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If I apply two or more target painters to the same target, is their bonus stacked additively or multiplicatively?

For example, the M4 target painter provides a signature bonus of 30% without training Signature Focusing. If I apply two of these to a frigate with a base signature of 100m, is the resulting signature bonus 160m or 139m?

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up vote 3 down vote accepted

The exact same stacking penalty applies to their use as most every other module in the game:

S(n) = 0.5^(((n-1) / 2.22292081) ^2)

1st mod: 100.0% effectiveness
2nd mod: 86.9% effectiveness
3rd mod: 57.1% effectiveness    
4th mod: 28.3% effectiveness 
5th mod: 10.6% effectiveness
6th mod: 3.0% effectiveness

roughly.

So, with a Tech1 target painter bonus of 30% and a target signature radius of 100m, the first would give a sigrad of 130m, the second would be 163.8m, the third 191.85, etc. It is multiplicative (though not in the sense you're asking), but also subject to stacking penalty.

To use an in-game example ( just tested on Singularity to confirm ): The Moa has a sigrad of 135m. A T1 painter has a 25% bonus to sig radius. This is what I observed:

No modules: 135m
One module: 168 // +25% // net +24.44% (EVE truncates)
Two modules: 205m // +21.725% = ( 25% * 86.9%) // net +51.85%
Three modules: 234m // +14.275 = ( 25% * 57.1% ) // net +73.33%

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This means the second module is MORE effective than the first, I don't think that is correct. Maybe it is additive. (first = 30m bonus, 2nd = 33.8m bonus) –  Resorath Aug 15 '13 at 0:58
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@Resorath Of course the second module is more effective - it has a larger base to multiply, even though the bonus is less. If the base effect was smaller (say.. 10%) the second module would be less effective, because it had less to work with in the first place. –  Phill.Zitt Aug 15 '13 at 2:05

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