So I have a Marauder with 290hp/s base shield boost and 580hp/s with bastion (+100%).
If I have Pith X-type amplifier base becomes 420hp/s and with bastion 806hp/s instead of 840hp/s.
I am missing 4%. I was wondering how the math looks behind it?
P.S. No wonder amplifiers cost nothing compared to multispectrum hardeners.
Edit: thank you, everyone, for teaching me and explaining how diminishing returns work.
because the game has stacking penalties for things that effect the same stat
Well with multispectrum hardeners you get the percentage for each u use. No matter of my resistances and how many hardeners I already have, if hardener is 20% I will get 20% effective resistances compared to what I already have. Meaning +20% to boost AND base shield tank effectiveness. While amplifiers have a lot bigger fitting requirements and suffer from some random diminishing return.
Hardeners too have diminishing returns.
how come it is better to use on Marauder 3 Pithum B-type(39.4%) hardeners than 2 hardeners(39.4%) and 1 amplifier(44.75%)?
Not taking into account that amplifier is 77CPU while hardener 32
Could be various reasons.
Innate resistance profile, incoming damage.
I donât know why or if it is better in this case, I havenât calculated or simulated it.
All Iâm saying is that all resistances suffer from diminishing returns. All except for the Damage Control which is itâs own category together with the reactive armor hardener.
the math does not make sense to me, that is why I am looking for answers
Diminishing Return (stacking penalty) mechanics is explained in great detail here: Stacking penalties - EVE University Wiki
This does not seem to apply to this case. If it applied, the end result would be greater than 840 given my example
Can you provide a fit youâre using for your testing? will help us understand what is going on.
A Golem with Bastion and Pith X-type X-large shield booster. I have Marauders 5 skill.
I am just trying to understand why I get much more value from 3rd hardener(39.4%) than 1st amplifier(44.75%). Thank you!
I do not see what you are seeing.
Iâm simulating a Golem equipped with:
[Golem, Golem Forum Question]
[Empty Low slot]
[Empty Low slot]
[Empty Low slot]
[Empty Low slot]Pith X-Type X-Large Shield Booster
Pithum B-Type Multispectrum Shield Hardener
Pithum B-Type Multispectrum Shield Hardener
Pithum B-Type Multispectrum Shield Hardener
Pith X-Type Shield Boost Amplifier
[Empty Med slot]
[Empty Med slot]Bastion Module I
[Empty High slot]
[Empty High slot]
[Empty High slot]
[Empty High slot]
[Empty High slot]
[Empty High slot]
[Empty High slot][Empty Rig slot]
[Empty Rig slot]
If I turn off the third multispectrum hardener I get 870 EHP/s:
But if I instead turn off the amplifier and keep the third multispectrum hardener active I get 642 EHP/s:
Clearly the amplifier is a lot better here.
Am I missing something?
The amplifier is already better than the second hardener:
Two hardeners: 626 EHP/s,
hardener + amplifier: 689 EHP/s.
Could you perhaps post screenshots of the fitting screens (including displayed stats) of the two identical fits except the single difference you mention? That would help people give better advice what is going on. 
The ingame fitting window uses an average of all 4 resists to then give you that number (which is part of the reason why the ingame fitting window sucks and you should use Pyfa instead). If you use a multispectrum you âplug the holeâ meaning that on average the number is better. Depending on use you generally just need 2 resists tanked, for pvp thatâs different.
Still the point stands: stop using the ingame fitting window, not only does it lie to you, it omits important info.
Pyfa also âaveragesâ the resistances by assuming the incoming damage is an even 25% split for all four damage types unless specified otherwise.
But in this case Iâm not sure what number v m x is looking at.
Yup.
And yes, OP being vague is not a good sign.
Ok, first of all let us tackle your (presumably) misunderstanding of Stacking Penalty.
