D&D 5E Mirror Image Math

[FrogReaver]

My goal today is to find the formula to determine mirror image's accuracy benefits per round. I believe this spell may actually provide more overall defensive benefits than blur in many situations. I believe it's likely an overlooked spell.

Variables:
Let N = number of attacks per turn
Let X = Player Chance to be hit
Let Y = Mirror Image chance to be hit
Let T = Mirror Image chance to be targeted when all 3 images are up
Let T' = Mirror Image chance to be targeted when 2 images are up
Let T'' = Mirror Image chance to be targeted when 1 image is up

Where I am at. Case N=1 (for simplicity).

Turn 1: (1-T)*X
Turn 2:
Turn 3:
Turn 4:

 

[Stoutstien]

I agree that mirror image is better in most cases than blur even with the concentration factor but I've failed to find a formula for it or at least one that encompasses all the number of images at once. I've had to do each separately.
The best part of MI is that each image adds EHP equal to the damage dealt by that attack.

 

[FrogReaver]

I agree that mirror image is better in most cases than blur even with the concentration factor but I've failed to find a formula for it or at least one that encompasses all the number of images at once. I've had to do each separately.
The best part of MI is that each image adds EHP equal to the damage dealt by that attack.

I think the formula should be fairly straight forward - it's just going to expand rather quickly. There's 4 events that can happen on any given turn (until you are out of images).

1. you are attacked, chance to target image fails, you are hit
2. you are attacked, chance to target image fails, you are missed
3. you are attacked, chance to target image succeeds, it is hit
4. you are attacked, chance to target image succeeds, it is missed

Only 1 state causes you to drop a mirror image
Only 1 state causes you to take damage
The remaining states represent no change

This may not be quite as bad as we are thinking.

 

[FrogReaver]

Well - not my goal but useful info.

I've calculated Blur's damage reduction for the nth attack coming at you.

Let C = Chance Concentration remains up through hit < 21 damage. X = Chance to be hit. N = Number of attacks. Then,

X - C^N * (X-X^2)

Unless you have extremely high concentration then blur actually loses value pretty quickly the more attacks come at you.

Someone else double check my work on this one!

 

[FrogReaver]

Well - not my goal but useful info.

I've calculated Blur's damage reduction for the nth attack coming at you.

Let C = Chance Concentration remains up through hit < 21 damage. X = Chance to be hit. N = Number of attacks. Then,

X - C^N * (X-X^2)

Unless you have extremely high concentration then blur actually loses value pretty quickly the more attacks come at you.

Someone else double check my work on this one!

This isn't working - Made a mistake here. Will need to work through the fix.

 

[Paul Farquhar]

One feature of Blur that isn't included in your calculations - it protects from Sneak Attack.

 

[FrogReaver]

One feature of Blur that isn't included in your calculations - it protects from Sneak Attack.

Which makes for a nice caveat bullet point but is complexly irrelevant when it comes to computing the normal amount of damage is will prevent.

 

[Stoutstien]

Well - not my goal but useful info.

I've calculated Blur's damage reduction for the nth attack coming at you.

Let C = Chance Concentration remains up through hit < 21 damage. X = Chance to be hit. N = Number of attacks. Then,

X - C^N * (X-X^2)

Unless you have extremely high concentration then blur actually loses value pretty quickly the more attacks come at you.

Someone else double check my work on this one!

I'll post my math once I clean it up. Currently it is a pile of chicken scratch.
Blur- works best if the users AC is moderately good against incoming attack bonus and the number of attacks per round are less than 4. Blur is at its best if the users AC is in the sold cap range(on hit is critical) and almost pointless if the target AC is so low the disadvantage doesn't help.
Things that have a meaningful impact on results:
Higher AC
Higher Con saves
Advantage on Con saves (warcaster)

Mirror image is better if only a few ,high bonus, attacks are targeting the user or numerous very weak attacks. The cross over points are about where the incoming attack has over 50% hitting you or if the weaker attacks have less than 50% chance of beating your mirror image AC.
The only way to buff this spell is a higher Dex modifier.

Both spells have the least effect facing moderate number attacks with a moderate chance to hit. Shield spell wins hands down here.

I'm going to attempt to graph all this.

 

[Paul Farquhar]

Which makes for a nice caveat bullet point but is complexly irrelevant when it comes to computing the normal amount of damage is will prevent.

I would argue that the ability to (almost) completely block massive damage matters more than a few hp either way of average damage.

 

[FrogReaver]

I would argue that the ability to (almost) completely block massive damage matters more than a few hp either way of average damage.

It matters when it can. It typically does it so rarely that it's a bullet point instead of something to factor into the formula. Get it?