Spreadsheets towards a better combat balance: Armor and Shields (including comprehensive plots)

[Gratak]

TLTR:
Replacing the quite complicated armor damage reduction formula by a "simple" DR=1-1/(1+(3-ShipSize/5)*ArmorPoints) (numbers not final ) would be a huge step towards a balanced combat system that is actually "paper, scissors, stone" instead of "well, that is the obvious best choice against everything".


If you do not believe me the "simple", check the current formula. Anyway, the player would not need to understand the formula (anymore). He would just see the final DR% and never have to worry about useless extra armor anymore.


Kudos @Frightning for giving me this base formula. It is indeed better than exponential scaling.

The spreadsheets:
I've set them up as read-only. But you can simply create yourself a copy and start editing/selecting ship type, weapon type, tiers. Generally, yellow marked cells are cells to be changed to get the different plots.
Main spreadsheet:
https://docs.google.com/spreadsheets/d/1llltLAZmIHjONjSY6aU2EPJ6twuIUQDBukj5qyPuYAM/edit?usp=sharing
Experimenting with exponential system (discarded as it may again lead to insane damage reduction, especially with a lot of bonus armor percent):
https://docs.google.com/spreadsheets/d/1ZqQdWLsj07qatdi4H7hBeH-yJ0OdAx-WFwsW1Y9M7iQ/edit?usp=sharing
Experimenting with removing base armor (and point-wise armor piercing):
https://docs.google.com/spreadsheets/d/1RruxH3hk5Y_cuocxCE9TwnX3Ts37ZIuhAt_87YNaR3I/edit?usp=sharing

I have completely ignored dps of the weapons. This is a totally different thing to balance and AFAIK there are a lot of changes coming here. Yet, a balanced armor/shield/weapon bonus system, is necessary to even start really balancing the dps...

Disadvantages of the current additive DR system:
- It is very easy to reach 90% DR with Cruisers and especially battleships. 90% DR means increasing the Hullpoints by a factor of 10, which makes armor piercing weapons mandatory in late game. A battleship of an empire with a bit of extra armor % (from repeatable tech or resource) is almost certainly going to have 90% DR.

Plots: Battleship,40% Armor Bonus}. First row: "no bonus weapon", Second row: Missile L, Third Row: Lance.

Result: Lance is better against full shields than Missiles, simply because they are strong in destroying the baser armor of the Battleship. If the battleship has maxed Armor and adds shields, Lance is way better against a mostly shielded ship.

- Early game armor is useless: Due to the nature of the additive DR system, the more armor you have, the more powerful an additional armor point is until you hit the cap. In order to have the cap at least slightly above the base armor of a battleship, they had to scale the whole system in a way that the first ~30% of DR you get are way too low. You get less extra effective hullpoints than you would with shields and shields to regenerate way faster...

Plot: Tier 2 Corvettes

Result: No reason ever to use armor

- Laser are useless: Early game they are useless because nobody uses early game armor. Late game they are useless, because their armor penetration is simpy too small to work against 90% DR

Example: Hey "Laser S" is stronger against Armor than shields, right? Nope:

- Disruptors are useless: TBH, there are many other reasons for this: Too low base dmg and non-working targetting system. But assuming they are fixed: You can destroy shields 3 times as fast but take 10 times as long to destroy the hull. Sounds like a bad deal...

- The DR-cap itself: I have played Stellaris for 222 hours and only while doing the research for this post, I realized that I have gone above cap in every game... The ship designer does not display bonus armor %... If you always go for 90% DR in the ship designer, you will be wasting utility slots as soon as you get your first bonus armor %. This problem is removed as soon as there is no need for a cap anymore.

- Destroyer uselessness: IMHO, one of the reasons why destroyers are so useless is that they are slightly below the region where armor starts to become useful.

T5:

- Try yourself with the Spreadsheets I have provided and find more imbalanced things (I will add suggestions to this post)

Disadvantages of the suggested DR system with linear effective hullpoint growth:
- Late game weapons would probably need a bit of rebalancing. Basically all of them have quite some armor penetration. They probably did this to make them less useless (in which they failed) with the current system. This would probably make late-game armor a bit weak in the current system. But I guess such a rebalance would turn this into an advantage of the new system (since you still have a "paper, scissors, stone" in late-game.
- Try yourself with the Spreadsheets I have provided and find more imbalanced things (I will add suggestions to this post)

Further examples:
-Early game balance:
Plots: First Row: Corvette Tier 1; Second Row: vs Laser S; Third Row: vs MassDriverS; Forth Row: vs Missile S

Current: Shields are better, Shields are better, Shields are better
Suggested: Armor is better, Shields are slightly better, Shields are slightly better

-Destroyer balance:
Generally stronger destroyers with suggested system:

-Cruiser/Battleship balance:
Slightly stronger shielded
Much weaker armored

 

[Frightning]

Really cool stuff, and thank you for the acknowledgement. I can't really take credit for the general mathematical model itself though, as I have seen it in quite a few games before, but I do think it's important to have most stats scale linearly (even if several of them play into the final results, allowing for multiplier stacking). The current armor formula and its interaction with armor penetration makes it so that there is no real way to differentiate weapon effectiveness against armor, either its armor penetration value is too low, and it provides no significant benefit, or it's too high and it invalidates armor entirely, and there isn't much a middle ground (~40-60% is that middle ground, but there, either it's effect isn't that significant, or it's really not enough to not be completely overshadowed by anything with higher armor penetration values).

