What is a MK upgrade really worth?

[Wanderer]

So, my personal curiousity was what is a MK upgrade really worth when upgrading.  I just wanted some generic values to work from mentally.

I took the fighter as my base.  I ignored armor piercing for the moment because most ships don't have its extreme levels.  As I said, I just wanted a simple baseline.

So, a MK I fighter can kill a single MK I fighter before it dies.  It will take it 144.35 seconds to kill the other fighter, and they both die in a glorified boom.  How do I construct these values?  Glad you asked!

Alright, Fighter stats are from Dazio's excellent updates to the wiki at: http://www.arcengames.com/mediawiki/index.php?title=Fighter

I don't feel the need to retable that.  It starts at 4800 dmg, rof 4, Health 162400, Armor 300.  Each time it goes up a mark, add a mark I to its own stats.  Simple and linear.

Now, how do you compute the time to kill?
HealthOfTarget/((MK1Damage (4800) - ArmorOfTarget)/Mk1ROF (4)).  For MK II vs. MK I this looks like: 324800/((4800-600)/4).  That's 309.33 seconds for a single MK I to kill a MK II.

The real question, though, is how many MK Is can the MK II kill before it dies.  The results may stagger you.  The calculation:
(TimeToDieToMK1*((MKDamage-MK1Armor (300))/MKRoF))/MK1Health (162400).  This looks like, for MK 2: (309.33*((9600-300)/4))/162400.

What's that look like?

Fighter MK Level	MK1 Time To Kill (s)	MK 1s killed before death
1	144.35	1
2	309.33	4.42
3	499.69	10.84
4	721.77	21
5	984.24	35.9

What this equates to is a MK IV (best you can reasonably produce) is worth 21x a MK I.  Yep, that's right.  Makes more sense why in an even fight a MK IV world is incredibly difficult to take, and why you can roll over low-end worlds with your fleet without batting an eyelash.  MK upgrades are really that powerful.

But, I ask myself, but, what's the real difference between, say, and II and III, or a III and IV with the II/Is as backup firepower?

The calculations don't change, just the assumptions of who's the baseline values.

Ship Mk	Time To Kill MK II	Kills x MK IIs	Time To Kill MK III	Kills x MK IIIs	Time to Kill MK IV	Kills X MK IVs
2	144.35	1
3	224	2.38	144.35	1
4	309.33	4.43	196.85	1.85	144.35	1
5	400.98	7.22	251.78	2.99	183.5	1.61

So, what's this mean to me in plain english?
A MK II is worth ~4x a MK I
A MK III is worth ~2.5x a MK II
A MK IV is worth ~4.5x a MK II
A MK IV is worth ~1.8x a MK III
finally, a MK V is worth ~1.6x a MK IV

So, take EVERYTHING to MK II.  Against the coreworld MK Vs you will only be a 7:1 underdog instead of a 35:1 underdog comparitively (note, I'm not dealing with cap adjustments or cap stacks, just ship to ship).  MK III seems to be the underdog here.  It's 6000K to take it to MK III, but you get MK IV for free.  So, really, compare MK II to MK IV.  A MK IV is worth ~4.5x a MK II.  Ah, okay.  It actually IS an improvement in stats alone (and remember, you also get free a free MK III stack as well, so figure 2500 to MK III with 3500 to MK IV as the K price).

Someone with higher mathmatical training can try to figure out the final odds of 4 caps of I-IV vs. a cap of MK V for the odds makers, but I'd put a full I-IV against a V cap at ~1.3:1, roughly, in their favor.  That's not bad, considering I've got a few advantages of my own other than raw firepower if I can actually do that.

So, I really just put this up here because I was going through the exercise and figured it'd spark up some good discussion.  Opinions and comments are welcome.

