So, turret balance

[Faulty Logic]

Here's an interesting formula to consider when balancing ships with different caps.  If you take a ship and change its cap but leave its CapHealth and CapDPS unchanged, you modifier its total damage over the course of a fight in which in which it is wiped out by a constant amount of incoming DPS.  The total damage multiplier for going from a cap of C to a cap of N is: ((N+1)C^2) / ((C+1)N^2).  So for example, going from a cap of 96 to a cap of 1 gives you 190 times more total damage output over the course of a fight.  Going from a Cap of 96 to a Cap of 192 reduces total damage output by about half.

If someone wants, I can break down the origin of that formula.  It's just a little long and awkward to type in the forum  .

True in weird, idealized circumstances. But your calculations may be disrupted by the flying pigs and the AI offering peace 

In any large-scale battle, individual unit strength doesn't matter, just the ratio of HP to DPS.

[TechSY730]

Here's an interesting formula to consider when balancing ships with different caps.  If you take a ship and change its cap but leave its CapHealth and CapDPS unchanged, you modifier its total damage over the course of a fight in which in which it is wiped out by a constant amount of incoming DPS.  The total damage multiplier for going from a cap of C to a cap of N is: ((N+1)C^2) / ((C+1)N^2).  So for example, going from a cap of 96 to a cap of 1 gives you 190 times more total damage output over the course of a fight.  Going from a Cap of 96 to a Cap of 192 reduces total damage output by about half.

If someone wants, I can break down the origin of that formula.  It's just a little long and awkward to type in the forum  .

True in weird, idealized circumstances. But your calculations may be disrupted by the flying pigs and the AI offering peace 

In any large-scale battle, individual unit strength doesn't matter, just the ratio of HP to DPS.

Yes, but for any large scale battle "to the death", the side that will lose will get their forces down to 0. Of course, on the way, they go below what can be considered "large scale" (the attacker might get below that magnitude as well, depending on how evenly matched the two forces are). In which case, the "you only need to consider ratio of HP to DPS" approximation begins to become too inaccurate. It is in those cases where how that HP and DPS are distributed start counting, in some cases (like nearly evenly matched forces in terms of HP and DPS), big time.

Plus, when doing "guerrilla" or raiding operations, you deliberately avoid large scale fights.

[keith.lamothe]

Well, in terms of effective dps-over-time in a battle, I think the worst (for the high-caps stuff) case situation can be illustrated thus:

1) Imagine Ship A has 10,000 HP, fires one shot per second, and does 100 Damage Per Shot

2) Imagine Ship B has 10,000 HP, fires one shot per second, and does its currentHP/100 Damage Per Shot (so it starts at 100)

3) Assume opponents fire at each other exactly the same time, and that the shot travel time is less than a second, and they keep firing until one is dead.

4) Test 1: Ship A vs Ship A.  100 seconds will elapse, and both will be dead at the end.  Dead-even match (of course).

5) Test 2: Ship A vs Ship B.  100 seconds will elapse, but because Ship B's Damage will be 100 + 99 + 98 + ... + 2 + 1 instead of 100 + 100 + 100 + ... + 100, Ship A will have 50% of its health left when it wins.


Ship B in that case is just a stand-in for a theoretical "infinite cap" ship in that every bit of damage done to it reduces its outgoing damage.  And it does half the damage of the "1-cap" ship.

So can the actual impact of a cap shift actually be more than a 50% reduction or a 100% increase?

[Hearteater]

In any large-scale battle, individual unit strength doesn't matter, just the ratio of HP to DPS.

Demonstrably false.  Starships prove it.

When I get home I'll write the whole thing out.  I did a sanity check on my formula and I think I need to revise it slightly.  It still shows total DPS output goes up or down based on changes to cap size, just not quite as extreme.  I need to sit down and work it out slower.

[keith.lamothe]

When I get home I'll write the whole thing out.  I did a sanity check on my formula and I think I need to revise it slightly.  It still shows total DPS output goes up or down based on changes to cap size, just not quite as extreme.  I need to sit down and work it out slower.

Conceptually I just think of:

- the "1-cap vs 1-cap" case as having a "rectangular" dps-over-time graph: it starts at full, runs for X time, and then goes to zero.  Area under curve (total damage done) is a rectangle.

- the "infinite-cap vs 1-cap" case as having a "triangular" dps-over-time graph: it starts at full, and declines linearly towards zero at X time.  Area under curve is a triangle.  If cap health and cap dps are same as the 1-cap ship then it's (in theory) equal to exactly half the area of the first case's rectangle.

[TechSY730]

When I get home I'll write the whole thing out.  I did a sanity check on my formula and I think I need to revise it slightly.  It still shows total DPS output goes up or down based on changes to cap size, just not quite as extreme.  I need to sit down and work it out slower.

I was about to say. 1/2 expected damage output for 2x caps seems too extreme of what I tend to see. If I were to guess, it would be about 75% to 85% for 2x caps.
EDIT: (That's 75% to 85% of the "base case expected effectiveness", not a 75% to 85% reduction. If you want it in terms of percentage reduction, that would be 15% to 25% reduction)

[Faulty Logic]

So can the actual impact of a cap shift actually be more than a 50% reduction or a 100% increase?

