I'm trying to make a spell casting villain, and I'm not sure how Mirror Image will effect his CR. Thoughts? His Armor Class is 17 and he has 99 HP, so his defensive CR is 4, but I'm not sure how Mirror Image would effect that.
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"Halt your wagging and wag your halters, for I am mastercryomancer!"
Presume the villain has cast Mirror Image, and is standing still. Presume a fighter is standing within melee range, and that the fighter is able to consistently deliver 99 damage per hit. Presume his attacks always hit, and ignore crits (it's a one-hit-KO anyway.)
Without the Mirror Image, it's straightforward. The villain has an effective 99 HP, as that's what it takes to put him at 0.
With Mirror Image, you can choose any of various (somewhat arbitrary) methods to calculate how much damage, on average, it takes to drop the villain. I'll go with a longer, more straightforward method: Figure out all possible outcomes ((1) hit the villain, (2) hit an illusion, then hit the villain, etc.), determine how likely each outcome is, and assign a "damage spent" value to each outcome (I'm going to say that a hit on an illusion is a "spend" of 49 damage... realistically, a 1 damage attack can uncover the villain, but large attacks will still be used, so I'll just average it to 49.) Finally, multiply each outcome's damage spent by its likelihood, and add the adjusted damage from each outcome. It should give something close to a "average damage spent."
OUTCOMES: 1) Hit the villain first time - 25% chance - 99 damage spent - 24.75 adjusted damage spent (ADS) 2) Hit one image, then the villain - (.75 x .35) = 26.25% chance - (49 + 99) = 148 damage spent - 38.85 ADS 3) Hit two images, then the villain - (.75 x .65 x .5) = 24.375% chance - (49 + 49 + 99) = 197 damage spent - about 48.02 ADS 4) Hit three images, then the villain - (.75 x .65 x .5) = 24.375% chance - (49 + 49 + 49 + 99) = 246 damage spent - about 59.96 ADS
TOTAL DAMAGE SPENT = 24.75 + 38.85 + 48.02 + 59.96 = 171.58 average damage spent to take the villain to 0... so it acts as if it has 73% more than the 99 listed hit points.
So presuming the villain can consistently cast Mirror Image before the players attack, then you can get a better feel for his CR by treating him as if he has 73 HP more than he has listed on his sheet. If you want to go the extra mile, you might also chop off maybe 10-25% of those extra virtual HP, depending on the likelihood of the players having access to (and successfully using) blindsight, Dispel Magic, etc.