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Posted by: Charlie Beeler
« on: October 17, 2013, 09:02:25 AM »

It's not so much that speed rules the other factors, but that speed is the easiest one to understand enough it's impact on the results. 

The second easiest to manipulate, but is usually discounted by players, is salvo count within volley.  You can usually sacrifice a small number (1 or 2) launchers to add an additional MFC.  This will reduce the number of missiles in an individual salvo but raise the number of salvos in a task group volley.  By raising the salvo count you increase the potential of saturating the defenses.  Paul's formula does touch on this, but I suspect that several players do not notice the effect.

Back to the OP's query about missile design.

In reality, trying to design any system in game only is a bad idea.  The various game components are just too complex to do it reliably.  The best approach is build tools outside of the game for design analysis.  For missiles this is actually quite easy to do since all the relevant data points and formulas have been extensively discussed in several topics over the last year and half.  The primary starting point is the discussion of the changes for v6.0 in suggestions. 
Posted by: Paul M
« on: October 17, 2013, 03:52:17 AM »

Sorry will correct that...actually "significant advantage" is not present, that is my point.  Even if you assume both missiles hit 100% of the time, the difference at the end of the day between 15% to get through the counter missiles and 20% will be lost in the noise of the statistics and probably even more so given you are talking about a bog standard PC random number generator which isn't completely random.   One of two places where speed turns out to be critical is deriving the number of such intercepts since that will drive down the to-hit chance extremely rapidly, even if their chance to be interecepted is low.  The other place is in determining that function k, which is the "maximum effective range" of your missile against a running target.  After that at some point velocity will saturate in terms of effective results, as I said earlier you just get to a point where you can say "fast enough."  But that point won't be universal.

Yeah, it is why I usually avoid doing stuff like this but then I make a general statement and people get all nit picky about some small part.  But when you are actually doing a chain like that either you do it or you can lead yourself down the merry path to la la land.  But I think Aurora has a problem in that speed becomes "the one stat to rule them all" in the game.  The reality is that relative velocity should be more critical to missile interception chances, where the missile should have a to-hit chance that has something like (missile_velocity-target_velocity) factors.  So a missile should hit best if it is moving at say twice the target velocity or something but with a fall off if the missile is too slow or too fast.  This would probably keep missile velocities a lot more sane.

This whole situation also contributes significantly to the size 1 missile spam.  As it becomes harder and harder to produce a large fast missile, and easier and esier to make a 1 pt warhead carrying missile that goes at speeds that render interception difficult.  Basically it comes down to the part of the formula that looks like (1-hit_chance)^m^n where m is an integer between 1 and 5, and in practical terms n is an integer between 1 and 3.  m is the art of interception 1v1 to 5v1 and n is the number of such interception attempts.  The problem is that for m=3 and n=2 that is (1-hit_chance)^6 which for just about any value of hit_chance is a small number.  So in practice you need a lot of inbound missiles for even 1 of them on average to hit.  Thus snowing the target under with size 1 missiles which are far easier to make fast enough to reduce n to 1 and equally easily numerous enough to make m also 1, becomes the optimal solution...as experience has shown.
Posted by: Cocyte
« on: October 16, 2013, 10:13:13 AM »

Quote from: Paul M on October 15, 2013, 03:38:29 AM

So if I just toss some numbers in there (from Coyote):
Missile 1 has a final to hit of 92% and an AAM interception chance of 45%
Missile 2 has a final to hit of 67% and an AAM interception chance of 33%


don't forget those to-hit are against a 10000 km/s target - this kind of speed is quite uncommon for med game warships. Up to 6500 km/s, both missiles have a 100% to-hit chance, so the faster one have a significant advantage.

One of the computer-played race in my current game have a higher propulsion tech than me (i'ld say one or two levels above mine), and 80% of their ships are cruising at no more than 6000 km/s.

All in all, this kind of analysis is nicely summed up in the title of the thread.

