How much should balance consider cap-quantity when setting cap-health?

[keith.lamothe]

No particular reason to bring this up right now, but it's one of those things that tends to come up a lot: Specifically, 100 ships with 100,000 health each are typically considerably less useful than 1 ship with 10,000,000 health even though the total hp is identical (and, indeed, the former tends to absorb more total damage due to overkill).

I didn't think this would be as big a deal as it's turned out to be, but "dies in a sneeze" is a common criticism (accompanied with a more-or-less dismissal of the unit) of a lot of the more swarm-oriented fleet ships, and on the other hand a lot of small-cap stuff (fleet ship and starship) winds up being quite durable indeed if balanced on the same health scale as the little guys.

Anyway, assume that a standard mkI cap-health for a normal-cap-quanitity (98 ships on normal) is 15 million hitpoints.  What should cap-health be for a similar ship type that has a double-cap (196), or for another such with a cap of 1?

One approach, which is more or less the current one, is to just have cap-health be 15 million for all three types.

Another approach would be to double the cap-health for the double-cap and halve it for the 1-cap type.  That's based on a quick visualization of the "DPS over time curve" during a battle as parts of the double-cap die off (the shaded area is roughly a right triangle, tapering more slowly toward the end due to enemy casualties) and the 1-cap's DPS stays constant (the shaded area is a rectangle nearly twice the area of the other's triangle).

And of course there's various middle grounds, like a 50% increase for the double-cap and a 50% decrease for the 1-cap, etc.

Anyway, just looking for thoughts.  I'm thinking mainly in mathematical terms of "how much is this health actually worth?" rather than intentional differences in balance (starship types generally have more durability and less firepower than fleet ship types, etc), but other thoughts are welcome too.

[Martyn van Buren]

I think i'd tend toward something on the closer end of the scale to equal cap health, perhaps with cap DPS used as a primary tool for balancing. I feel like swarmers should be something that messes a ton of stuff up if they get to it but evaporate when you manage to shoot them.

[keith.lamothe]

I think i'd tend toward something on the closer end of the scale to equal cap health, perhaps with cap DPS used as a primary tool for balancing. I feel like swarmers should be something that messes a ton of stuff up if they get to it but evaporate when you manage to shoot them.

The main thing I'm trying to determine here is what two types with the same cap-DPS but different cap-Quantity should have in cap-Health.  Obviously if the two types have different cap-DPS that's another thing to factor in, but one variable at a time

[Draco18s]

I think i'd tend toward something on the closer end of the scale to equal cap health, perhaps with cap DPS used as a primary tool for balancing. I feel like swarmers should be something that messes a ton of stuff up if they get to it but evaporate when you manage to shoot them.

I agree, and I was just thinking about the factor of allowing swarming units to get some kind of "dodge" factor, where individual shots miss/do less damage, but things like AOE hurt bad.  I know the game isn't really slotted for random rolls in this department any more, but I wonder if it's something that could be factored in.

The main thing I'm trying to determine here is what two types with the same cap-DPS but different cap-Quantity should have in cap-Health.  Obviously if the two types have different cap-DPS that's another thing to factor in, but one variable at a time

I think the +50%/-50% sounds about right.  The low-cap unit is still going to be "more valuable" for various reasons (individual survivability, individual DPS, use-in-anti-blob situations) but that the swarmers (the double-cap units) won't feel flimsy.  Matched with a proportionally higher DPS (because they SHOULD hit like a ton of bricks before dying like flies) they'll have the great "And I threw wave after wave of my own men against them" feel.
(That's kind of where I thought younglings would fit: produced very rapidly, hit hard, and die instantly, only to be replaced by two more.  Unfortunately the space dock can't produce them fast enough, they can't be force-loaded into a regeneration chamber, and they tend to be a hyperspecialized unit where they actually function best in a fleetball of other younglings).

[TechSY730]

Actually, one ship with a ton of HP can be tricky to use as well due to the Tendancy of both players and the AI to focus their fire on very strong ships.

Anyways, the optimal for ease of use, from what I have experienced, is average HP per ship across average ship cap.

IMO, this is a perception issue mostly. As such, I think cap health should be the focus for health balancing, not individual health.

EDIT3: Post finished, http://www.arcengames.com/forums/index.php/topic,11309.msg114533.html#msg114533

EDIT2: I will say that +50%, -50% seems way too much. Something closer to +10-15%, -5-10% seems more reasonable to me. I'll give my reasoning when I complete this post.

[_K_]

Yeah, double cap getting double cap-hp sounds reasonable to me if both caps have the same DPS and other stats.

The general equation can be made into something like ((98/cap)^X)*(cap HP)*(cap DPS) = c . And what you do is try to keep that "c" constant for different caps. X could be set to 1 to work as you originally said, or it could be set to, say, 0.5 so that when the cap is 2x, the HP or DPS should be increased by 2^0.5, or ~1.4 and so on.

