Gauss turret PD vs 10cm Rail - Dispelling common myths with math

[Energyz]

Mathwise it is NOT the same.

1 Shot with a 100% hit chance has a 0% miss chance. 
5 Shots with a 20% hit chance have a 80% miss chance, you don't get to simply add them to get to 100%, because doing so means you have a 400% chance of missing.

Mathwise it works like this:

5 shots with a 20% hit rate:  Probability of a hit = 1-(1-.2)^5 which equates to a 67.23% chance to hit.

One can never get a 100% hit number with a 20% hit chance, let's make a 20 gun turret 1-(1-.2)^20 still only equates to a 98.85% chance to hit.

So math says it is best to have as many 100% hit chance platforms as there are incoming missiles, if that is not achievable, one will want to have higher hit rate weapons.  There is a fairly insignificant difference of volume of fire and hit rate in a direct ratio, aiming for 50% is significantly worse than 100% and slightly better than 25%, significantly better than 10%.

Math with number of shots inverted with 1/number of shots hit chance.

1 shot = 100% hit chance = 100% hit rate
2 shot = 50% hit chance = 75% hit rate
3 shot = 33% hit chance = 70% hit rate
4 shot = 25% hit chance = 68% hit rate
5 shot = 20% hit chance = 67% hit rate
10 shot - 10% hit chance = 65% hit rate

You're not taking into account the times where multiple guns are hitting. This is a binomial distribution. The expected value of shot missiles stay the same (1), the standard deviation change.

[Energyz]

But if there is five salvos each with one missile as your other turrets managed to kill all the rest of the missile in those salvos. You now have only one missile left in each... this is what I say... there is no OTHER target for the second gun in the same turret to fire at.

I assume that there weapons are either turreted or fire multiple shots so can only target ONE salvo each.

As Pedroig explained above how it works so well.

We are comparing rail guns with gauss turret since the beginning? Not quad gauss with single turret

[Jorgen_CAB]

But if there is five salvos each with one missile as your other turrets managed to kill all the rest of the missile in those salvos. You now have only one missile left in each... this is what I say... there is no OTHER target for the second gun in the same turret to fire at.

I assume that there weapons are either turreted or fire multiple shots so can only target ONE salvo each.

We are comparing rail guns with gauss turret since the beginning?

This is a sepparate thing as you remarked on it... the example have to be easy to understand...

Have you EVER actually done any test in the game... it is very easy to see the result if you for example use full size gauss at 100% and then use double the number of 50% gauss and have them intercept missiles in a test scenario. The 50% Gauss will produce more leaking missiles than the 100% gauss even if they have the same AVERAGE number of kills theoretically.

Here is an "extreme" easier to understand example.

I have 10 turrets each with a single full size Gauss (4 shots) gun that hit incoming missiles at 100% accuracy.

There are 5 incoming salvos each with 8 missiles. My 10 turrets will shoot down ALL missiles at 100% probability.

I now have 10 turrets with two twin half size Gauss (2x4 shots) that have an accuracy of 50%.

The distribution might look something like this...

Turret / Kills
1 / 5
2 / 2
3 / 2
4 / 4
5 / 7

That mean after all salvos been engage once i have 5 salvos left with...

Salvo / missiles left
1 / 3
2 / 6
3 / 6
4 / 4
5 / 1

The next five turrets fire and do...
Turrets / Kills
1 / 2
2 / 5
3 / 6
4 / 1
5 / 6

The result is...

Salvo / missile left
1 / 1
2 / 1
3 / 0
4 / 3
5 / 0

I hope you understand the difference here?!?

[Pedroig]

Mathwise it is NOT the same.

1 Shot with a 100% hit chance has a 0% miss chance. 
5 Shots with a 20% hit chance have a 80% miss chance, you don't get to simply add them to get to 100%, because doing so means you have a 400% chance of missing.

Mathwise it works like this:

5 shots with a 20% hit rate:  Probability of a hit = 1-(1-.2)^5 which equates to a 67.23% chance to hit.

One can never get a 100% hit number with a 20% hit chance, let's make a 20 gun turret 1-(1-.2)^20 still only equates to a 98.85% chance to hit.

So math says it is best to have as many 100% hit chance platforms as there are incoming missiles, if that is not achievable, one will want to have higher hit rate weapons.  There is a fairly insignificant difference of volume of fire and hit rate in a direct ratio, aiming for 50% is significantly worse than 100% and slightly better than 25%, significantly better than 10%.

Math with number of shots inverted with 1/number of shots hit chance.

