As mentioned in my thread about RCS Accelerators, figuring out this problem has proved beyond my capabilities, so I'm hoping someone else can make more progress than I did.
Quote:
Originally Posted by MustrumRidcully
Q: How do armor consoles work? The number listed on t he console don't seem to be the resistance I get?
A: The armor console displays a resistance value that first has to be used in a formula to gain an actual resistance percentage.
The formula is: 1  (100/(100 + Resist value)). (This gives a fractional value, multiply it with 100 to get a percentage.) So an armor mod of +50 gives only about 33 % of resistance. Remember that you might have passive resists from accolades or other sources (powers.) There is a cap that is not accounted for by the formula  you don't get above 75 % (Exception for the Long Range Science Vessel Refit Ablative Armor).

This struck me as a rather elegant formula, with a built in diminishing return (each additional point is worth slightly less than the last). Unfortunately, like many elegant formulas over the years, when tested against realworld data, it doesn't quite hold up.
Mustrum Ridcully uses an armour mod (please excuse my insistence on using a u in armour... I am Canadian
) of +50 in his demonstration. Unfortunately, I haven't found any such consoles to test with, and am restricted to the maximum value I could find, which is +32.
1  (100 / (100 + 32))
= 1  (100 / 132)
= 1  0.75757... (repeating ad infinitum)
= 0.24242424...
Which would leave us with an expected Damage Resistance (against whatever types the console helps against) of 24.2 %
However, you'll find that you actually get 24.3%
Not too far off the mark, you might say. However, note that even if you round off the numbers, the result should still be 24.2%. The only way I could find to get a result that worked out to 24.3% was to truncate, rather than round, working from 0.757.
Continuing on, and adding a second +32 of the same type, would give us the following (skipping the easy 100 + n step for brevity's sake, from now on):
1  (100 / 164)
= 1  0.6097570975... (repeating)
= 0.3902439024...
= 39.0% damage resistance
Except when actually installed, the damage resistance is 38.5% (note, this is without any points in the Starship Battle Strategies skill, and without any damage accolades; I will discuss both later).
No truncating or rounding could produce that particular result. Which means either there's some additional diminishing returns at play based on additional consoles (I'll come back to that later, as well), or that the basic formula is itself inaccurate.
Continuing on, with a third +32 console.
1  (100 / 196)
= 1  0.510204081... (if this number repeats, it's a longer sequence than my calculator can handle)
= 0.489795919
= 49.0% damage resistance
Actual damage resistance provided: 47.5%
Off by an even larger margin, yet still close enough that it seems the formula must at least be in the right ballpark.
Finally, maxing it out with a fourth +32 console.
1 = (100 / 228)
= 1  0.438596491...
= 0.5614035508...
= 56.1% damage resistance
Actual damage resistance provided: 53.5%
Close, but no cigar.
I have been unable to figure out a formula capable of producing all of those results... especially not an elegant one. Perhaps someone with better math skills than I can do so.

What about the damage resistance granted by the accolades for receiving a certain amount of damage of a specific type? All of them grant 2.0% damage resistance.
Working backwards, this time.
2.0%
= 0.02
= 1  0.98
= 1  (100 / 102.04081632...)
Let's round that off to 102.04, and say that n is 2.04. It produces a result of 0.98000784 which is close enough to work with.
Working with the formula, using 34.04, 66.04, 98.04, and 130.04, we get (work not shown, for brevity):
Expected results: 25.4%, 39.8%, 49.5%, 56.5%
Actual results: 25.4%, 39.2%, 47.9%, 53.8%
One result fits the prediction... but as before, the later results do not.

The Starship Battle Strategy skill, one of the skills added after launch, is much more informative in what it gives us than earlier skills were. Still, some information is lacking (it tells us how much Damage Resistance 1 point gives us, and how much 9 points gives us, but leaves it up to us to do the math for the rest). Maxing out the skill gives 9.88 damage resistance. Plugging that in to the formula...
1  (100 / 109.88)
= 1  0.910083727...
= 0.089916273...
= 9.0% damage resistance
Actual damage resistance 9.0%
So clearly the formula isn't completely off the mark. However, here are the predicted and actual results...
Consoles + Skill (no accolade)
Predicted: 9.0%, 29.5%, 42.5%, 51.4%, 58.0%
Actual: 9.0%, 29.4%, 41.6%, 49.5%, 54.9%
And finally, combining consoles, skill, and accolades
Predicted: 10.7%, 30.5%, 43.2%, 51.9%, 58.3%
Actual: 10.6%, 30.3%, 42.2%, 49.9%, 55.2%

Two possible solutions suggested themselves to me, but neither seems to hold up to testing, at least not without some additional factor being involved.
The first was that the numbers listed on armour consoles (such as that +32), are themselves rounded, and not what the actual console gives us. If that 32 was actually 32.1, then the predicted result for one console would match the actual. However, the predicted result for two consoles would be further off than the current prediction, with the error increasing as more consoles are added.
The second was the idea that there was an additional diminishing return attached to multiple consoles, on top of the formula's built in diminishing returns. However, four consoles each with +5 armour grant the exact same bonus as a single console granting +20.

So there you have it. I can't figure it out. Hopefully someone can, as I'd like to be able to predict the results of consoles BEFORE I pay for them, rather than finding out through trial and error.