In concert with the suggestion given by the OP, I think that armor penetration could be implemented differently. League of Legend's model for penetration in that game allows for both flat penetration (which basically subtracts a fixed amount of armor points for the target when calculating DR) and % penetration (which removes a % of the total armor points when calculating DR). One or both of these could be used in Stellaris. In that model, flat penetration is most effective against targets with low-medium armor as it has a more significant effect on their effective hp (up to the point where their effective armor value is 0). I could also see benefits to having weapons with increased damage to hull, but no armor penetration (idea being: they are effective against unarmored, unshielded hull, but could perhaps have a penalty to shields as downside for their above average performance against hull).

With nicer mathematical models, it will be much easier to carve out interesting and worthwhile strategic niches for the various weapon types in the game which will introduce meaningful choices for ship design (which the current system lacks, especially early and late in the game).

 

[Gratak]

Really cool stuff, and thank you for the acknowledgement. I can't really take credit for the general mathematical model itself though, as I have seen it in quite a few games before, but I do think it's important to have most stats scale linearly (even if several of them play into the final results, allowing for multiplier stacking). The current armor formula and its interaction with armor penetration makes it so that there is no real way to differentiate weapon effectiveness against armor, either its armor penetration value is too low, and it provides no significant benefit, or it's too high and it invalidates armor entirely, and there isn't much a middle ground (~40-60% is that middle ground, but there, either it's effect isn't that significant, or it's really not enough to not be completely overshadowed by anything with higher armor penetration values).

In concert with the suggestion given by the OP, I think that armor penetration could be implemented differently. League of Legend's model for penetration in that game allows for both flat penetration (which basically subtracts a fixed amount of armor points for the target when calculating DR) and % penetration (which removes a % of the total armor points when calculating DR). One or both of these could be used in Stellaris. In that model, flat penetration is most effective against targets with low-medium armor as it has a more significant effect on their effective hp (up to the point where their effective armor value is 0). I could also see benefits to having weapons with increased damage to hull, but no armor penetration (idea being: they are effective against unarmored, unshielded hull, but could perhaps have a penalty to shields as downside for their above average performance against hull).

With nicer mathematical models, it will be much easier to carve out interesting and worthwhile strategic niches for the various weapon types in the game which will introduce meaningful choices for ship design (which the current system lacks, especially early and late in the game).

Thanks

I actually implemented a mixture of a flat and percentual armor penetration in the spreadsheets. I have set the flat part to zero for the plots, as I wanted to suggest something as simple as possible. But yeah, that could also be something to be added and you can try playing around with this by setting the values "!DataJ9" or "!DataJ5:Y5". It could certainly be useful for weapons that are actually meant as anti-shield, but are late game and need to still take care of the base-armor of cruisers and battleships.

 

[EntropyAvatar]

It looks like nice work! I think the armor system as it exists currently is the source of a lot of issues. It would be great if they adopted your suggestions.

Originally they were going to go with a fairly pure subtractive armor system (e.g. each small armor component of a particular tech level reduces damage from each hit by k, med by 2*k, large by 4*k, with some minimal amount of damage that can leak through). Apparently they dropped it due to problems balancing, but I don't know why that system would be hard to balance. Any ideas?

 

[Gratak]

It looks like nice work! I think the armor system as it exists currently is the source of a lot of issues. It would be great if they adopted your suggestions.

Originally they were going to go with a fairly pure subtractive armor system (e.g. each small armor component of a particular tech level reduces damage from each hit by k, med by 2*k, large by 4*k, with some minimal amount of damage that can leak through). Apparently they dropped it due to problems balancing, but I don't know why that system would be hard to balance. Any ideas?

Yeah. A purely subtractive armor system is really hard to balance. The "well-balanced" space in between "no damage at all because armor is too high" and "armor is irrelevant compared to weapon damage" is even smaller in such a system than it is in the one they ultimately adopted. The smaller this space is, the more similar different ships and weapons need to be too each other in order to get a balanced combat system. And very similar weapons and ships are terribly boring. You see one such effect in the armor penetration of L weapons: They had to add armor penetration to almost every single late game weapons, since they otherwise simply failed hard against the 90% armor values. No such thing for shield damage (since that system is easily balanced, except maybe for the problems with re-targeting and shield regenerating because of this).

 

[Frightning]

It looks like nice work! I think the armor system as it exists currently is the source of a lot of issues. It would be great if they adopted your suggestions.

Originally they were going to go with a fairly pure subtractive armor system (e.g. each small armor component of a particular tech level reduces damage from each hit by k, med by 2*k, large by 4*k, with some minimal amount of damage that can leak through). Apparently they dropped it due to problems balancing, but I don't know why that system would be hard to balance. Any ideas?

As Gratak pointed out, the problem is that subtractive armor gives very asymmetric changes in effective DPS, which is essentially the same problem that the current system has. Starcraft uses a subtractive system along with a few damage types which are adjusted by a % very effectively, but that's because the game has a few, set designs that could be, carefully and individually balanced (and even that took quite a bit of time and high-level play to get right)....no such analog with Stellaris and it's customizable ship designs.

 

[Drachenfels]

Starcraft uses a subtractive system along with a few damage types which are adjusted by a % very effectively, but that's because the game has a few, set designs that could be, carefully and individually balanced (and even that took quite a bit of time and high-level play to get right)....no such analog with Stellaris and it's customizable ship designs.

Worth to note that subtractive component in starcraft is 1-2-3 damage less per hit, while unit can be hit with shell that takes 40hp. I believe it plays a factor why substractive system works in this game.