1 shot = 100% hit chance = 100% hit rate
2 shot = 50% hit chance = 75% hit rate
3 shot = 33% hit chance = 70% hit rate
4 shot = 25% hit chance = 68% hit rate
5 shot = 20% hit chance = 67% hit rate
10 shot - 10% hit chance = 65% hit rate

You're not taking into account the times where multiple guns are hitting. This is a binomial distribution. The expected value of shot missiles stay the same (1), the standard deviation change.

That's because multiple guns hitting the same target have no effect on the probability.  You don't get to apply cumulative distribution because the success or failure of any given "shot" has no effect on any other "shot" taken before, during, or after.  And since the calculations are done on a salvo basis per BFC you don't get to apply hypergeometric distribution either, in otherwords whether you have 1 gun firing at 1 missile out of 10 or 10 guns firing at 1 missile out of 10 makes no difference, if the one missile is destroyed or has no effect on the other 9, the targeting is not dynamic WITHIN a salvo.

[Father Tim]

Thankfully, I have no intention of equal-tech PvP Aurora duels, so it doesn't matter.  Gauss Cannons are better when you want to use gauss cannons and Rail Guns are better when you want to use rail guns.

And nothing is any use when spoiler race uses inertia-cancelling super-tech to inflict massive unsoakable internal damage.

[skoormit]

...whether you have 1 gun firing at 1 missile out of 10 or 10 guns firing at 1 missile out of 10 makes no difference, if the one missile is destroyed or has no effect on the other 9, the targeting is not dynamic WITHIN a salvo.

Clarify this for me.
Let's say I have a single BFC controlling 10 guns.
I target a salvo with 10 missiles.
Will all 10 guns shoot at the same missile, even if the first gun destroys that missile?

[Jorgen_CAB]

...whether you have 1 gun firing at 1 missile out of 10 or 10 guns firing at 1 missile out of 10 makes no difference, if the one missile is destroyed or has no effect on the other 9, the targeting is not dynamic WITHIN a salvo.

Clarify this for me.
Let's say I have a single BFC controlling 10 guns.
I target a salvo with 10 missiles.
Will all 10 guns shoot at the same missile, even if the first gun destroys that missile?

No...

One BFC can target ANY amount of missiles salvos.

One weapon or turret can only target ONE salvo.

If you have 10 turrets they can all target the same salvo OR ten different salvos.

[Iceranger]

Conventional wisdom concerning PD has been that 10cm railguns beat gauss turrets at all but the highest of tech levels.

As I have pointed out on discord, this is under the context of hull-mounted weapons. Comparing hull mounts to turrets is like... compare apples to oranges. The consensus is basically for fast ships, hull-mounted railguns are better than hull-mounted gausses for PD. Otherwise, stick with gauss turrets.

[Exultant (OP)]

As I have pointed out on discord, this is under the context of hull-mounted weapons. Comparing hull mounts to turrets is like... compare apples to oranges. The consensus is basically for fast ships, hull-mounted railguns are better than hull-mounted gausses for PD. Otherwise, stick with gauss turrets.

And I agree with you Iceranger - That's what my math shows, and it's what I explain. However, I'm not sure you can say there is consensus, as I have been told I was wrong on discord multiple times over the past week. I don't wish to point fingers at people, however - I just wanted to make my case in an easier-to-understand format, and direct people to it if there was further disagreement.

[Energyz]

That's because multiple guns hitting the same target have no effect on the probability.  You don't get to apply cumulative distribution because the success or failure of any given "shot" has no effect on any other "shot" taken before, during, or after.  And since the calculations are done on a salvo basis per BFC you don't get to apply hypergeometric distribution either, in otherwords whether you have 1 gun firing at 1 missile out of 10 or 10 guns firing at 1 missile out of 10 makes no difference, if the one missile is destroyed or has no effect on the other 9, the targeting is not dynamic WITHIN a salvo.

You're sure of that? That doesn't seem consistent with the changelog : "A fire control in this mode will continue to fire on incoming salvos as long as it has unfired weapons remaining. Each individual weapon or turret will only be able to engage a single salvo. This means point defence ships no longer need a large number of fire control systems, although there is still a design choice in terms of redundancy."

Seems to me it indicates a sequential calculation.Something like that : One gun shoot, if it hits, remove one missile of the salvo. If the salvo is empty, next salvo. Next gun.

What makes you think it's doing something else? You experimented?

EDIT: also that in the changelog : "Point Defence Fire Control

VB6 has a restriction that each fire control can only engage a single target during point blank fire. I've removed that restriction for C#. Each weapon can still only engage a single salvo.

In VB6, missiles moved in descending order of speed. In C# that has changed to descending order of speed then by descending order of salvo size, so the largest salvos of the same type of missile will move first. Consequently, your point defence will engage the largest salvos first."

[Jorgen_CAB]

Here are some of the Gauss versus Rail-gun cost benefit examples...

