As an example of my points above, see below. Paul notes the demilich is a statistical deviant, but doesn't / can't tell us why. I am hoping to figure out why in my own analysis
Hmm...let's see...
If the team is using rules similar to the 2014 rules (and it seems that they are), they're averaging Defensive CR and Offensive CR (which is another thing the "average"-focused analysis can't take into account).
Defensive CR contributions
HP: 180 [x1.25, +90, = effective: 315]
AC: 20
DCR = 17. OK, pretty close.
+: 3x Legendary Resistance. At CR 18, that's +90 effective hp
+: 3+ Immunities at CR 18 mean the HP multiplier is 1.25. 2014 doesn't tell me if that goes before or after the Legendary Resistance bonus, so I put it before (so it's (180*1.25)+90, as opposed to (180 + 90)*1.25).
Offensive CR contributions
DPR: 166-167
Attack Bonus / DC: +11/19
OCR = 22. Very high
DPR Analysis
1st round = 212 | 140 (Howl x2 targets) + 72 (3x Legendary Action: Necrotic Burst)
2nd round = 144 | 72 (Multiattack: Necrotic Burst) + 72 (3x Legendary Action: Necrotic Burst)
3rd round = 144 | 72 (Multiattack: Necrotic Burst) + 72 (3x Legendary Action: Necrotic Burst)
Total Average CR = 19.5, or CR 20.
This lines up with the "average" analysis noting that the damage has increased in 2025. I
suspect there are new bands for damage, especially at the high end. If, say, the 2025 band put 166-167 DPR in the CR 19 band, that would line up with the published CR.
It could also be the case that the immunities aren't adding anything to the defensive CR calc here, which would give us a DCR of 16 and an average CR of 19...which is still high for what's published. Given that the monster hp and AC hasn't dramatically changed in 2025, I suspect there's no real change to the defensive math here.
A strict calculation like "7.5 * CR" wouldn't take into account these bumps to higher CR damage bands. Based on average data, it's a reasonable place to get to, but the average is going to be weighted to the lower CRs (where the 2014 math holds up reasonably well). You'd expect higher CR critters built using that math to hit weaker than the critters in the 2025 MM actually hit overall.
I wanna know where those bumps are and how big they are. I wanna know the new OCR bands. And I think that's going to take a lot of this kind of backwards analysis: finding out the Defensive CR, finding out 2014's offensive CR, and finding out what 2025's offensive CR
should be, and then getting DPR numbers assigned to a CR band based on what it should be.
Not impossible, probably, but a heck of a lot of work. For now I can say that a CR 19 OCR in 2025 is probably ~ 166 dpr. It'd be curious to test that on some CR 17-22 critters.