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

[Exultant (OP)]

Conventional wisdom concerning PD has been that 10cm railguns beat gauss turrets at all but the highest of tech levels. However, this was not always the case in VB6, and since the updates to turret sizes in C#, the scales have tipped even further toward gauss.

I have created a spreadsheet calculator with the intention of demonstrating that by the time you hit gauss tech 3 (5000RP), nuclear pulse level tech, rail guns are only slightly better at cruiser speeds, and by the time you hit Gauss tech 4 (15000RP), ion level tech, quad gauss has already overtaken rail in terms of HS efficiency for non FAC/fighter speeds.

Link to spreadsheet. Make a copy to play around with numbers yourself.

The TL;DR is that rail effectiveness drops off at Ion tech because it is based on ship speed. You can define the speed at which rail overtakes gauss in terms of multiples of the racial tracking speed. For example, rail is more effective than Gauss 2 at speeds 91% or higher of racial tracking speed. However, by the time you get to gauss 4, you need to be 1.83x faster than your tracking speed in order for rail to be more efficient. Speeds in excess of 4x racial tracking are of no benefit at all, but the necessary speed multiplier rail needs caps out at 3.65x (vs. gauss tech 8), meaning you will not run into a tech level where rail cannot be superior to gauss. Fighter rail will always be more effective than a turreted gauss design for PD at expected fighter speeds. I did not check unturreted gauss fighters but since railguns are 4 shots for 3 HS (not considering crew and reactor sizes), and unturreted to hit chances are identical, it logically follows that parity is achieved around gauss 6- 8 (4shots/3HS = 8gauss/6HS, but crew sizes are different and rail needs a reactor)

The detailed explanation:

PD ability can be defined in terms of km/s of missiles able to be shot down. For example, if a laser (1 shot per tick) has a tracking speed of 4000 and it's BFC has a 100% chance to hit at point blank (not true in practice) then it has a 100% chance to hit a missile at 4000km/s and a 50% chance to hit a missile at 8000km/s. So if you have a missile traveling at 32,000km/s, you will need 32,000km/s (32,000/4000 = 8 guns)  worth of PD to reliably shoot it down.

Thus, PD effectiveness = # of shots * BFC hit chance at 10kkm * Gauss factor (if applicable) * weapon tracking speed. Divide this by HS of (weapon + crew quarters + reactor for rail) to get the efficiency of the setup.

Also, rail gun and gauss turrets have a constant size at a given tech level. 10cm rails are 3HS. A quad .85 gauss turret is always 25.12HS when geared to 4x racial tracking speed assuming your turret gear ratio has kept up with BFC tracking speeds. Thus, size ratios of weapons are constant, so the only factors that matter are the gauss tech and ship speeds.

This test setup does not factor the size of the BFC into the equation. If you want a complete determination including auto calculating of the most efficient BFC to use, please check out my full PD Calculator

[Jorgen_CAB]

One other note is that rail-guns with a lower chance to hit also are MORE vulnerable to ECM on missiles too. So they can become a severe liability if you have no ECCM in the fire control or you have not stayed competitive in that technology line.

The ECM modifier which is an addative modifier is applied after the tracking speed and tracking bonus is applied, this make high speed tracking weapons and fire-controls much less suceptable to ECM interference.

Example..

Incoming missile at 20.000km/s

Rail-gun fire at 4000km/s with a tracking bonus of 10% for a total of 4400km/s or 22% to hit rate, then deduct -10% for ECM difference to ECCM and you are down to 12%

Gauss turret at 16.000km/s with tracking bonus of 10% for a total of 17.600km/s or 88% hit chance, then deduct -10% for ECM difference to ECCM and you are down to 78%

After this you multiply with stuff such as Crew Grade and Officer Tactical bonuses.


We also should not forget that one shot hitting at 100% is much better than five shots hitting at 20% from a math perspective when you compare volume of fire versus quality of fire.