I agree, and I was just thinking about the factor of allowing swarming units to get some kind of "dodge" factor, where individual shots miss/do less damage, but things like AOE hurt bad.  I know the game isn't really slotted for random rolls in this department any more, but I wonder if it's something that could be factored in.

Thats done through giving them some specific chasis class (in fact we have some: Ultra-light, light, swarmer, and probably some more), buffing their HP, and then giving the AOE weapons a bonus against these. In fact, i think its that way already.


Also, how is the situation with Cap resource costs on high-cap ships? In most of my games i felt that even capped, their cap cost is extremely cheap. Which made me not complain too much about them feeling useless.

Oh, and its also the time to grab that unit spreadsheet someone posted around here, probably Keith. Can you post it again? Finding it in those threads would take ages.

[Winge]

Actually, one ship with a ton of HP can be tricky to use as well due to the Tendancy of both players and the AI to focus their fire on very strong ships.

Anyways, the optimal for ease of use, from what I have experienced, is average HP per ship across average ship cap.

IMO, this is a perception issue mostly. As such, I think cap health should be the focus for health balancing, not individual health.

EDIT: More to come

EDIT2: I will say that +50%, -50% seems way too much. Something closer to +10-15%, -5-10% seems more reasonable to me. I'll give my reasoning when I complete this post.

Agreed.  The only reason to even have a difference is that low-cap vessels will more likely be used to crack things like AI Eye planets (higher overall stats on a lower cap = more likely to succeed without spawning zombies.  The last thing the galaxy needs is a Zombie Terminator Apocalypse...).

[Toranth]

I think i'd tend toward something on the closer end of the scale to equal cap health, perhaps with cap DPS used as a primary tool for balancing. I feel like swarmers should be something that messes a ton of stuff up if they get to it but evaporate when you manage to shoot them.

I agree, and I was just thinking about the factor of allowing swarming units to get some kind of "dodge" factor, where individual shots miss/do less damage, but things like AOE hurt bad.  I know the game isn't really slotted for random rolls in this department any more, but I wonder if it's something that could be factored in.

This.  A quick glance shows that low health swarms are more vulnerable to:
AI Eyes (Sentry Eyes)
AI Eyes (Ion Eyes)
AI Eyes (Parasite Eyes)
Grenade Launchers
Electric Shuttles
Beam Frigates
Autobombs
Nanoswarms
Beam Starships
AI Eyes (Sentry Eyes - yes, I listed it twice)
Parasites (all varieties except Botnet)
Flak Guardian
Heavy Beam Guardian
Lightning Guardian
Self-Destruction Guardian
Electric Guard post
Warheads
Attritioners
AI Eyes (Just making the point)

Swarmers are also hit harder by enemy armor - Armor is much better against 10 weaks shots than 1 strong shot.
And in case someone missed it, there is a nasty game mechanic deliberately implemented to shut down large groups of human ships.  The AI Eyes are a hard counter to almost all swarming ship types.


In comparison, large HP low-cap ship types are more vulnerable to:
Artillery Golems
Maws/Disassemblers
Spire Rams (Mini- and Full-sized)

However, large expensive ships tend to have more immunities (Instakill, emp, swallow, etc) which makes them even more survivable.


So, since swarms have so many drawbacks, a little extra health bonus might be nice.

[_K_]

Swarmers are also hit harder by enemy armor - Armor is much better against 10 weaks shots than 1 strong shot.

Oh, it works against swarmers in both ways. They have low individual DPS, so larger % of their DPS is soaked by armor, they also have low individual armor, so larger % of ENEMY DPS damages them directly.

[chemical_art]

the 50 / 50 rule sounds about right.

My favorite youngling combo is the parasite and the weasel combo. The parasites live so short their health is moot usually, but the weasels I like because as far as younglings go they are the strongest in health with decent dps, which makes them not like tissue paper but rather wax paper.

[TechSY730]

OK, now for my "long awaited" completion of my post.

WARNING: Lots of mathematic reasoning ahead,

There are two factors (that I can think of) that make differing caps with same cap HP not the same in terms of matchups. (Armor is being ignored, as that more influences offensive effectiveness more than survivability over changes in ship cap, all other things being equal, especially if the armor mechanics are being changed)


1. The overkill vs. focus fire effect. This makes larger caps, lesser individual HP forces stronger, as more damage is more likely to be wasted by heavy hitters.
2. The diminishing DPS effect. This makes smaller caps, larger individual HP forces stronger, as it takes more to take out one ship and thus it takes more to reduce a fleet's DPS by any amount. (AOE also falls under this category)

So basically, there are thing influencing the cap/individual health tradeoff and how it relates to overall effectiveness both ways.
However, at least in the current balance, factor 2 has an overall average greater effect than factor 1. However, because of factor one, low cap ship's shouldn't be penalized too much.