Yes, of course (imagine a ship doing 1 damage/second with 1 hp). 4000 of those is a lot more effective than a fighter. But my point was that these situations are vanishingly rare in this game, so shouldn't have a high weight in the balance thereof.

Demonstrably false.  Starships prove it.

You may be using a different definition of "large-scale" than I am.

But starships surviving is to be expected. They have a low DPS:HP ratio, so they are fairly low on the autotarget list (as they should be). Skirmishes and raids are where HP and toughest-individual-unit matter.

If you are in a battle where the toughest single ship can die really fast, then the ratios are all that really matter.


Take a ship with 4 hp and 1 dps. The mkII has 8 hp and 2 dps. Cap of 24, say.

Two ships mkI lose to a mkII, with the victor having no losses.
Two caps of mkI lose to a cap of mkII, but just barely. Here's how it breaks down:
Edit: also included the results of 20 caps mkI vs 10 caps mkII:

48/24   480/240
36/18   360/180
27/14   270/135
20/11   203/102
15/8    153/76
11/6    115/57
8/5      86/44
5/4      64/33
3/3      48/25
2/3      35/19
1/2      ...
0/2      0/6             

As the size of the battle increases, individual unit strength relevance approaches zero. It is quite close to zero for the whole game, and thus should not be a major factor in balancing.

[Hearteater]

Fixed the formula: c(n+1) / n(c+1) where c is the old cap, and n is the new cap.  The result is the percentage of the total damage dealt by the old cap that the new cap will deal.  So going from 96 to 48 you'd use c=96, n=48, and you'd get 101%.  So a +1% damage dealt by reducing their cap.

@Faulty_Logic:
Two caps of Mark Is (48 ships) vs one cap of Mark II (24 ships) is like using the above formula with c=48 and n=24.  You find the cap of 24 deals 102% more total damage.  And your example shows this with the lower cap wining, but just barely.  Both sides have the same HP:DPS ratio, which you claimed is all that matters.  But it doesn't, because one side had a 2% edge.  Hence, your claim that HP:DPS ratio is all that matters is incorrect.

[Faulty Logic]

@Faulty_Logic:
Two caps of Mark Is (48 ships) vs one cap of Mark II (24 ships) is like using the above formula with c=48 and n=24.  You find the cap of 24 deals 102% more total damage.  And your example shows this with the lower cap wining, but just barely.  Both sides have the same HP:DPS ratio, which you claimed is all that matters.  But it doesn't, because one side had a 2% edge.  Hence, your claim that HP:DPS ratio is all that matters is incorrect.

Yes, once the vast majority of casualties has been inflicted, then the individual unit toughness matters. But by then the result of the battle has already been decided, and it isn't a large battle anymore.

Yes, I exaggerated a little bit. But I, of all people, should be able to get away with it. Look at my handle 

[Hearteater]

I don't think it is large battles per-say, but rather when total ships on each side are in the say range.  At the same HP:DPS ratio, 1000 ships vs 1 is a blowout for the 1.  But it would be the same for 10 vs 1.  But for 6 vs 5 or 6000 vs 5000, you are right, HP:DPS is more important.

[KDR_11k]

Back to the turrets, I have about 20-50 on regular planets with high priority ones getting around 100. Even small AI waves are around 200-300 ships so no way I can stop those without sending my mobile fleet. The main concern with turrets is running out of cap and having planets be so undefended that a single ship can destroy the command there. Some turrets (e.g. lasers) only see use because of missile-immune enemies negating the important rocket turrets.

[TechSY730]

Back to the turrets, I have about 20-50 on regular planets with high priority ones getting around 100. Even small AI waves are around 200-300 ships so no way I can stop those without sending my mobile fleet. The main concern with turrets is running out of cap and having planets be so undefended that a single ship can destroy the command there. Some turrets (e.g. lasers) only see use because of missile-immune enemies negating the important rocket turrets.

And there my friend is the challenge.
You have only so many turrets, so where do they really count? What places can afford less turret protection? What places need more? How can you shape the AI response such that they will usually (or must) go through where you have the turrets?
If you don't think trying to answer those questions are worth what turrets give you, well, maybe you aren't a "relying on turrets for a large portion of your defensive duties" kind of player.
It only starts showing a large balance problem if most players say that trying to answer those questions is not worth what turrets give you, and the turrets themselves may be at fault (which may be what is happening here)

Also, since when does 50-100 turrets fail to stop a equally marked 200 fleetship fleet? It should be able to unless they are like 200 low cap ships or something, in which case, the "effective fleet ship count" would really be in the thousands. Especially if you are using gravs and tractor turrets, and maybe mines too.

[Hearteater]

As a rough metric for unit power Keith, you could probably use this: CapHealth * CapDPS * 192(Cap+1) / (193 * Cap)

This scales everything around a cap of 192 (which is just an arbitrary cap to scale off).  Golems and probably Spirecraft should use a Cap of 1 (and CapHealth and CapDamage equal to a single ship's values).

[Dichotomy]

So I come back after getting distracted by Arcens other titles (which were ridiculously cheap for a week, there), to this rebalancing storm.

I'd keep turrets at roughly the same current DPS, with slightly lower k costs and high durability.

[keith.lamothe]

So I come back after getting distracted by Arcens other titles (which were ridiculously cheap for a week, there), to this rebalancing storm.

Relatively little actual rebalancing has taken place, it's mainly a forum storm