[_K_]

Now, how do you compute the time to kill?
HealthOfTarget/((MK1Damage (4800) - ArmorOfTarget)/Mk1ROF (4))

So you put your MKII's in successive 1v1 duels against MKI's. This is wrong not only because you ignore the cap difference, but also massively limits the MKIs ability to deliver damage, as they have to wait in line instead of fighting all the time.


http://en.wikipedia.org/wiki/Lanchester%27s_laws
The VERY, VERY, VERY basic estimate of a ship's strength can be calculaed as DPS*HP. For groups can be estimated as (total DPS)*(total HP). So if you have 2x more units, their total strength is (2x DPS)*(2xHP)= 4x.
Works the same way for units being stronger. MKII has 2x better stats HP and DPS, so its 4x stronger. MKIII is 9x stronger and MKIV is 16x. You get the idea.

This is a rough estimate, as for unit group strength, lots of important details are omitted.
But still, with this, you can then add such factors as cap difference, resource cost efficiecy, etc. to get some idea how different marls differ from different perspectives.

[PokerChen]

These stats explain how hard it is to fight on a 10-planet snake map with your homeworld at one end. If you had to go up against 200 mark-V ships using 19K worth of knowledge, it's not going to be pretty. If your plain english is true:

A MK II is worth ~4x a MK I
A MK III is worth ~2.5x a MK II
A MK IV is worth ~4.5x a MK II
A MK IV is worth ~1.8x a MK III
finally, a MK V is worth ~1.6x a MK IV

Then a mark I-IV is equal to 1 + ( 1 / 1.8 ) + ( 1 / 4.5 ) + ( 1 / 21 ) ~ 1.825 of mark IV. This puts them at about 1.1 of a mark V. A slight advantage. One could probably take mark-Is just to soak up the damage by sheer overkill of a mark-V shot against their flimsy hulls...

= = = = = =

The above analysis will need to be expanded somewhat to include hull-bonuses, as ships will generally target the ones that they can damage the most in battle. Let's do some triangle-ship analysis: we'll always have lots of them to face up against in an average AI world, and these bonuses will factor into odds and survival.

The shots-to kill for the optimal combinations look like this from the Reference chart. (L) means that a cap-for-cap battle will results in a loss for the attacking ships:

Attacker	Defender	Shots	to..	kill	for	marks I-V
Fighter-I	Bomber	7	14	22	30	40
Fighter-II	Bomber	4	7	10	14	18
Fighter-III	Bomber	3	5	7	9	11
Fighter-IV	Bomber	2	4	5	7	9
Fighter-V	Bomber	2	3	4	6	7
Bomber-I	M. Frig.	3	6	9(L)	11(L)	14(L)
Bomber-II	M. Frig.	2	3	5	6	7
Bomber-III	M. Frig.	1	2	3	4	5
Bomber-IV	M. Frig.	1	2	3	3	4
Bomber-V	M. Frig.	1	2	2	3	3
M. Frig.-I	Fighter	3	6	9(L)	12(L)	15(L)
M. Frig.-II	Fighter	2	3	5	6	8
M. Frig.-III	Fighter	1	2	3	4	5
M. Frig.-IV	Fighter	1	2	3	3	4
M. Frig.-V	Fighter	1	2	2	3	3

Let me point out the same result as Wander, in a different way: Mark-Is really suck(!) due to mark-scaling. It's always worth upgrading Frigs and Fighters to mark-II in the following scenarios (Bombers are always worth upgrading [TM]):
(1) AI progress gives them tech-III ships or above. They will start to 1hKO your weaklings.
(2) You are assaulting an mark-III/IV/V world where there are more than a few ships at each guardpost. At the start of the game, you can out-muscle a IV-world with 50~100 ships with a cap. Definitely not true later.

A few things of note:
* The Mark-V worlds are quite interesting. Thankfully, AI missile-frigate-V will not *quite* take out your fighter-IIs in one shot. Speaking on this theoretical type-for-type basis, fighter-IIs are effectively identical in survivability to fighter-IIIs, and will be just as good damage soakers. This also applies to AI Bombers versus your Missile Frigates.


EDIT: What we probably want is a better function to describe actual combat than the Lanchester's since that assumes continuous distribution of damage. Way too many ship-types have significant alphas and bend this estimation rather oddly.

[TechSY730]

Pretty interesting stuff.
In case you did know, in general stats of ships scale linearly with Mark.
So a Mk. N has their health, firepower, and sometimes other stuff multiplied by N relative to their Mk. I version.

