Lt. Commander
Join Date: Dec 2007
Posts: 120
# 1 How do armour consoles work?
06-29-2011, 02:31 AM
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 real-world 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.
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 2
06-29-2011, 11:06 AM
I am not sure if there aren't more updated formulas available after some of the STOKed podcasts with CaptainGeko (see here: http://www.jupiterbroadcasting.com/5...iew-stoked-73/). Currently too lazy to extract the data from the excel sheets. I seem to remember something that actually worked in the 75 % resistance cap into the formula, but made it a lot more complex and harder to read and understand. I presume that this aspect is missing.

In the end, the exact numbers don't really matter, the principle is still the same - you add these numbers, and that is inserted into some arcana formula to get an actual resistance values. The key aspects of this formula is that they can't get you a resistance value of 100 % or more, and that there is something in the game mechanics to make it impossible to go above 75 % as well. And Ablative Armor gets to break the rules.

But while you are at it - try figuring out how negative resists stack with positive resistances. :p

PS:
Turns out I am quite as lazy as I first suggested, though still pretty much, and decided to actually include the information from the podcast in my insights thread, but I don't write out the formual. it's more complicated, unfortunately.

Quote:
please excuse my insistence on using a u in armour... I am Canadian
Does this mean I can write "Panzerung" instead of armor? I am German!
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 3
06-29-2011, 03:22 PM
Thank you, MustrumRidcully, that's quite helpful.

To anyone else following the link, I definitely suggest watching the podcast (particularly the math part), as I found deciphering the Excel spreadsheet is a bit tricky even with the explanations.

Unfortunately the spreadsheet doesn't give me exactly the same results as my in-game testing, so either the formula is a bit off (despite coming directly from Cryptic), or I'm missing some source of Damage Resistance in my calculations.

Still, the numbers are a lot closer than they were, so it's a useful enough tool until something better comes along.

Quote:
Originally Posted by MustrumRidcully View Post
Does this mean I can write "Panzerung" instead of armor? I am German!
Heh, that'd be awesome, but unfortunately Cryptic's language policy...
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 4
06-29-2011, 05:07 PM
Look at the STOKED episode's show notes. They show the armor formulas used in the spread sheet. They do use the Dam / ( 1 + Armor) type forumla but it's a bit more complicated to to give a much steeper curve as you approaching the damage resistance cap of 75%.
Lt. Commander
Join Date: Dec 2007
Posts: 120
# 5
06-29-2011, 06:32 PM
Quote:
Originally Posted by fuzun View Post
Look at the STOKED episode's show notes. They show the armor formulas used in the spread sheet. They do use the Dam / ( 1 + Armor) type forumla but it's a bit more complicated to to give a much steeper curve as you approaching the damage resistance cap of 75%.
Yes, I'm saying that even that formula and that spreadsheet (which appears to be directly from CaptainGeko) produces results not precisely in line with what my in-game testing shows, which would indicate either there's an error in the sheet, the formula has changed, or that there's some variable acting on my in-game numbers that I've failed to take into account.

Here are the revised predictions, produced via the spreadsheet, for one, two, three, and four +32 consoles (without the complications of accolades or the Starship Battle Strategy skill), presuming I'm correctly understanding how to use the spreadsheet:

24.1%, 38.2%, 47.1%, 53.2%

and again, my actual in-game results:

24.3%, 38.5%, 47.5%, 53.5%

So, still off by 0.2 to 0.3 (suggesting an actual deviation of around 0.25, being rounded). Compared to the results produced without knowledge of the diminished magnitude curve formula, a great gain in accuracy. I'm still left slightly puzzled by the deviation.

For those who haven't followed the link, here's the formulas given (both in the podcast and in .pdf and Excel file forms):

First, let's define some terms.

Magnitude (MAG) - The number given on a console is referred to as the Magnitude, or MAG of the console. Note that the MAG used to calculate DR is actually the listed number divided by 100 (or multiplied by 0.01, if you prefer). The magnitudes of all armour and other DR are modified by a diminishing return formula, which gives you...

Diminished Magnitude - The magnitude, adjusted via a formula that curves the results so that they can reach but not surpass the DamRes%Max value. Also referred to on the Excel sheet as Curved Magnitude.

DamRes%Max - The maximum damage resistance % allowed. Excluding the case of the LSRV-R's Ablative Armour, damage resistance cannot exceed this value. The value is known to be 75% (though one cannot achieve that with passive bonuses alone, as far as I can tell). This is to prevent players from basically becoming immune to damage.

Damage Resistance % - The actual damage resistance granted. This is the number that gets listed on your ship's character sheet/status page, and it's also the percentage by which all hull damage of the appropriate energy type is reduced.

The formula given for determining Diminished Magnitude is... unwieldy. I think it can be reduced to something a little easier to look at, but for now, here's the formula as it was given:

(1/(1-DamRes%Max))-1-(((1/(1-DamRes%Max))-1)/(1+(MAG/((1/(1-DamRes%Max))-1))+((MAG/((1/(1-DamRes%Max))-1))^2)))

That's a lot of brackets. Given that the DamRes%Max is a known value, I think we can simplify that down a few steps.

=(1/(1-0.75))-1-(((1/(1-0.75))-1)/(1+(MAG/((1/(1-0.75))-1))+((MAG/((1/(1-0.75))-1))^2)))
=(1/0.25)-1-(((1/0.25)-1)/(1+(MAG/((1/0.25)-1))+((MAG/((1/0.25)-1))^2)))
=4-1-((4-1)/(1+(MAG/(4-1))+((MAG/(4-1))^2)))

=3-(3/(1+(MAG/3)+((MAG/3)^2)))

Which, while still too complicated for me to do in my head, should be mathematically equivalent, and much easier to look at.

Regardless, the Diminished Magnitude is then plugged in to the Damage Resistance formula, which is

=-((1/(1+DiminishedMag))-1)
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