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The monster's manual archmage is overpowered, but has a CR12!? It is a monster with Time Stop from 9th circle, mind blank and teleport. If you put him with some other melee monsters (meat for the players to hit), he becomes almost untouchable with teleport and wall of force. In summary, what are the reasons for this monster be CR12 only?

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    \$\begingroup\$ I’m voting to close this question because it's about designers intent and reasoning, something only designers can reliably answer. \$\endgroup\$
    – Mołot
    Nov 14 at 16:02
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    \$\begingroup\$ I disagree (evidently) with the notion that this is a designer-intent question: OP thinks archmage CR should be higher than 12, the text of the DMG shows why it's not. \$\endgroup\$
    – nitsua60
    Nov 14 at 17:11
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    \$\begingroup\$ @Mołot Explaining how the CR calculations work out is not an uncommon question kind here. Unless a given player or DM has tried to make a homebrew monster or has compared monsters of the same CR and see wild differences, it may not register on how it is done and the experiences of site experts. \$\endgroup\$ Nov 15 at 13:19
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    \$\begingroup\$ ‘if you put him with some other melee monsters’ Well yes, but that’s no longer the archmage, that’s a combat encounter with a by definition higher CR. The CR of a monster only cares about that monster, not how they interact with other monsters. \$\endgroup\$ Nov 15 at 20:53
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"By the book," the archmage is CR10. (Or even 12; zacm's answer makes some different assumptions than I do below and comes out right at CR12.)

The DMG covers how these numbers are crunched, but I'll give you the bottom line: the archmage has a Defensive Challenge Rating of 3 compared to its Offensive Challenge Rating of 17. (I assume mage armor's up and running for AC 15. I don't count Stoneskin, since L12 characters aren't doing much non-magical Bludgeoning/Piercing/Slashing damage in my experience. I've assumed cone of cold hitting three PCs, three rounds in a row, for the archmage's best expected damage. I might be a touch low, since they could upcast and maybe squeak out an OCR of 18.)

Averaging the archmage's DCR and OCR gives a preliminary (naive) CR of 10; the adjustment up to 12 is presumably due to playtesting during D&DNext. (See also this article where Mike Mearls mentions the Ogre's CR calculation, or any of the many questions we have around CR calculations in D&D5e for plenty more commentary on where official CR doesn't quite match the number-crunching CR.)

Your instinct is sound, though: this is a spellcaster who can do a lot. Your observation that it'd be good strategy to pair him with some meat balances the archmage's obvious weakness: a defensive CR of 3 (I emphasize again)! He's got time stop and teleport and globe of invulnerability and is generally hard to pin down and just hammer on.

But having played against archmages and run them as a GM, I have no problem thinking that 4-5 L12 PCs aren't really in trouble running up against just an archmage.

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    \$\begingroup\$ I'll tell you, though: an archmage paired with an archdruid... that was a tough twosome to take down. Foresight still gives me headaches. \$\endgroup\$
    – nitsua60
    Nov 14 at 16:05
  • \$\begingroup\$ yeah, even if it timestops and casts its best buffs (it can't cast all of them, because many of them are concentration, he still dies quickly. I even had one with an altered spell list wtih forcecage instead of teleport so he can isolate some of the party. He had globe of invulnerability up, and a potion of fly, and yet the level 10 aprty (albeit slightly oversized party) still beat him easily. One of the PCs misty stepped out of the force cage (and succeeded on check to do so). \$\endgroup\$ Nov 14 at 20:55
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    \$\begingroup\$ The party ate a cone of cold, but then they succeeded on dispel magic check to bring down the globe of invulnerability, and the forced him to flee (with a scroll of teleport) the very next round. So no, not overpowered, just hard to track down and actually kill. That's the point \$\endgroup\$ Nov 14 at 20:55
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    \$\begingroup\$ @nitsua60 Maybe a paragraph on how such a high OCR either compares to CR 17-18 creatures' offensive powers, or on how quickly it could kill level 12 characters? My worry isn't about the correct use of CR counting, it's about how this answer looks like the only step was looking through that lens. I can tell that you actually do understand this creature and why it really does fit at CR 12, but I don't think that's completely reflected in this answer. \$\endgroup\$
    – Phoenices
    Nov 15 at 17:24
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    \$\begingroup\$ I guess the fact that it's offensive and defensive CR are so far apart tells you that the archmage's actual challenge level is "unstable", with a high potential for the actual context it appears in to make it much tougher or easier than it looks on paper. Depending on whether that context mitigates the archmage's offensive strength or defensive weakness, you could end up with a much higher or lower "effective CR" (a concept I'm totally making up; static CR isn't intended to reflect all the potential variables of an actual game context). \$\endgroup\$
    – Ben
    Nov 17 at 4:32
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CR12 for Archmage is exactly in line with the rules for determining CR of a monster in the DMG Chapter 9 (Pg. 274).

Defensive CR is easy-- we take Mage Armor plus the HP and resulting AC to get a Defensive CR of 3.

For Offensive CR we assume the Archmage is playing optimally* for damage: upcasting Cone of Cold three consecutive turns using their 9th level slot, then 8th and finally 7th level slot dealing 12d8, 11d8, and 10d8 respectively, with a conservative estimate of hitting 3 creatures each time, resulting in our 3 turn Damage Per Round (DPR) to be 148.5, which combined with a spell save of DC17, gets us the offensive CR20.

With Defensive CR 3 and Offensive CR 20, we average the two and get 11.5 which can be rounded up or down, which allows us to achieve CR12.

*Cone of Cold is the highest level damage spell we're given, and the one that when upcasted lets us do the most damage with the Archmage-- Mind Blank and Teleport don't do damage which is all CR really cares about. Time Stop doesn't really let us do more damage, although it may on some uses allow the Archmage to cast Fire Shield before then casting 3 Cone of Colds (8th, 7th and 6th level), which is possibly why the CR is rounded up, but that's just speculation.

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    \$\begingroup\$ +1 for showing that even when the archmage is run at its "blasty-est," CR still works out to 12. \$\endgroup\$
    – nitsua60
    Nov 15 at 11:02

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