This does mean that there are decreasing returns (aka utility(Mk N+1)/utility(Mk N) decreases as N goes up, asymptotically proportional to (N+1)/N), thus explaining why Mk. II has the biggest difference in terms of effectiveness compared to their previous Mk.

[keith.lamothe]

FYI, the reference screen shows shots-to-kill and seconds-to-kill, and you can do the comparison as one-vs-one or cap-vs-cap (or one-vs-cap or vice versa, but that's not very useful for this).  That won't be accurate for aoe/line-aoe cases but should work just fine for direct shots (of however many shots per salvo).  And the cap-vs-cap will adjust for the cap reduction in higher mark fleet ships.

Anyway, yea, higher mark stuff is substantially more powerful because hp, armor, and damage all scale linearly with mk (in almost all cases when talking about triangle and bonus fleet ships).  Previously some had shots-per-salvo or seconds-per-salvo also scale with mk, creating an even steeper curve, so it used to be more intense   In any event, mkII is by far the biggest jump due to the linear scaling starting with 1.

The tech upgrades to mkII for fleet ships are intentionally more attractive than mkIII to encourage diversification rather than beelining for the higher tech stuff.  But of course as the game goes on this is less of an issue because you get both mkI and mkII out of an ARS so you've only got 4 combat fleet ship types (on 1HW) that need a II upgrade, and once you get mkIV capability those mkIII upgrades become pretty attractive (if you have the m+c to produce the higher mark ships).

[Diazo]

Sounds about right.

I'd never done any math on it but I was aware of the stats being multiplied by the mark level so when I look at a planet summary it's a direct comparison for me.

The AI have 60 Mk III? That's roughly the same as 180 Mk I or 90 Mk II.

Adding in guardians and guard posts, I need at least double that if I'm going to attack the system.

Rough, but it works for me.

This is also the reason I quite often start unlocking turrets before Mk III fleet ships, it feels like I get more bang for my buck.

D.

[Wanderer]

So you put your MKII's in successive 1v1 duels against MKI's. This is wrong not only because you ignore the cap difference, but also massively limits the MKIs ability to deliver damage, as they have to wait in line instead of fighting all the time.

Considering a cap vs. cap battle of II vs. Is (88 ships vs. 98 ships), it's roughly right to me.  Yes, you'll have some Is shooting at the same II, but they're basically just wailing away on each other 1 to 1. 

I am vaguely familiar with Lanchesters, though I haven't looked at it in an age.  What about this breaks the Lanchester model, that I'm not using unit on unit?  In a concentrated fire scenario the marks actually go up in multipliers, not down.

The VERY, VERY, VERY basic estimate of a ship's strength can be calculaed as DPS*HP. For groups can be estimated as (total DPS)*(total HP). So if you have 2x more units, their total strength is (2x DPS)*(2xHP)= 4x.

Was too basic for me, and doesn't include the effects of increasing armor on the DPS model.  The multipliers I found are higher than simple square law.

But still, with this, you can then add such factors as cap difference, resource cost efficiecy, etc. to get some idea how different marls differ from different perspectives.

Caps are different, I won't argue, and I omitted them for simplicity's sake.  However, resource cost efficiency means nothing in a fight when you're not in a system that can replace them easily.  By midgame my econ is either 0'd out or flying towards 1 mill each. I rarely am between the two.  I care about the fights.

The above analysis will need to be expanded somewhat to include hull-bonuses, as ships will generally target the ones that they can damage the most in battle. Let's do some triangle-ship analysis: we'll always have lots of them to face up against in an average AI world, and these bonuses will factor into odds and survival.

The reason I didn't try to do triangle analysis was because thier triangles are doing the same to your ships, and because the range variance starts to get involved.  That's a signficant calculation that I don't have the time to puzzle out.  Simply you'd have to estimate fighters lost to frigates before combat started, bombers lost to fighters as the two groups met while the bombers approached the frigates, and finally frigate losses as the two groups finished optimal range closing.  I don't have the time, nor probably enough mathmatical training, to really puzzle that down before the next Einstein is born.