Also complicating things, the magnitudes of how much 1 and 2 matter are non linear. For below average caps, factor 1 is about linear, but for above average caps, it starts out about linear, but will "accelerate" upwards as cap gets bigger. (Imagine 98 vs 1 billion ships, even if of those 1 billion ships were scaled down accordingly)
However, I wouldn't worry about that. If my thought experiments are right, it would take like 5x average cap before you really start seeing the super-linear nature of factor 1 begin to be noticeable. Nothing in the game currently has more than 3x the average cap, meaning adjusting for this factor linearly would be a decent approximation.

A similar story for factor 2, but with directionality reversed (noticeably super-linear for less than cap, about linear for more than average cap). However, the point where the super-linear case would start noticeably showing around 5-10 (numbers, not multipliers), which DOES happen in the game.

Taking all this together, at average cap (98 on medium caps), the cap health "adjustment" would be 1x (to form a baseline), as the cap goes up and individual health goes down, the cap health "adjustment" would go up (due to factor 2's greater influence) about linearly (but slowly), but then at around 4x cap, would start to taper off some (due to factor 1's super linear nature starting to assert itself), and then once you really get high, would actually start decreasing back to 1x (due to factor 1's super linear nature finally overtaking factor 2). As mentioned, you don't really have to bother modeling this, as there are no 4x of average caps in the game currently.
A similar effect as cap goes down and individual health goes up. The cap health adjustment would go dow about linearly (probably at a slower pace than it went up when caps went up), until around 15 or so where it would taper off and decrease more slowly, until around 5, where it would actually start heading back up to 1x, getting close to 1x once cap reaches 1.

I can try to graph this is you want.

Some critical points need to be established though. Let N be the average ship cap. Then, with the cap health adjustment needed to offset utility change over ship cap, (function H), with H(N) = 1, what would H(N/2), H(2N/3) (or possibly H(3N/4)), H(10), H(5), H(1), and H(2N) be? (As mentioned, for now, we can model H(x) for x>N pretty much linearly, as caps don't really get big enough to start hitting that "tapering off" point where the wasted overkill effect starts to overcome the reduction in DPS per ship loss effect, unless someone can show that 3.2x, it does start to come into play significantly, in which case we will need some more "shape defining" points to be determined for H(x) for x > N).

Also, I am still of the opinion that the 50/50 rule (which, expressed in terms above, H(2N) = 2, H(1)=.5) is a bit much. Something closer to 25/80 seems more like it (H(2N) = 1.25, H(1) = .8)
But then again, someone will need to figure out some more quantitive data about how much factor 1 and factor 2 come into play, especially with regards to each other, to figure out where the "critical points" of how utility varies over ship cap.




See, balancing is easy.

[Ricca]

Well, Keith. I think it should be about, say, 5 to 15% either way.

Thing is, with the swarmer units, they either have a way of sneaking in close (Autocannon, Space Plane), being annoying to the AI (Space Plane again), or have other benefits (Deflector Drones being amazingly annoying to EMP Guardians). I mean, if Infiltrators got, say, immunity to attrition or to area effect damage, then I'd fear them in waves.

I mean, I won't complain about getting Laser Gats or Infiltrators from an ARS, but I wouldn't go out of my way to get them as my starting bonus unit.

[chemical_art]

After further review, something along the lines of between 15 - 30 % bonus for smaller ships would be better I think.

[Bognor]

Oh, and its also the time to grab that unit spreadsheet someone posted around here, probably Keith. Can you post it again? Finding it in those threads would take ages.

I guess you mean this: http://www.arcengames.com/forums/index.php/topic,9879.msg93183.html#msg93183

It's a bit old now, though there haven't been many changes to fleet ships since I last updated it.  Teleport Battlestations have been buffed significantly.  I'm intending to update when the next expansion comes out.

[relmz32]

[...math and awesome ...]

Also, I am still of the opinion that the 50/50 rule (which, expressed in terms above, H(2N) = 2, H(1)=.5) is a bit much. Something closer to 25/80 seems more like it (H(2N) = 1.25, H(1) = .8)
But then again, someone will need to figure out some more quantitive data about how much factor 1 and factor 2 come into play, especially with regards to each other, to figure out where the "critical points" of how utility varies over ship cap.




See, balancing is easy.

I agree with TechSY completely. A modified range of 80% for tiny caps up to 125% for high caps feels less extreme

I kinda think that splitting the bonus for low cap ships among their damage as well as their health could be good.
To be clear, The 25% bonus should be split between the two, such as 25/0, 15/10, 0/25.