phindar said:
But its really not. Assuming 5-6 images are created in the casting of the spell, Blur will save one of them, and Displacement will save 2-3 of them. In either case, the caster would be better off casting Mirror Image and then casting it again when it starts to run low. Using a 3rd level slot for Displacement comes close (because of the 2-3 images that will likely be saved, 1-2 might survive again), but thats still a 2nd and a 3rd level spell to get something about as effective as casting the 2nd level spell (MI) twice.
Interesting analysis. Flawed, but interesting.
The point you dropped on the floor is that with my interpretation, Mirror Image gives 5-6 images and Displacement merely protects the caster.
Cost: 1 2nd level spell + 1 3rd level spell.
Gain: 1 2nd level spell + 1 3rd level spell.
With the opposing interpretation, Displacement changes the Mirror Image into the equivalent of an Empowered Mirror Image.
Cost: 1 2nd level spell + 1 3rd level spell.
Gain: 1 4th level spell + 1 3rd level spell.
With regard to the rest of what you wrote, the caster is not better off with two Mirror Image spells (as you claimed) since they are totally ablative whereas a Mirror Image combined with Displacement is only partially ablative. The gain is not about as effective (or better off, you claimed both) as 2 2nd level spells as you claimed, rather it is a gain of a 3rd level spell (Displacement) and the equivalent of a 4th level spell (Empowered Mirror Image or a Mirror Image with 7 to 9 images) with this interpretation.
Having the Displacement and MI up is a larger protection versus the back to back Mirror Images that you proposed. The chances to get targeted (let alone hit) as images get popped drops by:
MI (6 images followed by casting 6 images again when down to 1 image) = 16.7% / 20% / 25% / 33.3% / 50% / 16.7% / 20% / 25% / 33.3% / 50% / 100% / 100%, etc. (average 40.8% of getting targeted after 12 successful attacks)
versus
Disp followed by casting MI (6 images) = 50% / 8.3% / 10% / 12.5% / 16.7% / 25% / 50% / 50% / 50% / 50% / 50% / 50%, etc. (average 35.2% of getting targeted after 12 successful attacks)
Most of the time (except for a few successful attacks after casting a second MI), it is better to have up a MI and a Displacement (using my interpretation) than it is casting a second MI. At higher level with opponents having more attacks per round, the dual MI spells come down fast whereas the Displacement lasts much longer (shy of a Dispel).
The other interpretation yields (assuming alternating attacks miss the images due to the combined displacement with the images of that interpretation):
Disp followed by casting MI (6 images) = 50% / 8.3% / 10% / 10% / 12.5% / 12.5% / 16.7% / 16.7% / 25% / 25% / 50% / 50%, etc. (average 23.9% of getting targeted after 12 would have been successful if it did not run into displacement attacks)
As can be seen, this is much stronger than my interpretation where Displacement does not affect Mirror Image (as I originally claimed and you claimed it was not much stronger).
If an opponent Fighter type averages 20 points of damage (combining both to hit and damage), your two MI solution would have the caster taking 98 points of damage, my interpretation with Displacement and MI would have the caster taking 84.5 points of damage, and the alternative interpretation with Displacement and MI would have the caster taking 57.4 points of damage.
So yes, that interpretation of Displacement combining with Mirror Image would be 1.7 times as effective at stopping damage than using two Mirror Image spells. You claimed using Mirror Image would be more effective (or about as effective, you claimed both of these). It's actually much worse off in the long run, espeically at higher levels where opponents get more attacks per round.