FYI, the reference screen shows shots-to-kill and seconds-to-kill, and you can do the comparison as one-vs-one or cap-vs-cap (or one-vs-cap or vice versa, but that's not very useful for this).  That won't be accurate for aoe/line-aoe cases but should work just fine for direct shots (of however many shots per salvo).  And the cap-vs-cap will adjust for the cap reduction in higher mark fleet ships.

I've yet to really use the reference screens, but that's good to know.  Thank you.

Some of this stemmed from one of our short discussions on me estimating the troop strength of my fleet ball vs. escaping MK V backwash during one of the Raid Engine runs.  It was just kicking around in my head.

@Dazio: Yeah, that's basically what I needed to do, was get myself some 'rough numbers' to work from for my own internal processing.


I should note, though, this is all a lie.  None of this is accurate.  WHAT?!  Nah, seriously.  If MK II was truly THAT strong compared to MK I, then on Schizo opening waves on 10/10 of ~100 ships would lay waste to your ~400 ship force equivalent of MK Is.  They don't.  This is of course affected by tactical factors of gravity wells, damage boosters, and anything else, but it's not a direct comparison.

[_K_]

 

Yes, you'll have some Is shooting at the same II, but they're basically just wailing away on each other 1 to 1. 

The problem is that your model will only hold as long as all fights are successive 1v1's. If your fleet has more ships, if you are using MKI cap+MKII cap to fight a MKIII cap, your model stops working, as the fights stop being 1v1. If your fights takes longer than 10 seconds, and one side starts suffering losses while the other suffers less, its falls apart as well.

You make statements such as "MKIV fighter is worth 21 times stronger than a MKI" based on your model. This conclusion is wrong. Your model only says that a MKIV can kill 21 MKI's in successive 1v1 fights. If you put 1 MKIV vs 21 MKI's, the outcome will be very different. And stating that  1 MKIV is worth 21 MKI's is supposed to mean exactly that, - that 1 MKIV can fight as well as 21 MKIs, and will not lose in a 1vs21 scenario.

[Nodor]

Yes, you'll have some Is shooting at the same II, but they're basically just wailing away on each other 1 to 1. 

The problem is that your model will only hold as long as all fights are successive 1v1's. If your fleet has more ships, if you are using MKI cap+MKII cap to fight a MKIII cap, your model stops working, as the fights stop being 1v1. If your fights takes longer than 10 seconds, and one side starts suffering losses while the other suffers less, its falls apart as well.

You make statements such as "MKIV fighter is worth 21 times stronger than a MKI" based on your model. This conclusion is wrong. Your model only says that a MKIV can kill 21 MKI's in successive 1v1 fights. If you put 1 MKIV vs 21 MKI's, the outcome will be very different. And stating that  1 MKIV is worth 21 MKI's is supposed to mean exactly that, - that 1 MKIV can fight as well as 21 MKIs, and will not lose in a 1vs21 scenario.

And this is why health pools make Zenith Chameleons so dangerous.

[Wanderer]

You make statements such as "MKIV fighter is worth 21 times stronger than a MKI" based on your model. This conclusion is wrong. Your model only says that a MKIV can kill 21 MKI's in successive 1v1 fights. If you put 1 MKIV vs 21 MKI's, the outcome will be very different. And stating that  1 MKIV is worth 21 MKI's is supposed to mean exactly that, - that 1 MKIV can fight as well as 21 MKIs, and will not lose in a 1vs21 scenario.

Ah, now I see your concern.  Okay, let's do that:

21xFighter Is vs. 1xFighter IV:

Fighter 4: 19200 dmg - 300 Armor / 4 second ROF = 4725 DPS.
Fighter 1s: 21 * 4800 dmg - 1200 armor / 4 second ROF = 900 * 21 = 18900 DPS.

Fighter Is: With no losses kill the Fighter IV in 34.37 seconds.
Fighter IV kills *1* in that time.

Net: 20 Fighter Is are still alive

Yep, sounds right.

