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[Cryovolcanic]

Hoping the strong mathematical people can help me understand something about damage reductions:

Since damage reductions are usually multiplicative, does there come a point where the incremental gain of adding one more damage reduction is not worth the OP or skill point cost? Meaning, do damage reductions have increasing returns to scale, or diminishing returns to scale? In many games the relationship between "armor" and EHP gives the defensive stat an increasing return to scale, e.g., if you go from 90% to 95% damage reduction, you double your EHP and survivability. I'm trying to understand how this relationship works in Starsector, because I think it's different.

Example

Aurora

.6 shield * hardened shields .8 * solar shielding .9 * s-mod shield conversion front .95 * elite sysex .9 * Field modulation .85 = .31 efficiency shield, or enemy spends 3 flux to do 1 flux of damage

So stacking all this stuff basically doubles the Aurora's survivability. But if we drop the 2 skills, and just do the hullmods, we get

.6*.8*.9*.95 = .41 efficiency, or enemy spends 2.5 flux to do 1 flux of damage

I'm having a hard time thinking about the relationship mathematically. In theory, if I could spend 15 OP unlimited times to improve efficiency by .9 each time, would I want to do that? Or are there diminishing returns to scale in here?

[SCC]

Damage reductions being multiplicative means that a given buff always increases your effective ship HP, armour or shields by the same fraction, regardless of what else is affecting the ship. The difference in shield EHP for two loadouts of a given ship, otherwise identical except for one having Hardened Shields hullmod, will always be relatively the same. Hardened Shields always increase your shield EHP 1/0,8=1,25 times, regardless of whether you put it on a Dram, a Conquest or a 15 combat skill Medusa flagship.

A single damage reduction will always increase durability by the same amount, when comparing a ship with and without that reduction. The reason why getting some damage reductions might be not worth it is for opportunity costs (e.g. sometimes Hardened Shields adds less shield EHP, than simply adding that many capacitors).

[Hatter]

What SCC said, but since I already typed this out:

The Starsector method gives a 'flat' scaling in that damage reduction will give a multiplicative  bonus to effective HP.

Damage reduction can be thought of as effectively an HP bonus. -50% damage reduction effectively gives 100% more HP. -10% damage reduction gives 1/0.9 = ~1.11 = 11% more effective HP.

If the damage reduction was additive, taking -10% ten times would give a -100% damage reduction, or an infinite increase in effective HP.

Multiplicatively, 10% damage reduction ten times gives 1.11^10 = ~2.87 HP factor = +187% effective HP.

There are not diminishing returns, the damage reduction stacks multiplicatively. Every damage reduction multiplies both the base HP and the 'HP' effectively added by every other damage reduction.

I'm not going to get into how this works with the Armor mechanics.

[Cryovolcanic]

Ok, this is helpful, thanks Hatter/SCC. Said another way, I want to think of these as the reciprocal of the damage reduction, as a multiplier. So as you pointed out

Hardened Shields is a 25% shield HP increase
Sysex is a ~11% shield HP increase
etc

That also makes it a lot easier to understand in terms of the tradeoff vs. caps. So it's likely that adding raw caps will at some point be more efficient than adding another multiplier of shield HP reduction. It also looks like Hardened Shields should be added for a 25% increase in shield HP sooner than Solar Shielding for 11% only against beams, but SS does help hull and armor... hmm. It's complicated.

When I'm planning out an SD/DO build, -25% hull damage from Damage Control is 1/.75 = a 1.33x increase in hull HP, which is multiplied by the 40% hull increase of Reinforced bulkheads, for a ~1.862x increase hull HP, reduced by residual armor. And Solar Shielding would increase this against beams.

Any thoughts on when the s-mod for Stabilized Shields is worth it? Transforming 10% of incoming damage to soft flux which can then be dissipated.

I know the armor calcs get mad complicated.

[Phenir]

Ok, this is helpful, thanks Hatter/SCC. Said another way, I want to think of these as the reciprocal of the damage reduction, as a multiplier. So as you pointed out

Hardened Shields is a 25% shield HP increase
Sysex is a ~11% shield HP increase
etc

That also makes it a lot easier to understand in terms of the tradeoff vs. caps. So it's likely that adding raw caps will at some point be more efficient than adding another multiplier of shield HP reduction. It also looks like Hardened Shields should be added for a 25% increase in shield HP sooner than Solar Shielding for 11% only against beams, but SS does help hull and armor... hmm. It's complicated.

When I'm planning out an SD/DO build, -25% hull damage from Damage Control is 1/.75 = a 1.33x increase in hull HP, which is multiplied by the 40% hull increase of Reinforced bulkheads, for a ~1.862x increase hull HP, reduced by residual armor. And Solar Shielding would increase this against beams.

You said it twice so I want to point out, just in case, solar shielding works against specifically energy damage, not just beams. That means it works against mjolnir (energy damage ballistic) but not against HIL (high explosive energy).

[Cryovolcanic]

Ah, thanks for catching that. Yes, I didn't quite understand what SS does. By beams I meant "energy weapons," not "energy damage."

Thanks for the correction and clarification.

[Vanshilar]

Yes quite a few modifiers, when they say for example -20% damage, it really means the incoming damage is increased by 20%, which really means you get +25% to your effective hit points (EHP) i.e. your flux bar. However, you still dissipate your flux at the normal rate, so it's quite often better to take the damage reduction over more caps if it's close, since you'll dissipate the flux more quickly that way. For example if the incoming damage is 200, if you chose more caps then you have to dissipate 200 flux, but if you chose Hardened Shields (-20% damage) you only have to dissipate 160 flux.

With armor/hull it becomes more complicated, since reducing the incoming damage also reduces its hit strength. For example, Impact Mitigation says -25% armor damage taken. This does not mean "if the shot would've done 100 damage to armor, it now does 75 damage instead". Instead, it means the shot is calculated as coming in with 75 damage, which also means its hit strength is now 75 instead of 100 instead. That latter part also decreases the damage further. For a good number of armor-to-hit strength ratios, it'll actually reduce the damage by around 40% -- so if the shot would've done 100 damage to armor, it now does 60 instead. So those damage reductions are actually significantly stronger when you consider the armor mechanics.

[Cryovolcanic]

How about Damage Control? What is the best use case for the skill? It seems that it's the simplest raw HP increase.

Perhaps only useful if you can regenerate the lost hull with elite skills.