bit wobbly around the lower levels (going down, then up, then down again, then up again), but not so extreme looking, and hovering around 3.00.
Except the CRs are established "as is" to be used for encounter creation, etc. Changing their values by relabeling them changes the corresponding DPR per CR because you are dividing by a new CR, which makes the results... well, sort of misleading.

Even given that, why are you starting at CR 1/8 (relabled to CR 1), instead of CR 0? I mean, if you are going to relabel it CR 1, you aren't dividing by 0... so???

#### Quickleaf

##### Legend
Challenge Rating numbers are just labels, so deriving a value using them is only useful in comparing to other Challenge Ratings. As the lower CRs are fractions, math with them tends to exaggerate differences. If we recalibrate the CR labels so they start at 1 instead of 1/8, we get the following:
ADJUSTED CRDPRDPR PER CR
133.00
252.50
3103.33
4123.00
5173.40
6233.83
7294.14
8354.38
9414.56
10474.70
11534.82
12594.92
13655.00
14715.07
15775.13
16835.19
17895.24
18955.28
191015.32
201075.35
211135.38
221195.41
231325.74

Still a bit wobbly around the lower levels (going down, then up, then down again, then up again), but not so extreme looking, and hovering around 3.00.
How did you end up with that table?

I'm just not recognizing your numbers from my own reading/rough analysis (such as the Forge of Foes, link to preview) , which is why I ask.

#### Ancalagon

##### Dusty Dragon
@Rabulias

I must admit it took me a moment to understand what you were doing. is your "adjusted" CR 1 a CR 0 or CR 1/8 creature? (I have more comments but I want to be sure I understand you)

#### Clint_L

##### Legend
I'd love to see what this chart looks like assuming a 2024 monk. Going by the current UA, that monk, naked, would have:

AC 25 (new capstone should give a dex of 26 and wis of 24)
HP 143 (assuming 14 con)
Evasion (with +14 to dex saves)
Resistance to all but force damage (superior defence)
Proficiency in all saving throws
Deflect attack, all damage types, 1/round for an average of 35 hp blocked

It's a lot. I'm currently playing a Mercy monk using the UA rules, and given her current equipment (ring of protection, bracers of defence, eldritch claw tattoo), at level 20 she easily solos an Ancient red dragon (hand of healing/harm means the dragon always has disadvantage, and the monk can heal an extra 41 hp on demand, not that she needs it in this scenario).

#### ezo

##### Where is that Singe?
This was fascinating to me, as my expectation would be the trend should go in the opposite direction – i.e. increasing damage per CR for monsters intended to challenge high-level characters.
Hey, you know, I just realized I never really posted my results concerning your OP. So, here's how it works out and the assumptions made:

CR 0 is not included, as you cannot divide a number by 0.

Tiers and CR:
• 0 (CR 0-0.5)
• 1 (CR 1-4)
• 2 (CR 5-10)
• 3 (CR 11-16)
• 4 (CR 17-20)
• Alpha (CR 21+)
Average PC Armor Class by Tier:
• AC 15: tiers 0 and 1
• AC 16: tier 2
• AC 17: tier 3
• AC 18: tier 4
• AC 19: tier A (alpha)
Using the Attack Bonus by CR listed on the Monster Statistics by Challenge Rating table (DMG p. 274), I calculated the probability of successful attacks given the Average PC Armor Class by Tier and its impact on average Damage/Round to weight the effective Damage/Round. Since this calculation involves an Attack Roll analysis, I've included the adjusted damage for rolling a critical hit as well, which has been factored into the effective Damage/Round.

Dividing the (effective) Damage/Round by the Challenge Rating, and calculating the average across the range of the tiers, we have:

Tier 0: 8.80 eDPR per CR vs. AC 15 (45.0% average hit probability)
Tier 1: 4.78 eDPR per CR vs. AC 15 (48.7% average hit probability)
Tier 2: 4.25 eDPR per CR vs. AC 16 (57.5% average hit probability)
Tier 3: 4.23 eDPR per CR vs. AC 17 (60.8% average hit probability)
Tier 4: 4.47 eDPR per CR vs. AC 18 (65.0% average hit probability)
Tier A: 6.85 eDPR per CR vs. AC 19 (71.0% average hit probability)

As you can see, from tier 1 to tier 4, the effective DPR against average AC remains within a range of 4.23 to 4.78 per CR. While not exactly very narrow proportionally, it is fairly consistent.

An interesting observation IMO is that despite average PC Armor Class increasing by tier, the average hit probability across the tier also increases! It it remained relatively constant, we could say that creature attacks "keep pace" with average PC Armor Class. However, it increases more than PC armor class to keep the effective DPR close.

The jump in eDPR in Tier A is due to the increased average hit probability, but moreso because we see increases in the maximum damage/round of 18 in most of this range, instead of just the 6 points we see in tiers 1-4 (excluding CR 20, since it is the first 18-point increase). Frankly, I'm a bit surprised it isn't even higher.

Last edited:

#### Rabulias

##### the Incomparably Shrewd and Clever
Even given that, why are you starting at CR 1/8 (relabled to CR 1), instead of CR 0? I mean, if you are going to relabel it CR 1, you aren't dividing by 0... so???
I used Quickleaf's original table as a source of data, and they did not include CR 0, so I did not either. One could easily recalibrate the CR scale to have current CR 0 relabeled as CR 1, for my purposes here.
How did you end up with that table?

I'm just not recognizing your numbers from my own reading/rough analysis (such as the Forge of Foes, link to preview) , which is why I ask.
I used the DPR data in your original tables, but I renamed CR 0.125 to CR 1, CR 0.25 to CR 2, CR 0.5 to CR 3, CR 1 to CR 4, etc., and then did the division with the new CR values. As I said, doing any math with the CR number is arbitrary as the CR is a label we all agree to. I recalibrated the scale of CR so that dividing by CR would not exaggerate the lower CR results (dividing by fractions). I think this makes it easier to compare the relative increase of DPR as CR increases, but it does not reflect the CR as in the rules.

As ezo points out, the current rules use CR numbers for encounter building, so I am not saying that my new CR numbers should replace those in the current rules. I found it hard to look at the numbers you generated and see things like 24 DPR per CR at CR 0.125, which seemed out of whack, but it's just an artifact of dividing by 0.125. By shifting the scale, the numbers don't reflect true DPR per CR, but the relative trend is easier to examine (IMO).

ezo

#### Rabulias

##### the Incomparably Shrewd and Clever
I must admit it took me a moment to understand what you were doing. is your "adjusted" CR 1 a CR 0 or CR 1/8 creature? (I have more comments but I want to be sure I understand you)
CR 1/8.

#### Ancalagon

##### Dusty Dragon
It's clear that CR 0 to 1 has a different set of rules than most other CRs. But the core is remarkably consistent

#### Sulicius

I am loving seeing people duke it out with math and graphs.

Whatever the numbers might say, in my experience the power of PC’s scales far more. I do believe that is common knowledge.

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