Low efficiency mods, esp. combo mods (having two stats but not that good in either) may not be worth installing. Here is how to tell:

decks of the module / total decks (with the module added) = % damagecap increase
hull of the module / total hull (with the module added) = % hull increase OR
def of the module / total def (with the module added) = % def increase

If the damagecap % increase is more than the hull or def increase, then the module is counter productive. For example if you have something that increases your decks by 5% but only gives a 3% increase in your defense, you are taking more damage than the module offsets, so it's not worth having. This usually only applies to combo modules where the hull/def efficiency is less than half the max tech efficiency (like 8.04 def/decks divided by 2, anything under 4.0 def/decks might not be worth it). Note the more crew you have, the better a module has to be to be worth it. In fact at very high natural def/hull, stripping off a lot of combo mods actually improves your situation and frees up deck space.

This sounds better then what I'm doing and will help to see when a mod gets out dated , but I'm still not removing my Composite Ray - Type D's when there def gets out dated.

Well those have a good ratio for the attack portion -- any combo mod with att is generally worth keeping, as attack is harder to boost. Combo hull/def + energy mods you only need when you rank if it's not otherwise worth it.

the hull increase based on % current hull is true

The defence one isn't.

That is, given a 10% dmg cap increase, a 10% defence increae will NOT always reduced the damage down back to its "orginal" level. It depends on the ratio of attack to defence.
As far as I know, the damage formula is roughly tanh( attack*(random(0.6 to 1.666)) / (defense * 5) ) * damagecap
Now, it would be a bit complicated to consider random, so let's just take a semi-average value of random=1.
For that, I have calculated the following. The first column is the attack/defence value. The 2nd column being the effect of a 10% increase in defence, in term of % damage reduced. (for example, this row 3.974 0.0689 means that if the attack power is 3.974 times that of defence power, a increase of 10% in defence power will reduce damage taken by 5.89%)

The full list and formula will be at the bottom of this post, because it's long and boring... But at a fairly common 2:1 atk:def, for example, there is around 9% decrease in damage taken should you be able to improve defence by 10%. And that supports the OP idea fairly well. Buf if your defence was more or less a "fail" to start with... well, consider the chart values~

11.3382 0.011
10.3074 0.0148
9.3704 0.0193
8.5186 0.0244
7.7441 0.0299
7.0401 0.0357
6.4001 0.0417
5.8183 0.0476
5.2894 0.0534
4.8085 0.059
4.3714 0.0642
3.974 0.0689
3.6127 0.0733
3.2843 0.0771
2.9857 0.0805
2.7143 0.0835
2.4675 0.0861
2.2432 0.0883
2.0393 0.0902
1.8539 0.0918
1.6853 0.0931
1.5321 0.0943
1.3929 0.0952
1.2662 0.096
1.1511 0.0967
1.0465 0.0973
0.9513 0.0977
0.8649 0.0981
0.7862 0.0984
0.7148 0.0987
0.6498 0.0989
0.5907 0.0991
0.537 0.0993
0.4882 0.0994
0.4438 0.0995
0.4035 0.0996
0.3668 0.0997
0.3334 0.0997
0.3031 0.0998
0.2756 0.0998
0.2505 0.0998
0.2277 0.0999
0.207 0.0999
0.1882 0.0999
0.1711 0.0999
0.1556 0.0999
0.1414 0.0999
0.1286 0.1

This should contain all relevant value. Any lower atk/def value would yield a 10% increase regardless of amount, any any higher will be under 1%, unlikely ignorable.
It's not hard to make a chart like this, just use excel. For each row I have the following inputs:
row 1(in order, they are attack, defence, dmg cap(irrelevant tbh), random(more or less an average is used), damage, attack/defence ratio, damage reduction ratio compared between this and next row, growth index(the % amount def is increased to):
1000, 1, 1000, 1, =TANH(A1*D1/B1/5)*C1, =ROUND(A1/B1,4), =ROUND(E1/E2-1,4), 1.1
row 2 and onward:
=A1, =B1*1.1, =C1, =D1, =TANH(A2*D2/B2/5)*C2, =ROUND(A2/B2,4), =ROUND(E2/E3-1,4), =F1
once you are done with the 2 rows, just select all of row 2 and pull down.

