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 Post subject: Armor vs Weapons
PostPosted: Thu Apr 27, 2017 11:05 pm 
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Space Dragon
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Posts: 258
I saw some discussion regarding the disparity of costs between armour and weapon ship parts. For example, as commented by afwbkbc here.

I wonder if he is right about best design being 1 weapon and rest of external slots for armor.

Some scenarios for self-gravitating (6 ext. slot) hull. I'll be using the values I get from an advanced game (turn 285, full tech researched, 4.5 PPs and 1.5 RPs), but I guess that does not matter as cost increases are proportional for every ship part.

Model A: Self-grav. with 1 x D.R., 5 x N.A., structure=300, dmg=30, cost=608.5
Model B: Self-grav. with 5 x D.R., 1 x N.A., structure=140, dmg=150, cost=1170 (92% more than model A)

If we pitch 2 model A against 1 model B we get:

Assuming worst luck for model B (i.e. alternating hits between the two enemies)
Round 1:
A1 and A2 do 60 dmg to B (80 left)
B does 90 dmg to A1 (210 left) and 60 dmg to A2 (230 left)
Round 2:
A1 and A2 do 60 dmg to B (20 left)
B does 60 dmg to A1 (150 left) and 90 dmg to A2 (150 left)
Round 3:
A1 and A2 do 60 dmg to B (destroyed)
B does 90 dmg to A1 (60 left) and 60 dmg to A2 (90 left)


So armored model (A) beat armed model (B).

Assuming best luck for model B (i.e. focusing on one enemy)
Round 1:
A1 and A2 do 60 dmg to B (80 left)
B does 150 dmg to A1 (150 left)
Round 2:
A1 and A2 do 60 dmg to B (20 left)
B does 150 dmg to A1 (destroyed)
Round 1:
A2 does 30 dmg to B (destroyed)
B does 150 dmg to A2 (150 left)


So again armored model beat armed model (B).

If we add the best shield to this and misiorla pilots, things stay the same. If we add just the shields (15 strength), the DRs get severely handicapped but that goes true for both models:

Assuming best luck for model B (i.e. focusing on one enemy)
Round 1:
A1 and A2 do 30 dmg to B (110 left)
B does 75 dmg to A1 (225 left)
Round 2:
A1 and A2 do 30 dmg to B (80 left)
B does 75 dmg to A1 (150)
Round 3:
A1 and A2 do 30 dmg to B (50 left)
B does 75 dmg to A1 (75 left)
Round 4 (1 of next turn, no repairings):
A1 and A2 do 30 dmg to B (20 left)
B does 75 dmg to A1 (destroyed)
Round 5:
A2 do 15 dmg to B (5 left)
B does 75 dmg to A2 (225 left)
Round 6:
A2 do 15 dmg to B (6 left)
B does 75 dmg to A2 (150 left)


So it seems shields do not change the advantage that armored model has.

Model C: Self-grav. with 3 x D.R., 3 x N.A., structure=220, dmg=90, cost=888.7 (42% more than model A)

Two model C vs three model A:

Assuming focused fire and black shields:
Round 1:
Cs do 90 to A1 (210 left)
As do 45 to C1 (175 left)
Round 2:
Cs do 90 to A1 (120 left)
As do 45 to C1 (130 left)
Round 3:
Cs do 90 to A1 (30 left)
As do 45 to C1 (85 left)
Round 4:
Cs do 90 to A1 (destroyed plus 60 dmg wasted)
As do 45 to C1 (40 left)
Round 5:
Cs do 90 to A2 (210 left)
A2 and A3 do 30 to C1 (10 left)
Round 6:
Cs do 90 to A2 (120 left)
A2 and A3 do 30 to C1 (destroyed and 20 dmg wasted)
Round 7:
C2 does 45 to A2 (75 left)
A2 and A3 do 30 to C2 (190 left)
Round 8:
C2 does 45 to A2 (30 left)
A2 and A3 do 30 to C2 (160 left)
Round 9:
C2 does 45 to A2 (destroyed and one shot of 15 dmg wasted)
A2 and A3 do 30 to C2 (130 left)
Round 10:
C2 does 45 to A3 (255 left)
A3 does 15 to C2 (185 left)
...
Round 16 (turn 8 ):
C2 does 45 to A3 (destroyed and one shot of 15 dmg wasted)
A3 does 15 to C2 (95 left)


So model C (half armour and half weapons) beats the armored model.

1 model B costing 30% more than model C, would have a bad time to beat it, staying alive with 5 structure after round 3.

Therefore, if we leave aside stealth, fighters and auto-repairs, the armour/weapon balanced design beats the extreme designs. I'm gonna assume this remains true for bigger hulls.


In the end, it seems armour prices do not need any balancing. I find it rather good.


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 Post subject: Re: Armor vs Weapons
PostPosted: Fri Apr 28, 2017 7:24 am 
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Joined: Tue Feb 17, 2015 11:54 am
Posts: 225
Oberlus wrote:
I wonder if he is right about best design being 1 weapon and rest of external slots for armor.


No. In general, ignore most of his posts.

As long as you only look at direct fire ships of the same type and disregard any decoys, fighters etc. it is pretty straight forward to give a very good analytical/mathematical description of the strength of a fleet or shipdesign. Assuming the remaining damage is proportional to the remaining structure (that makes immediate sense as you look at the limit of infinite ships), you can easily set up and solve a set of differential equations which will give you a pretty simple description of the strength of a fleet/design as

Code:
Damage*Structure


So in general, you will want to maximize that strength rating per cost squared (as the strength defined as above scales quadratic in number of ships).
This is, essentially, Lanchester's square law
Alternatively, you can also define the strength with a square root making it linear in the number of ships without changing the math.

Shields enhance the structure by the ratio of enemy damage without shields to the damage with shields.

Example thread covering the topic (pre fighters): viewtopic.php?f=28&t=10026

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 Post subject: Re: Armor vs Weapons
PostPosted: Sat Apr 29, 2017 6:12 am 
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Vacuum Dragon

Joined: Wed Aug 26, 2015 6:15 pm
Posts: 507
The only one-weapon ship I ever build is when I have to use Basic Large Hull, but I try never to build any warships until I have Robotic Hull, then it's either two weapons or three. The latter I don't build many of until I have shields. I know shields are expensive and there's argument about it being better just to build more ships, but I seem to have better results when I add shields as things progress.


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 Post subject: Re: Armor vs Weapons
PostPosted: Sat Apr 29, 2017 9:15 am 
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Space Dragon
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Joined: Mon Apr 10, 2017 4:25 pm
Posts: 258
defaultuser wrote:
The only one-weapon ship I ever build is when I have to use Basic Large Hull, but I try never to build any warships until I have Robotic Hull, then it's either two weapons or three. The latter I don't build many of until I have shields. I know shields are expensive and there's argument about it being better just to build more ships, but I seem to have better results when I add shields as things progress.
I do exactly the same. Shields are so good: against old weapons it renders your fleet invulnerable, against top-edge weapons it halves the damage you receive. Weapons are expensive but do something cool: kill enemies faster. I tend to have more or less the same amount of weapons and armour slots, and after the "simulation" I did in this thread I'm confident with that way.


Morlic wrote:
According to that wikipedia page, Lanchester's equations are not the more appropriate to simulate this kind of battles. Salvo combat model is more accurate. But the best way would always be a simulation.


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