After the shield shunt nerf, I got to thinking -- how bad or not bad is it now?
Since the armor damage reduction calculation is rather complex, it's unclear how well a +15% increase to armor actually translates to combat performance. So I devised a couple of metrics to quantify how strong armor is in practical terms, as well as to gauge how strong skills and hull mods that affect armor actually are.
A note: I am making some simplifications for this analysis. First, I'm only going to consider a single block of armor, and I'll assume that that single block contributes all of its armor value, rather than taking an average over many surrounding blocks. Next, I'm going to assume that weapons deal continuous damage with two parameters: a hit strength H, and a base DPS B. Projectiles weapons can be approximated as beam weapons with B equal to their stated DPS and H equal to the projectile damage. The continuous assumption is what makes an analytical solution possible; otherwise, we'd be looking at some ugly recurrence relations.
For those who are unfamiliar with the armor mechanics, I'll give a brief recap. Suppose that A is the total armor of your ship. This is the number that appears in the refit screen, and is modified by hull mods like shield shunt, heavy armor, armored weapon mounts. However, it doesn't account for skills like polarized armor (which gives invisible armor for damage reduction purposes only) and impact mitigation (which reduces damage taken by armor, and used to give a flat invisible armor bonus). The total effective armor, which is the number actually used for damage reduction purposes, can be written as e(A) = uA + v, where u accounts for bonuses of the form "grants x% armor for damage reduction calculation purposes only," and v accounts for bonuses of the form "grants y (flat) armor for damage reduction calculation purposes only."
Suppose your ship currently has X armor. When your ship's armor gets hit by a beam with stated DPS B and hit strength H (usually H = B/2 for beams), the DPS sustained by the armor is (1 - R) * B, where R is the damage reduction fraction. Normally, R = e(X) / (e(X) + H) . However, there are two exceptions: if e(X) / (e(X) + H) > 0.85, then R is set to 0.85 (or 0.9 if you have polarized armor), so that your ship will always take a minimum fraction of damage regardless of how much armor it has. The second exception is if e(X) < e(0.05*A), in which case the armor value used is instead e(0.05*A), so that you will always have a minimum base armor value for damage reduction calculation, even if your armor is fully stripped.
A natural way to judge practical effectiveness of armor is to consider how long it takes for a particular weapon to fully strip it. I'll call this the strip time T. It turns out that, in the absence of the two exceptions above, T is quadratic in A -- that is, T is proportional to A^2. So, the more armor you have, the more effective the additional armor is. This makes flat armor bonuses -- heavy armor in particular -- more useful than they might initially seem.
What I'm really interested in is how much longer it takes to fully strip armor once we add certain skills and hull mods. For this, I'll consider the strip time ratio -- the amount of time it takes to fully strip armor with said skill or hull mod, divided by the amount of time it takes to fully strip armor without it. Skills and hull mods with higher strip time ratios are, in a very practical way, better. However, it comes as no surprise that the strip time ratio varies depending on the ship's base armor value. Here are graphs of strip time ratios of various skills, hull mods, and combinations thereof, for the following weapons: tactical laser (B = 75, H = 37.5), heavy mortar(B = 220, H = 220), and plasma cannon (B = 750, H = 500).
Some observations from these graphs:
- For most armor modifiers, strip time ratio increases with increased base armor until it hits a peak, after which it starts to decrease. The peak is the point at which the 85% damage reduction cap starts to kick in, since at this point the strip time goes from quadratic to linear. The obvious exceptions to this are polarized armor, which gains effectiveness past the damage reduction cap due to it increasing said cap to 90%; and heavy armor, due to being a flat increase.
- The general individual order of effectiveness of skills, along with shield shunt, is IM > SS (pre-nerf) > SS (post-nerf) > PA (assuming constant 25% bonus). PA dominates when the weapon's hit strength is low or base armor is high, due to gaining effectiveness once the damage cap is reached. With a 50% constant bonus (pre-nerf), PA actually competes with SS (post-nerf) against a plasma cannon, being weaker up until ~850 base armor and stronger after that. Note that since IM reduces damage and hit strength to armor by 25% (reference:
https://fractalsoftworks.com/forum/index.php?topic=22699.15), it is effectively increasing armor by 33%, which is better than even pre-nerf shield shunt.
- Individually, the skills aren't particularly strong, improving strip time by a modest factor. The strongest, impact mitigation, caps out at about a 1.5 strip time ratio. However, they are comparatively much stronger when combined. With a decent base armor, the strip time ratio can be improved by a factor of 2-2.5 when stacking all three of SS, IM, and PA together (assuming 25% bonus for PA). When combined with HA and AWM, you can triple to quadruple your ship's armor's strip time, even with upwards of 1000 base armor. The reason why the skills and hull mods work so well when combined is due to how they stack. Hull mods affect the visible armor value and stack additively with each other, but everything else stacks multiplicatively. Polarized armor affects effective armor and impact mitigation affects hit strength and damage taken, each of which are modified separately from the ship's base armor.
I've attached a pdf showing how I derived the strip time formula, as well as a Mathematica notebook that I used to create the graphs, for anyone who is interested in playing around with the values themselves.
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