Now, damage cap value is obivously irrelevant, and the EXACT value of atk/def is irrlevant(only thing that matters is the ratio). But those does make it easier to think about. and random value is technically random, but I don't wanna go and figure out what the real fair average is~ so~ meh~
You can mess around with the first 4 and last cell of row 1, that will change some numbers in calculation to suit whatever your purpose is(for example, you can enter your own defence value and the attack value of the target(known NPC, player etc) or theortical target(the ~average of a person who is likely to attack you) and figure out if the defence boost is worth it(by modifying F1 using the real increase you would get)

( attack*(random(0.6 to 1.666)) / (defense * 5) ) * damage cap

I know the above is not right because you need to have your attack 20x a NPC's defense to get max damage EVERY time.
10x attack you do 85%-max damage.

It something more like a X/(X+Y)=damage. The closer you get to cap the more you need to change it.
NOTE: I'm not saying the above is any where near the damage formula , but its more on that line.

This is actually correct if you don't put into account that HELMSMEN can be added as well that does not add into the deck count. I have the most massive ship right now (in my knowledge) at 5771 decks. my damage cap is at 2885.5 XRP Warp stations are not able to hit my damage cap, without the Debuff the damage of the station is only 200-350 per attack on me, with the Debuff which halves my Defense the XRP Warp station is able to deal 650 damage every time I attack it.

Even base fights are not able to damage me on my DAMAGE CAP. The most that I have seen done to my ship is about 1200 and thats a base with 60K Attack.

My Take on this, If you have no plan of adding Helmsmen, either by Rank points or via AP pull Android helmsmen, Then don't install inefficient modules. but if you have decent Artifact/per hour then adding whatever modules you want is a good idea.

u dropped tanh, that's not a typo of than or whatever... it's a part of the formula.... it's VERY important
tanh( attack*(random(0.6 to 1.666)) / (defense * 5) ) * damage cap

and for anyone that doesn't know what tanh is...
it's the "hyperbolic tangent" function (don't get it confused with the regular tangent function)

Glad to know that... I always thought it was this: H

That makes more sense.

Well I didn't want to make it overly complicated but yes the benefit of def is never the full % you are adding, esp. if you have fixed rank mission npcs in your regular mix. But it was meant as a general guide, for me I am fitting tech mods and efficient def npc drops, but no mission mods. At that point the question is whether any mission mods are worth adding decks to put on specifically (assume you've got "everything" on already). My point is the people who have 5500 decks to fit all the mods actually went too far and are taking more damage, although people who are in that position probably have such high AP, hull, and def now that it doesn't really matter.

Yeah, but before I figured that out I imagined having a cool ship with everything on it, and when I did figure this out I decided that living that dream was worth it. Of course, it's still a while away for me...

EDIT: It also hurts you for raids and hacking; someone with the same amount of crew would be better if they didn't add the decks to install everything, and somebody who only has enough decks for the most efficient scan and cloak modules would be better at hacking than someone with all the modules. But neither of those things really matter for me, so I'm still just gonna go for the decks.

How does this work? I wouldn't have thought this was the case due to total cloak/scan being higher for the latter player.

I'm pretty sure decks factor into both hacking and raiding; it's about efficiency and not totals. The only exception is you need to have a certain amount of cloak compared to their scan at all, but if you at least have that then I think the actual hack check is at least somewhat based on efficiency. Kaos was saying something about that while he was here, I know he was pretty bugged by it.

No... decks factor into neither hacks or raids, however, those with smaller ships tend to be better raiders as they will have more crew.

I think what you are remembering was his complaint that a lower rank gets more points from a hack/raid on a higher rank than a high rank will from a lower rank.

Could be. I've decided to go through his posts and see. Unless that was one of the posts he complained was deleted...

Finally found that post: viewtopic.php?f=7&t=5713

Flagitous was right that Kaos was just saying you get fewer resources against lower levels than they would against you, though Frail mentioned having less effectiveness raiding lower ranked people (who probably have fewer decks) than higher ranked. That may be based on level and not decks, or may not be entirely accurate, though.

Thanks for clearing that up.

My experience was crew + rank vs. crew + rank, not sure if decks matters to it. But, "smaller" ships which can be decks or rank (?) are "harder" to raid than they should be, at least it seems that way.