PS :I'm not a Coyote...
Posted by: Rolepgeek
« on: October 15, 2013, 06:47:27 PM »

TL dr; you need faster missiles. A lot faster. Less fuel, more engines, higher engine power multiplier. 100 m km is a good range to try for right now, I think. Try and make your missiles size 6 instead of size 8.5; they'll be harder to detect that way, as well as faster firing and more efficient use of the missile launcher space. As well, a WarHead(WH) of 4 would be better than 6, if you decrease the missile size. But mainly, reduce fuel, increase engine power and number, and make it smaller.

Bigger missile fire control, as well, should help. Should probably have your active sensor and your fire control at the same resolution.

Mostly, you just need more tech; nuclear pulse tech is really low tech, remember.
Posted by: Paul M
« on: October 15, 2013, 03:38:29 AM »

Going back to the optimization question, although I have to admit I try to avoid going into the math on something I do for fun, the full situation probably is helped if you stick a few formulas into the mess.

To determine the chance a missile will hit the target you are looking at a compound equation that is simple:

final_to-hit_chance = ((1-f)^n)*((1-g)^m)*(1-h)*k*l

f is an expression that takes into account the chance the missile is intercepted by long range counter missiles.  This is unfortunately complex.  It depends a lot on the enemy's technology, sensors, fire control, missile design, rate of fire, etc.  It also depends on if they are firing in 1v1 or something else.  It also depends on your missile design:  Armour, speed, ECM have effects on this.
n is the number of counter missile salvos you will have to evade.

f and n are linked and quite frankly vary from player to player since you are likely fighting different designs and so on.

g is an expression that takes into account all close range point defence fire on a missile from consorts.  It is influenced by the enemy defences mainly, but also by your missile parameters.
m is how many attempts are made and I'm simplifying somewhat in that I doubt all ships assisting have a similiar chance to hit.  Likely the (1-g)^m should be (1-gm)*(1-gm-1)...(1-g0)

h is the point blank point defence fire probability function of the target

k is a a fuction of missile range, launch range, target velocity, missile velocity, and missile endurance.  This says if the missile can hit the target.  It will have a value of 1 or 0.  You should ignore it during an analysis and simply say I will always launch when I can hit the target for sure.

l is the basic to-hit formula (missile speed/target speed)*agility

Now it should be, I hope obvious, this is a non-tractable problem.  It is dependent on circumstance (ex: launch range), target, and launcher.  There is unlikely to be a single optimal solution but instead a large area of parameter space where the overall expression is maximum and possibly this is not single valued so you have several possible solutions that give you essentially identical maxima.

If you make even some guesses on what these values are then you can do a simple bit of number crunching to get a extimate on effectiveness:

So if I just toss some numbers in there (from Cocyte):
Missile 1 has a final to hit of 92% and an AAM interception chance of 45%
Missile 2 has a final to hit of 67% and an AAM interception chance of 33%

I assume that no PD exists and that the 3v1 will be used for interceptions.   I assume in both cases that only 1 interception chance is possible.

M1 = (1-0.45)^3*0.92 = 0.15 (15% chance to hit)
M2 = (1-0.33)^3*0.67 = 0.20 (20% chance to hit)

If the number of interception chances is different so M1 is intercepted twice and M2 only once then:

M1 = ((1-.45)^3)^2*0.92 = 0.025 (2.5% chance to hit)

If both are intercepted twice:

M2 = ((1-0.33)^3)^2*0.67 = 0.06 (6% chance to hit)

If you factor in PD then the chance of any missile getting through drops.  If you then sum it up (to account for a typical salvo) though it becomes different, and substantially so if you say you can saturate their point defence or not, since in any case there isn't much difference in performance point defence wise so missiles intercepted by point defence fire will likely be eliminated.

Assume 8 missiles fired: 4 intercepted by AAM fire; 4 not:

Number of M1 hitting target = 4*.92 + 4*0.15 =   4.28
Number of M2 hitting target = 4*.67 + 4*0.20 =   3.48

At the end of the day the performance between the two missiles isn't exactly overwhelming different (for that particular situation anyway).  Those two numbers aren't going to look too much different in a battle since they are the mean and there is the deviation to account for.