[SevenOfCarina]

I don't have time for a proper rebuttal right now, but gauss cannons only barely break even with railguns at RoF4, and don't really supersede them in the final fire point defence role until RoF5, around when you have magnetic confinement fusion drives. Your analysis regarding hull space is spot on, but point defence efficacy per hull space is a less useful metric than missiles shot down per unit cost. Additionally, railguns do not need additional research investment to be good at point defence - a basic 10 cm version with 10,000 km range and capacitor 3 is dirt cheap and all that's necessary, so it's important to consider what technologies will need to be neglected in favour of gauss research (RoF + turret tracking speed) which adds up really fast. Gauss cannons are way more expensive on a per HS basis than railguns, though this is somewhat offset by the additional engine cost.

But I'm a little concerned about some of your spreadsheet assumptions - 5,000 km/s seems really slow for the 15,000 RP mark,which is approximately magnetoplasma drives. Buff that to 8,000 km/s and now the railguns are as good as the gauss cannons at point defence.

[Jorgen_CAB]

I don't have time for a proper rebuttal right now, but gauss cannons only barely break even with railguns at RoF4, and don't really supersede them in the final fire point defence role until RoF5, around when you have magnetic confinement fusion drives. Your analysis regarding hull space is spot on, but point defence efficacy per hull space is a less useful metric than missiles shot down per unit cost. Additionally, railguns do not need additional research investment to be good at point defence - a basic 10 cm version with 10,000 km range and capacitor 3 is dirt cheap and all that's necessary, so it's important to consider what technologies will need to be neglected in favour of gauss research (RoF + turret tracking speed) which adds up really fast. Gauss cannons are way more expensive on a per HS basis than railguns, though this is somewhat offset by the additional engine cost.

But I'm a little concerned about some of your spreadsheet assumptions - 5,000 km/s seems really slow for an ion-engine vessel. Buff that to 8,000 km/s and now the rail-guns are as good as the Gauss cannons at point defence.

Also then note that cost is not as much a factor anymore due to changes in maintenance mechanics.

Using low tech rail guns are probably by many a game exploit so it is kind of dubious to use low cost rail-guns as we generally compare up to date technology in these kinds of comparisons.

So space on your ships IS very important as space is no longer infinite at maintenance facilities throughout your empire. As long as you can keep all your ships docked at Earth it might not matter much, but when you need to spread out ships and defences in many dozen locations it does count quite allot.

If you a building your beam concepts around rail-guns in particular then I would not bother with Gauss technology... but if I use Laser or Particles then I would certainly consider Gauss to augment my anti missile capabilities... I can use lasers in the early game as a defence too as lasers are decently good too.

[Jorgen_CAB]

But I'm a little concerned about some of your spreadsheet assumptions - 5,000 km/s seems really slow for the 15,000 RP mark,which is approximately magnetoplasma drives. Buff that to 8,000 km/s and now the railguns are as good as the gauss cannons at point defence.

The base rate of cruising speed for any engine technology is about 1/3 of ship weight in engines at 100% power efficiency... that I think is a common consideration. For Ion engines in C# that is 4166km/s.

[SevenOfCarina]

Also then note that cost is not as much a factor anymore due to changes in maintenance mechanics.

Using low tech rail guns are probably by many a game exploit so it is kind of dubious to use low cost rail-guns as we generally compare up to date technology in these kinds of comparisons.

So space on your ships IS very important as space is no longer infinite at maintenance facilities throughout your empire. As long as you can keep all your ships docked at Earth it might not matter much, but when you need to spread out ships and defences in many dozen locations it does count quite allot.

Why would that be a dubious assumption? Why is it an exploit? What matters is what works, not what is more 'advanced'.

As I understand, maintenance costs are dependant on the cost of the vessel itself, so the cheaper railgun ships would also be cheaper to maintain. Regarding maintenance capacity, it's not like ships will constantly be at a maintenance location, but yes, more facilities/modules will be required.