Now, what happens in a (for round numbers) 50 vs. 50 fight, which is where Lanchesters comes in:
4725 DPS * 50 = 236250 DPS starting
900 DPS * 50 = 45000 DPS starting

MK IV kills 1.5 fighters per second.  In the time it will take the MK Is to kill a single MK IV (14.43 seconds) the MK IVs will have killed 21 fighters.  Using this as our baseline time interval, since it actually leans towards supporting MK Is by ignoring in-between attrition rates (and thus is more appropriate to salvo methodology than Lanchesters, I'm aware), Those 29 remaining fighters have a dps of 26100 DPS once they've killed a single MK IV.  That's 24.8 seconds to kill the second one.  With the remaining 49 MK IVs with a current DPS of 231525, they're now killing 1.42 fighters/sec.  They can kill 35 MK I fighters before the second 1 died, far above the cap strength.

So, in this scenario, they're 50:1 stronger.  As I said, I was simply ruling myself some guidelines out.  If you bring in cap vs. cap and concentrated fire into the scenario, the numbers skew far further towards to the higher marks being much higher ratio'd.  If you go many vs. 1, yes, things skew differently again, this time in favor of zerg vs. protoss.  Zerg always won with infinate equivalent differences, but that's why those were balanced the way they were.  Also, most of Zerg's million man army had to close to physical range, which had a limited number of at-one-time combatants, but I'm going off on the wrong game again.

If two fleets of equivalent size arrive and everyone grabs a target, what was the result?  That was my original curiousity.  To truly get accurate ratios between marks, you'd probably have to end up with a formula that incorporates fluid dynamics, optimization errors (out of range, new target just in range and still targetting old one, etc), range differences with speed incorporations, and any other number of items.

Yes, K, I agree, this is over-simplified.  Utterly, and completely, over-simplified.  It's a game, not my doctorial thesis nor a space shuttle trajectory.   If you can find a better computational solution to help find rough guidelines like this, I'm all ears, though, part of why I posted my thoughts originally. 

[Nodor]

Alright, back of the envelope math.

Are 8 caps of different Mark 4 ships capable of defending a factory 4 against Fallen Spire 7-10 exo-waves with 7-10 golems? 

(Fighter, Bomber, Frigate, Blade Spawner, Impulse Reaction Emitter, Raider, Eye Bots, & Munitions Boosters)

i'm thinking the answer is no, with a side of maybe.

[keith.lamothe]

Alright, back of the envelope math.

Projected outcome: you'll get a few lines into the preliminary calculations just as the first artillery golem shot blasts the envelope to bits.

[Wanderer]

Alright, back of the envelope math.

Projected outcome: you'll get a few lines into the preliminary calculations just as the first artillery golem shot blasts the envelope to bits.

Then you realize it'll come down to three things.  1) How far away the MK IV is from the wormhole.  2) How many grav turrets are between the two.  3) Did they build the CnC in the chapel or not.

[Eternaly_Lost]

Alright, back of the envelope math.

Are 8 caps of different Mark 4 ships capable of defending a factory 4 against Fallen Spire 7-10 exo-waves with 7-10 golems? 

(Fighter, Bomber, Frigate, Blade Spawner, Impulse Reaction Emitter, Raider, Eye Bots, & Munitions Boosters)

i'm thinking the answer is no, with a side of maybe.

Glances at the Hunter-Killers in those Exo-waves.

Not without a Spirefleet or a ton of FF to hold them in place. H-K just much on Normal Fleet ships like they were nothing.

[Wanderer]

Alright, back of the envelope math.

Are 8 caps of different Mark 4 ships capable of defending a factory 4 against Fallen Spire 7-10 exo-waves with 7-10 golems? 

(Fighter, Bomber, Frigate, Blade Spawner, Impulse Reaction Emitter, Raider, Eye Bots, & Munitions Boosters)

i'm thinking the answer is no, with a side of maybe.

No, they CAN be stopped.  Just takes a few systems.  Had to do it on the completionist 120 planet snake I played.  Let's just say "overwhelming firepower" and "Holy crap, there's an atmosphere inside that many forcefields" came into play.