But what I hope I have shown is that it is not a straighforward thing.  When you end up multiplying different probabilities together what may look like big differences tend to vanish.  They may come back in the standard deviation...plus I'm not sure at all what that to hit distribution function would look like (it is not likely to be guassian for example).

Also by choice of numbers in an example I can skew the results I present.  This is an unfortunate problem with this kind of analysis...it is a bias that anyone reading this stuff has to keep in mind. 
Posted by: Kaiser
« on: October 14, 2013, 05:05:42 PM »

Quote from: Erik Luken on October 14, 2013, 04:40:27 PM
Just remember Steve is British, and so skips the milliard thing. Sort of like us Americans :)

eheh sure ;))
Posted by: Erik L
« on: October 14, 2013, 04:40:27 PM »

Just remember Steve is British, and so skips the milliard thing. Sort of like us Americans :)
Posted by: Kaiser
« on: October 14, 2013, 04:37:44 PM »

I'm frakking stupid!! I thought it was 1.6 millions, instead it's 1miliard and 600millions Km!! Well, thanks to everyone guys
Posted by: Erik L
« on: October 14, 2013, 04:27:15 PM »

Loadout is the standard missile complement the ship carries. In your second example, the 30 AS - 8-5 Devastator Anti-ship Missile are the loadout.

And your missile has 1000x the range of your fire control. Now it's been a while since I designed any ships in Aurora, but that is striking me as very short ranged.
Posted by: Charlie Beeler
« on: October 14, 2013, 04:12:58 PM »

End is short for endurance.  As in your missiles will travel 4.1 days before running out of fuel.  The listed range for your Devastator missile is 1.6467 billion km not 1.6 million km. 
Posted by: Kaiser
« on: October 14, 2013, 04:05:14 PM »

Code: [Select]
Prinz Eugen class Cruiser    10,300 tons     290 Crew     1473.9 BP      TCS 206  TH 200  EM 0
1941 km/s     Armour 6-42     Shields 0-0     Sensors 12/12/0/0     Damage Control Rating 8     PPV 54
Maint Life 4.53 Years     MSP 715    AFR 106%    IFR 1.5%    1YR 56    5YR 846    Max Repair 160 MSP
Intended Deployment Time: 12 months    Spare Berths 0   
Magazine 254   

100 EP Nuclear Pulse Engine (4)    Power 100    Fuel Use 125.78%    Signature 50    Exp 12%
Fuel Capacity 1,000,000 Litres    Range 13.9 billion km   (82 days at full power)

AS Devastator Missile Launcher (6)    Missile Size 9    Rate of Fire 90
Missile Fire Control FC1-R18 (70%) (1)     Range 1.6m km    Resolution 18
AS - 8-5 Devastator Anti-ship Missile (30)  Speed: 4,700 km/s   End: 4.1d    Range: 1646.7m km   WH: 6    Size: 8.5    TH: 22/13/6

Active Search Sensor MR100-R110 (1)     GPS 17600     Range 100.7m km    Resolution 110
Thermal Sensor TH2-12 (1)     Sensitivity 12     Detect Sig Strength 1000:  12m km
EM Detection Sensor EM2-12 (1)     Sensitivity 12     Detect Sig Strength 1000:  12m km

Missile to hit chances are vs targets moving at 3000 km/s, 5000 km/s and 10,000 km/s

This design is classed as a Military Vessel for maintenance purposes

Here we are, this is the final project more or less: I designed a new fire control which has the same range as the missile. Only a question: what is this "End: 4.1d" in the missile's features?
Posted by: Kaiser
« on: October 14, 2013, 03:23:17 PM »

Quote from: Erik Luken on October 14, 2013, 03:05:58 PM
Your ship design has no standard loadout either. This means when one comes out of the yards, the magazines are empty. And if you forget to load them, they will end up in battle with no missiles.