The base rate of cruising speed for any engine technology is about 1/3 of ship weight in engines at 100% power efficiency... that I think is a common consideration. For Ion engines in C# that is 4166km/s.

Huh, that feels grossly underpowered. I'm not SerBeardian, but I tend to consider around 40-50% ship weight in engines at 100% power efficiency as a baseline, which might explain why I've generally found railguns to outperform gauss cannons.

[Exultant (OP)]

I don't have time for a proper rebuttal right now, but gauss cannons only barely break even with railguns at RoF4, and don't really supersede them in the final fire point defence role until RoF5, around when you have magnetic confinement fusion drives. Your analysis regarding hull space is spot on, but point defence efficacy per hull space is a less useful metric than missiles shot down per unit cost. Additionally, railguns do not need additional research investment to be good at point defence - a basic 10 cm version with 10,000 km range and capacitor 3 is dirt cheap and all that's necessary, so it's important to consider what technologies will need to be neglected in favour of gauss research (RoF + turret tracking speed) which adds up really fast. Gauss cannons are way more expensive on a per HS basis than railguns, though this is somewhat offset by the additional engine cost.

But I'm a little concerned about some of your spreadsheet assumptions - 5,000 km/s seems really slow for the 15,000 RP mark,which is approximately magnetoplasma drives. Buff that to 8,000 km/s and now the railguns are as good as the gauss cannons at point defence.

Thanks for your response!

Yes, I did not take into account cost per PD km/s. Rail will always win, because it's basic tech (slightly higher for capacitor 3 tech). But as others have said, cost will determine how many you can build for the same cost, but maintenance capacity is based on tonnage, so that tonnage isn't free anymore.

The spreadsheet assumption of speed was simply where I left it after tests. You will find that the rail gun line auto updates as you increase ship speed, and you can double check my breakpoints that I put in column L yourself. The highlighted breakpoints are what matter, they are based on speed's percentage of racial tracking speed.

Magnetoplasma era means your racial tracking speed is 5k, not 4k. This means that 8000km/s is 1.6x the racial tracking, which means that Gauss 4 is still more efficient (breakpoint multiplier vs Gauss 4  is  1.83x). You can double check that by updating the racial tracking value in the spreadsheet for tech of the era you desire.

You can find RP costs on the tech tree, which some one else on the forums posted and I found here

[Jorgen_CAB]

Also then note that cost is not as much a factor anymore due to changes in maintenance mechanics.

Using low tech rail guns are probably by many a game exploit so it is kind of dubious to use low cost rail-guns as we generally compare up to date technology in these kinds of comparisons.

So space on your ships IS very important as space is no longer infinite at maintenance facilities throughout your empire. As long as you can keep all your ships docked at Earth it might not matter much, but when you need to spread out ships and defences in many dozen locations it does count quite allot.

Why would that be a dubious assumption? Why is it an exploit? What matters is what works, not what is more 'advanced'.

As I understand, maintenance costs are dependant on the cost of the vessel itself, so the cheaper railgun ships would also be cheaper to maintain. Regarding maintenance capacity, it's not like ships will constantly be at a maintenance location, but yes, more facilities/modules will be required.

As with many other things in Aurora... some things are considered an exploit.. this is one such thing. Allot of people will just ignore it because it make no sense from a RP perspective that due to a quirk in game mechanic you can game the game... earlier technology should simply not be better than later technology weapons and that is why many people view it as an exploit.

No NPR will use it so there is no point in exploiting this gap yourself either.

[Energyz]

We also should not forget that one shot hitting at 100% is much better than five shots hitting at 20% from a math perspective when you compare volume of fire versus quality of fire.

Not sure why you would say that, it only affects the standard deviation not the expected value

[Jorgen_CAB]

We also should not forget that one shot hitting at 100% is much better than five shots hitting at 20% from a math perspective when you compare volume of fire versus quality of fire.

