# Stacking

Certain attributes in EVE are stacking penalized so you get less benefit from each additional module you fit to your ship affecting the same attribute. The information below describes the various methods of finding the penalties and are listed in most accurate order.

## Aenigma Formula

There is a very comprehensive paper on stacking penalties written by Aenigma at Battleclinic.<cite_reference_link> He comes up with a different formula to that shown above but his testing shows that it is accurate to 12 digits of precision. This is the most accurate way to find penalties to date. An [edited] excerpt from Chapter 2 of this article is provided below.

To scare most of you, here it is, in it’s rather elegant glory:

$X_n = X_0*\prod\limits_{i = 0}^{n - 1} {\left( {1 + {A_i}*exp\left( { - \frac{{{i^2}}}{{7.1289}}} \right)} \right)}$
With $n$ the number of modules and rigs fitted that all affect the same attribute.
With $X_0$ the start value of the attribute.
With $X_n$ the value of the affected attribute after fitting n modules.
With $i$ being an index number.
And $A_i$ being the bonus to the attribute (either positive or negative), and sorted so that
$\left | A_i \right \vert \le \left | A_{i+1} \right \vert$, which means that the largest bonus comes first.

Ok, what is it? It’s basically a multiplication that goes like this:

$X_n = X_0 * (1+A_0) * (1+A_i * exp(-\frac{1}{7.1289}) ) * \cdots * (1+A_{n-1}*exp(-\frac{(n-1)^2}{7.1289}) )$

Alternatively you could write:

$\begin{array}{lcl} X_1 & = & X_0 * (1+A_0) \\ X_2 & = & X_1 * (1+A_i * exp(-\frac{1}{7.1289})) \\ \vdots & & \vdots \\ X_n & = & X_{n-1} * (1+A_{n-1}*exp(-\frac{(n-1)^2}{7.1289})) \end{array}$

Which is basically the way you would program it.

## Penalty Table

The formula below and resulting table are from the findings of Aenigma at Battleclinic<cite_reference_link> from chapter 3 of his article. This table shows the benefit of stacking 1-11 modules effecting the same attribute based on the formula $h(n) = exp(- \frac{(n-1)^2}{7.1289})$, with $n$ as the number of modules.

Veritech has said the following about using static tables for determining effectivness<cite_reference_link>

(%Veritech) tables for stacking penalty will never be accurate
(%Veritech) [because] the resulting value skews with the value of the inputs
(%Veritech) this is clearly shown if you for ex. put 2 basic dmg mods, check the percentage effectiveness of the 2nd one, and then do the same with 2 officer ones
(%Veritech) you will not get the same effectiveness
(%Veritech) but yeah the difference is prolly not big enough to worry about it

# of Mods/Rigs Resulting Effectivness
1 100%
2 86.9119980800%
3 57.0583143511%
4 28.2955154023%
5 10.5992649743%
6 2.9991166533%
7 0.6410183118%
8 0.1034920483%
9 0.0126212683%
10 0.0011626754%
11 0.0000809046%

As you can see, it’s not very useful to use more than 3 modules that affect the same attribute, since the penalty gets pretty big (or small if you like to see it the other way) pretty fast. A very simple way to calculate an approximate result fast (using a pocket calculator for example) is to use:

$\begin{array}{lcl} X_1 & \simeq & X_0 * (1+A_0) \\ X_2 & \simeq & X_0 * (1+A_0) * (1+0.87A_1) \\ X_3 & \simeq & X_0 * (1+A_0) * (1+0.87A_1) * (1+0.57A_2) \\ X_4 & \simeq & X_0 * (1+A_0) * (1+0.87A_1) * (1+0.57A_2) * (1+0.28A_3) \\ \end{array}$

## About the numbers used for input

$X_0$ is quite easy to find. Most of the times it’s just the attribute the module affects and you can read it right from the screen. The situation is a bit different for shield and armor resistance. What you see on the screen is actually $1-X_0$. If you have a kinetic resistance of 20%, that means $X_0= 1 - 20% = 0.8$.

The numbers $A_0,A_1,\cdots,A_i$ in general are a bit more complex to find, since they are sometimes misrepresented in Eve. One example is the Damage Modifier from the Heat Sink II's. you will see it in game as 1.1x. In these cases you should use the fractional increase, which is 0.1.

The rest goes normally (keep in mind that percentages are fractions of 100, so 43% is equal to 0.43).

## Conclusions

Conclusion 1:

   Generally, don’t use more than 3 modules/rigs that affect the same attribute if they have a
stacking penalty. Exception to this are of course the Remote Sensor Boosters and the Tracking
Disruptors, because if you don’t use them all on the same target, each target will get his own
stack.


Conclusion 2:

   The sequence of fitting stacking penalized modules and rigs doesn’t matter. The biggest bonuses
will always contribute the most.


## FAQs

Q: Do Damage Controls get a stacking penalty with armor or shield resistance modules and rigs fitted?

   A: No, they don’t receive a stacking penalty and apply their full bonus.


Q: Do Remote Sensor Dampeners stack with Sensor Boosters fitted on the targetted vessel?

   A: As of patch 3896, the effects from Remote Sensor Dampeners are separately stacked from
the effects of Sensor Boosters. The same goes for Tracking Disruptors and counter-modules
like Tracking Computers.