Look on the Fighters/Ordnance tab of the ship class design window.

sorry I don't understand, what's "loadout"? do you mean missile already loaded? This is only the project, I have not any of this ship yet, I want design a better fire control ;)
Posted by: Erik L
« on: October 14, 2013, 03:05:58 PM »

Quote from: Kaiser on October 14, 2013, 02:48:32 PM
Well, I researched all that I needed and this is the result:

Code: [Select]
Prinz Eugen class Cruiser    10,400 tons     294 Crew     1515.1 BP      TCS 208  TH 200  EM 0
1923 km/s     Armour 6-42     Shields 0-0     Sensors 12/12/0/0     Damage Control Rating 8     PPV 54
Maint Life 4.4 Years     MSP 728    AFR 108%    IFR 1.5%    1YR 61    5YR 910    Max Repair 160 MSP
Intended Deployment Time: 12 months    Spare Berths 0    
Magazine 254    

100 EP Nuclear Pulse Engine (4)    Power 100    Fuel Use 125.78%    Signature 50    Exp 12%
Fuel Capacity 1,000,000 Litres    Range 13.8 billion km   (82 days at full power)

AS Devastator Missile Launcher (6)    Missile Size 9    Rate of Fire 90
Missile Fire Control FC76-R100 (70%) (1)     Range 76.8m km    Resolution 100

Active Search Sensor MR100-R110 (1)     GPS 17600     Range 100.7m km    Resolution 110
Thermal Sensor TH2-12 (1)     Sensitivity 12     Detect Sig Strength 1000:  12m km
EM Detection Sensor EM2-12 (1)     Sensitivity 12     Detect Sig Strength 1000:  12m km

This design is classed as a Military Vessel for maintenance purposes

I think there's only an "error" of projecting: my missile has range 1.6m Km, while I have designed a missile fire control having 76.8m Km. Should the missile fire control's range match that one of the missile?
Is it anyway necessary to have the active search sensor?

Your ship design has no standard loadout either. This means when one comes out of the yards, the magazines are empty. And if you forget to load them, they will end up in battle with no missiles.

Look on the Fighters/Ordnance tab of the ship class design window.
Posted by: Kaiser
« on: October 14, 2013, 02:48:32 PM »

Well, I researched all that I needed and this is the result:

Code: [Select]
Prinz Eugen class Cruiser    10,400 tons     294 Crew     1515.1 BP      TCS 208  TH 200  EM 0
1923 km/s     Armour 6-42     Shields 0-0     Sensors 12/12/0/0     Damage Control Rating 8     PPV 54
Maint Life 4.4 Years     MSP 728    AFR 108%    IFR 1.5%    1YR 61    5YR 910    Max Repair 160 MSP
Intended Deployment Time: 12 months    Spare Berths 0    
Magazine 254    

100 EP Nuclear Pulse Engine (4)    Power 100    Fuel Use 125.78%    Signature 50    Exp 12%
Fuel Capacity 1,000,000 Litres    Range 13.8 billion km   (82 days at full power)

AS Devastator Missile Launcher (6)    Missile Size 9    Rate of Fire 90
Missile Fire Control FC76-R100 (70%) (1)     Range 76.8m km    Resolution 100

Active Search Sensor MR100-R110 (1)     GPS 17600     Range 100.7m km    Resolution 110
Thermal Sensor TH2-12 (1)     Sensitivity 12     Detect Sig Strength 1000:  12m km
EM Detection Sensor EM2-12 (1)     Sensitivity 12     Detect Sig Strength 1000:  12m km

This design is classed as a Military Vessel for maintenance purposes

I think there's only an "error" of projecting: my missile has range 1.6m Km, while I have designed a missile fire control having 76.8m Km. Should the missile fire control's range match that one of the missile?
Is it anyway necessary to have the active search sensor?
Posted by: Paul M
« on: October 14, 2013, 09:02:01 AM »

The formula is a maximization of the to-hit chance experession and does not take into account other factors which may influence your design choice.  My statement was it needs only be fast enough to hit the target.  "fast enough" is determined by what experience says is "fast enough."  At some point you can say "fast enough" and go for agility.

Or put another way: a missile designed using that optimization is a good starting point for a new player.  They can then tweek the design as they choose based on experience.