What is the formula for damage mitigation in Ingress?

ingress

The mitigation stacks additively and its damage reduction is hard-capped at 95%.
1 mitigation = 1% reduced damage. The mitigation can go over 95, but the extra damage reduction won't apply. Apart from mitigation, a shield has a mysterious property called Stickiness. It is said, that it might affect the destructibility of a deployed shield.

Shield Type         Mitigation  Stickiness
Common shield       30          0
Rare shield         40          150k
Very Rare shield    60          450k
Very Rare "AXA"     70          800k
Links*:
     *the Ultra Link mod increases mitigation from links by 50 %

Portal defense boost based on number of links

A portal with 4 VR shields and with 10 links has 66 ~~100~~ ~~180~~ ~~260~~ 300 mitigation, BUT reduces only 95% damage. The extra shields have only the meaning of reserves, when some get destroyed.
It is wise to support shielded portal's defense with links.

The % damage reduction in action

An L8 burster with 2700 damage will do:
*Take a closer look at the defense effect of 80-95%

shield type  defense     damage
-            0%          2700
CS           30%         1890
RS           40%         1620
VRS          60%         1080
AXA          70%         810
RS + RS      80%         540
VRS + CS     90%         270   (same as 3x CS)
VRS + RS     95%         135   (same as 2x CS + RS)

damage reduction effectiveness

I am leaving the following only for historical reasons

first version

# IMPORTANT! # for old players

If you are an old player and you don't use shields much or you didn't play long time for some reason, it may happen that you will have OLD + NEW shields in your inventory. Don't know why it works like that, but if you drop all the shields of same rarity and pick them up again, they will get renewed.
C: 6->10, R: 8->20, VR: 10->30
*do not bother yourself with common shields though, it is only worthy for R and VR S.

EDIT 1 (7 Mar 2014)

The shield strength changed once again, from 10,20,30 to 20,30,50. As far as I can tell, all old shields are renewed automatically without the need of dropping them. I am leaving the hint for historical reasons.

EDIT 2 (3 Jun 2014)

New shield strength :) - from 20,30,50 to 30,40,60. All shields are renewed automatically. Already deployed shields remain with old stats.

EDIT 3 (21 Dec 2014) - AXA shield

New shield type was introduced as a result of sponsorship deal with the international investment banking firm AXA. The so called AXA Shield is very rare and its mitigation is 70. More reading here...

EDIT 4 (4 Feb 2015)

Significantly increased values for stickiness started to show for newly placed shields in the JSON answer in intel. (Reddit: Shield stickiness gone mad in IITC.)

Shield Type         Old   New
Common shield       30    0
Rare shield         40    150000
Very Rare shield    60    450000
Very Rare "AXA"     70    800000

EDIT 5 (20 Jun 2015) - Ultra Link mod

New sponsored item SoftBank Ultra Link was introduced during the end of Persepolis anomaly. It is said to grant additional 50 % of mitigation from links. It's not known (yet) whether this effect stacks with multiple ULamps used.

# NUMBER OF LINKS
          1   ->  6   ->  40
# MITIGATION
without:  +18 ->  +50 ->  +66.8
with UL:  +27 ->  +75 ->  +100 (surpasses the 95 hardcap)

Apart from the mitigation, the UL mod increases the maximum of outgoing links by 8 to a total of 40 outgoing links when using 4x UL (stacks additively), and increases the linkable range 5 times (diminished stacking). (to compare: RLA 2x, VRLA 7x)

Shields mitigations are :

common shield : 30
rare shield : 40
very rare shield : 60
AXA shield : 70

The mitigation of the shields is a percentage of absorption of damages. A (common) shield with a mitigation of 10 will absorb 10% of the damages made by the buster. A second (common) shield with mitigation 10 will catch 10% of the remaining damages.

For example, let's imagine a burster making 100 of damages on a resonator. First common shield will absorb 10% so damages will be reduced to 90. A second common shield will absorb 10% of the 90 damages and will reduce damages to 81...

In the worst/better case with 4 very rare shields mitigation 30, a burster making 100 damages will be reduced to 24.

To compute the total mitigation of shields on a portal you have to just multiply the percentages. A very rare shield will eat 30%, to compute the effects you'll have to do X - (X * 30 / 100) that will reduce to X * 0.7. So a very rare shield is equal to a 0.7 factor applied on the burster's damage, a rare shield is equal to 0.8 and a common to 0.9.

So the way of computing shield mitigation is :

SHIELDS_MITIGATION = SHIELD_1_FACTOR * SHIELD_2_FACTOR * SHIELD_3_FACTOR * SHIELD_4_FACTOR

To that, you have to add a defense mitigation made by links. The formula seems to be :

LINKS_MITIGATION = 4/9 * atan(NUMBER_OF_LINKS / e)

where e is the mathematical constant.

This will give you another mitigation to "add" (multiply) to the shield one to obtain final mitigation.

Then to compute the damages the formula is :

RESULTING_DAMAGES = BURSTER_DAMAGES * SHIELDS_MITIGATION * LINKS_MITIGATION