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Math behind Mitigation via Shields and Armor

By on April 29, 2012 2:11:40 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

samt9892

Join Date 07/2009
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Hey guys

I've always wondered how the relationship between shield mitigation and armor works.

Sins wikia has some infomation on how Shield Mitigation functions:

http://sinsofasolarempire.wikia.com/wiki/Shield_Mitigation

But I have been unable to find any infomation on how armor points relate to damage reduction, and whether mitigation from shields is applyed before that of armor (does shield mitigation also apply when shield hp is at 0% ?).

Does anyone have any insight to offer on this?

 

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April 29, 2012 2:24:12 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

Mitigation is always active, armor only for hull. Each point of armor basically makes each point of hull absorb a bit more damage, starting at 5% but with an element of diminishing returns (can't remember the exact formula), so even starbases with more than 20 armor are quite destructible.

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April 29, 2012 2:33:36 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

the damage the hull of a ship can take, not taking into account shield mitigation, or armor modifiers is equal to hullpoints*(1+0.05*armor)  so, a unit with 20 armor can take twice as much damage as a unit with zero armor.

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April 29, 2012 2:33:48 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

Thanks for the replies, all makes abit more sense now

 

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April 29, 2012 6:54:19 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

Here's a quick little chart showing the damage reduction values from armor.  For Shield Mitigation, it's just damage*shieldMitigationAmount, like 100dmg * 0.65 (65%) = 65 actual damage hitting your hull.

Sins - Armor Chart

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April 29, 2012 7:02:35 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

No, shield mitigation is the % of damage negated, so 65% mitigation means you only take 35% damage.

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April 29, 2012 7:19:48 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

For a unit with shields, the formula is as follows for damage.

Damage Applied = ((1-Shield Mitigation)*Raw Damage)/(1+0.05*Armor)

For a unit without shields, simply remove the (1-Shield Mitigation)* from the beginning while one would remove the /(1+0.05*Armor) for calculations where hull is not yet involved as shields have not yet been broken.

 

Let's go with the example of a unit with maxed mitigation at 60% and 20 armor.  To find the amount of damage reduction, just plug in a 1 for Raw Damage.

((1-0.6)*1)/(1+.05*20) = (0.4)/2 = 0.2

That is to say, a unit with such characteristics would take only 20% of incoming damage as actual damage when dealing with hull because 60% mitigation reduces incoming damage to 40% while 20 Armor cuts damage taken to hull in half, resulting in 20%.

EDIT:

The same principle of 1/(1+Y) applies in other regards as well.  If a ship were to have a buff applied to it that would increase damage by 100%, this would be extended to 1/(1+Y) where Y=1.00.  1/2=.5, therefore, damage output would actually be increased by 50%.  If the buff says 20% increase in damage, that'd be 1/(1+.2)=1-1/1.2=16.7% increase to damage output.

I do not know if this same concept applies to accuracy buffs and debuffs or not.

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April 30, 2012 1:13:19 AM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

Yeah, some of the in game tip numbers are a bit confusing... it would be really nice if they were converted to something more in line with "lay person" expectations.

 

Not all of us can do that kind of math in our heads while gaming. If we could, we'd probably be game devs

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April 30, 2012 1:20:17 AM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

Quoting Volt_Cruelerz,
The same principle of 1/(1+Y) applies in other regards as well. If a ship were to have a buff applied to it that would increase damage by 100%, this would be extended to 1/(1+Y) where Y=1.00. 1/2=.5, therefore, damage output would actually be increased by 50%. If the buff says 20% increase in damage, that'd be 1/(1+.2)=1-1/1.2=16.7% increase to damage output.

Are you sure about that? I know for decreases it uses that formula, so -100% means halving the attribute in most cases, rather than completely eliminating it (stealing planet income, max population, and shield bypass chance are some exceptions). However I thought +100% was still doubling it.

 

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April 30, 2012 1:35:46 AM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

geofan, I am fairly certain you are correct... but should be easilly testable with the tec loyalist titan.

 

there is, though, a really big ??? on the accuracy buffs and debuffs.

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April 30, 2012 1:37:24 AM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

Quoting TheEvidence,
Yeah, some of the in game tip numbers are a bit confusing... it would be really nice if they were converted to something more in line with "lay person" expectations.