Two stations...

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Victory I class Point Defence Base      9 994 tons       486 Crew       746.8 BP       TCS 200    TH 0    EM 0
1 km/s      Armour 5-41       Shields 0-0       HTK 77      Sensors 0/0/0/0      DCR 2      PPV 144
Maint Life 3.49 Years     MSP 126    AFR 296%    IFR 4.1%    1YR 16    5YR 237    Max Repair 60 MSP
Commander    Control Rating 1   BRG   
Intended Deployment Time: 3 months    Morale Check Required   


10cm Railgun V10/C1 (48x4)    Range 10 000km     TS: 4 000 km/s     Power 3-1     Accuracy Modifier 100%     RM 10 000 km    ROF 15       
Beam Fire Control R64-TS4000 (2)     Max Range: 64 000 km   TS: 4 000 km/s     84 69 53 38 22 6 0 0 0 0
Gas-Cooled Fast Reactor R6 (10)     Total Power Output 62    Exp 5%

Active Search Sensor AS10-R1 (1)     GPS 60     Range 10.7m km    MCR 1.2m km    Resolution 1

Code: [Select]

Victory II class Point Defence Base      9 911 tons       274 Crew       1 651.7 BP       TCS 198    TH 0    EM 0
1 km/s      Armour 5-41       Shields 0-0       HTK 64      Sensors 0/0/0/0      DCR 5      PPV 154.56
Maint Life 2.41 Years     MSP 541    AFR 151%    IFR 2.1%    1YR 128    5YR 1 924    Max Repair 94.40 MSP
Commander    Control Rating 1   BRG   
Intended Deployment Time: 3 months    Morale Check Required   


Twin Gauss Cannon R300-85.00 Turret (12x8)    Range 30 000km     TS: 16000 km/s     Power 0-0     RM 30 000 km    ROF 5       
Beam Fire Control R64-TS16000 (2)     Max Range: 64 000 km   TS: 16 000 km/s     84 69 53 38 22 6 0 0 0 0

Active Search Sensor AS10-R1 (1)     GPS 60     Range 10.7m km    MCR 1.2m km    Resolution 1
Both also need a maintenance station like this one...

Code: [Select]

Agincourt class Maintenance Base      40 960 tons       410 Crew       1 754.3 BP       TCS 819    TH 0    EM 0
1 km/s      No Armour       Shields 0-0     HTK 53      Sensors 0/0/0/0      DCR 1      PPV 0
MSP 26    Max Repair 200 MSP
Lieutenant Commander    Control Rating 1   BRG   
Intended Deployment Time: 3 months   
Maintenance Modules: 8 module(s) capable of supporting ships of 10 000 tons
The total cost of the Gauss station is roughly 3400 and the cost of the Rail gun station is 2500...

The Guass station will be roughly twice as effective and will have a build cost roughly 36% more expensive and will have maintenance cost over time about 120% more expensive.

If you put the guns on a ship you will have to pay for the fuel, engines and all that that will never work out cost wise. The rail-gun station will also be allot more vulnerable to ECM than the Gauss station which "might" be an issue in effectiveness depending on technology.

The Gauss station also save you crew if that is a concern for you... I usually use highest quality crewmen so it "might" be an important consideration.

[Energyz]

This is a sepparate thing as you remarked on it... the example have to be easy to understand...

So you are talking about off topic without saying it? Way to go, champ

[Jorgen_CAB]

As I have pointed out on discord, this is under the context of hull-mounted weapons. Comparing hull mounts to turrets is like... compare apples to oranges. The consensus is basically for fast ships, hull-mounted railguns are better than hull-mounted gausses for PD. Otherwise, stick with gauss turrets.

And I agree with you Iceranger - That's what my math shows, and it's what I explain. However, I'm not sure you can say there is consensus, as I have been told I was wrong on discord multiple times over the past week. I don't wish to point fingers at people, however - I just wanted to make my case in an easier-to-understand format, and direct people to it if there was further disagreement.

I agree that fast ship should use rail-guns for defence... I even think regular ship can do it as well if you only add a few cannons and don't want the expense or space needed for a full Gauss turret and PDFC.

Fast ships is very different than say using a PD station for example, the engine and everything surroundings it carry a huge cost even if the gun itself might be slightly more effective due to the speed of the ship.

[Jorgen_CAB]

This is a sepparate thing as you remarked on it... the example have to be easy to understand...

So you are talking about off topic without saying it? Way to go, champ

No... if does effect how you view high volume of low accuracy shot over lower volume high accuracy... I just explained it to you, did I not?

If you remark on it I will need to explain what I mean by it... I think that is fair. 

[Energyz]

That only affects gauss turret vs gauss turret, so not at all