1st [Pithum B-Type Multispectrum Shield Hardener] has a 100% effectiveness - i.e. you get the full 39.4%
2nd [Pithum B-Type Multispectrum Shield Hardener] has a 86.9% effectiveness - i.e. you get 39.4% multiplied by 0.869 which equals approximately 34,2%
3nd [Pithum B-Type Multispectrum Shield Hardener] has a 57.1% effectiveness - i.e. you get 39.4% multiplied by 0.571 which equals approximately 22,5%
Resulting in the resistance profile you can see in this image:
Removing any of the Shield Hardeners does not change the Shield Boost amount offered by the Shield Booster. It only changes the Resistance profile. However if you swap out one of the Shield Hardeners for a Shield Boost Amplifier you take a slight hit in your Resistance profile but you significantly increases the amount offered by your Shield Booster (see image below)
In the example with 3 Shield Hardeners you can calculate the Effective Hit Points (EHP), or in other words the raw DPS, you can tank:
Worst case [Lowest resist]: 496.7 / (1 - 81%) = 2614 raw dps.
Best case [highest resist]: 496.7 / (1 - 91%) = 5518 raw dps.
Swapping out one Shield Hardener with a Shield Boost Amplifier you have the following:
Worst case [Lowest resist]: 689.8 / (1 - 76%) = 2874 raw dps.
Best case [highest resist]: 689.8 / (1 - 88%) = 5748 raw dps.
In conclusion you can tank marginally more by using [2 Shield Hardeners + 1 Shield Boost Amplifier] than you do with [3 Shield Hardeners].
Amplifiers cost little because their use-case is very niche compared to multispectrum hardeners.
Nearly every shield ship will use multispectrum hardeners.
The high-end multispectrum hardeners are a staple of supercapital shield ship fits. Do you have a Ragnarok or a Wyvern? When your ship is in the double or triple digits of billions of ISK you donât mind paying a few hundred million or even billions for a multispectrum hardener for better survivability. This means that the prices of those modules will be dictated by players who are willing to pay a lot for them, as itâs little compared to their ship price.
Shield boost amplifiers on the other hand are a much more niche item. Not only restricted to shield ships, like the multispectrum hardeners, these modules also restrict themselves to shield ships that are active tanked and also have enough mid slots to also fit an amplifier after running into diminishing returns on hardeners.
Even if the amplifier is better than even the second hardener already in your use-case of a bastioned Golem, this doesnât mean the price of the amplifier should reflect that.
An example of the math:
The golem has 0% EM resistances.
With the Bastion online it gets +30% resists, so it has 30% EM resists.
Add a hardener with 39.4% resists, it now has 57.6% EM resists.
How?
Each resistance module reduces incoming damage by their specified amount. In other words first you reduce damage by 30% and then by 39.4%, reducing incoming damage by a combined factor of
1 - (1-0.30)*(1-0.394) = 0.576
Next, add a second hardener. Now that we have two similar sources of resistances (two hardeners) we get into diminishing returns: the second hardener is only 86.9% effective.
But the bastion also already gives resistances! The bastion is a unique different source of resistances that only has stacking penalties with damage controls and reactive armor hardeners, so that isnât reduced in this scenario.
So how does damage reduced by bastion and two hardeners look, of which the second hardener suffers diminishing returns?
1 - (1-0.30)*(1-0.394)*(1-0.394*0.869) = 0.721
or 72.1%
The third hardener then has 57.1% effectiveness:
1 - (1-0.30)*(1-0.394)*(1-0.394*0.869)*(1-0.394*0.571) = 0.784
Hopefully itâs a bit more clear now how the math behind resistances works?
Thank you guys, you managed to teach me quite a bit. I do not know why, but I believed that subsequent multispectrums worked a little differently than actual reality, my bad!
I am still curious how to arrive at 806hp/s when having 290hp/s base to which bastion(100%) and 44.75% amplifier get added.
Is it 290 Ă (1 + 100%) Ă (1 + (44.75% Ă 86.9%))?