 

Not all of us can do that kind of math in our heads while gaming. If we could, we'd probably be game devs

lol I'm a game dev, suck at calc, and still do the math for this in my head.  Sure, sometimes I end with an estimation, but it's pretty close.

Quoting GoaFan77,

Quoting Volt_Cruelerz, reply 6The same principle of 1/(1+Y) applies in other regards as well. If a ship were to have a buff applied to it that would increase damage by 100%, this would be extended to 1/(1+Y) where Y=1.00. 1/2=.5, therefore, damage output would actually be increased by 50%. If the buff says 20% increase in damage, that'd be 1/(1+.2)=1-1/1.2=16.7% increase to damage output.

Are you sure about that? I know for decreases it uses that formula, so -100% means halving the attribute in most cases, rather than completely eliminating it (stealing planet income, max population, and shield bypass chance are some exceptions). However I thought +100% was still doubling it.

 

I'm pretty sure it's not.  Researchables are straight percentages though.  Unless I'm mistaken, all buffs use the system though.

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April 30, 2012 5:55:16 AM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

But has it already been clarified whether the shield mitigation applies to the shield, or only to hull?

I always found there are two opposing statements about it.

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April 30, 2012 9:53:27 AM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

Shield mitigation is always applied on any unit that has shields, providing of course that there is/are no buff/buffs that reduce mitigation to zero.

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April 30, 2012 10:03:40 AM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

Shield mitigation is always on for a unit with any shields even if it's shields have been depleted. So it's applied to both shields and hull.

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April 30, 2012 3:09:04 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

and for shield mitigation, no one is really sure at what point the reduction occurs. So, you cant make a single formula that takes in damage and calculates the exact damage sustained.

I'm pretty sure the reason no one has figured this out has to do with the way mitigation increases per hit combined with in-combat regeneration...

actually... couldnt you mod a ship to start with maxed out mitigation and shut off shield and hp regeneration on a ship? make sure the damage modifier isn't changing the damage and I think you could figure it out.

after doing this, you could run similar tests on a ship with hp and sp regeneration on and see how it affects the numbers..

 

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April 30, 2012 3:21:44 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

Quoting Volt_Cruelerz,
I'm pretty sure it's not.  Researchables are straight percentages though.  Unless I'm mistaken, all buffs use the system though.

Not all research modifiers work like that...as an example, the Vasari credit/resource cost decreases for purchases do not, and neither do the bonuses to construction rates...

 

 

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April 30, 2012 5:16:07 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

Quoting Seleuceia,


Not all research modifiers work like that...as an example, the Vasari credit/resource cost decreases for purchases do not, and neither do the bonuses to construction rates...
 

Forgot about those... 

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April 30, 2012 8:29:21 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

This http://forums.sinsofasolarempire.com/305565 covers all the combat mechanics, including armor/shield mitigation pretty thoroughly, although it was posted shortly after the initial release (March 2008) so for all I know it might be completely wrong. 

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April 30, 2012 10:20:38 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

That was last updated in January of '09, but is right about most of the stuff. Some of the attack bonuses have been changed I think, and there's obviously been new ships and stuff added, so I would ignore the chart on there, but the rest is pretty timeless stuff.

In there, they mention the trouble with figuring out mitigation, but show how to figure out stuff anyhow.

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April 30, 2012 11:36:32 PM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

The problem is that multiplicatively a straight percent increase followed by a straight percent decrease dont cancel each other out. For example, if we start with 100 and increase by 25%, we get (1+.25)*100=125. If we follow that by a 25% decrease, we now have (1-.25)*125=93.75. However if we follow a 25% increase by a 20% decrease we get (1-.20)*(1+.25)*100=100. So a 20% decrease cancels out an initial 25% increase if the percents are applied multiplicatively.

In general, if X is the original increase and Y is the equivalent decrease, (1+Y)(1+X)=1, so 1+Y=1/(1+X). I'm not sure what the game actually does, but I think it displays X and uses X for increases and displays X and uses Y for decreases. That way a green 25% and a red 25% cancel each other out, even though one is a 25% increase and the other is a 20% decrease.

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May 1, 2012 10:45:41 AM from Sins of a Solar Empire Forums Sins of a Solar Empire Forums

Added to the Modders-Get-An-Answer page links.  Nice job all.

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