Not sure why you would say that, it only affects the standard deviation not the expected value

It matters as you often engage small or parts of volleys and high accuracy shots waste less ammunition.

1 shot at 100% hit 1 missiles 100% while 2 shots at 50% miss 1 missile 25% of the time. In Aurora we are limited to one weapon or turret per salvo so it does matter. It can be to the benefit of the Rail-gun too as it can use about 4 individual weapons to one Gauss as well.. so it is not entirely beneficial to Gauss here, hard to say actually. But generally when you do actual practical tests you will see that high accuracy produce less leakers, less now when BFC ignore salvos, but weapons still do.

[Energyz]

It matters as you often engage small or parts of volleys and high accuracy shots waste less ammunition.

1 shot at 100% hit 1 missiles 100% while 2 shots at 50% miss 1 missile 25% of the time. In Aurora we are limited to one weapon or turret per salvo so it does matter.

What? No it's one salvo per weapon, not the opposite. 2 shots at 50% hit 2 missiles 25% of the time, hence the same expected value.
And your argument about ammunition doesn't make sense for me, you're talking about the 1% failure chance ? Cause if that's the case, well we're also looking at a binomial distribution with somewhat linear MSP cost, so it's not relevant

[Jorgen_CAB]

It matters as you often engage small or parts of volleys and high accuracy shots waste less ammunition.

1 shot at 100% hit 1 missiles 100% while 2 shots at 50% miss 1 missile 25% of the time. In Aurora we are limited to one weapon or turret per salvo so it does matter.

What? No it's one salvo per weapon, not the opposite. 2 shots at 50% hit 2 missiles 25% of the time, hence the same expected value.
And your argument about ammunition doesn't make sense for me, you're talking about the 1% failure chance ? Cause if that's the case, well we're also looking at a binomial distribution with somewhat linear MSP cost, so it's not relevant

One weapon can only ever target one salvo not two, that is exactly what I meant. This means that often a small part of a salvo is left, perhaps one or two missles and this is when a high accuracy with low volume of fire is better than the reverse.

Say you engage a salvo with a laser at 100% accuracy, there only are 1 missile left, you will hit that missile 100% of the time so you are sure to destroy it. But if you instead fire at it with two lasers (in the same turret) which both have a 50% chance to hit then there is a 25% chance that you don't hit the missile at all, there also is a 25% chance you hit twice but that second hit don't matter as you can only shoot it down once.

This is also why you don't want to put too many Gauss into one turret, so you don't waste too many shots on overkill parts of salvos.

[Energyz]

You're pulling out a very specific situation that never arises to prove your general point?

Say you engage a salvo with a laser at 100% accuracy, there only are 1 missile left, you will hit that missile 100% of the time so you are sure to destroy it. But if you instead fire at it with two lasers which both have a 50% chance to hit then there is a 25% chance that you don't hit the missile at all, there also is a 25% chance you hit twice but that second hit don't matter as you can only shoot it down once.

You won't shoot it twice... You either managed to shoot the first time and the gun will find another target, or you fail to shoot the first time and then the second gun tries to get it

"We also should not forget that one shot hitting at 100% is much better than five shots hitting at 20% from a math perspective when you compare volume of fire versus quality of fire."

Math wise it's the same. And in the game, you have multiple salvoes with multiple missiles against multiple guns/turrets.

[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

[Jorgen_CAB]

You're pulling out a very specific situation that never arises to prove your general point?

Say you engage a salvo with a laser at 100% accuracy, there only are 1 missile left, you will hit that missile 100% of the time so you are sure to destroy it. But if you instead fire at it with two lasers which both have a 50% chance to hit then there is a 25% chance that you don't hit the missile at all, there also is a 25% chance you hit twice but that second hit don't matter as you can only shoot it down once.

You won't shoot it twice... You either managed to shoot the first time and the gun will find another target, or you fail to shoot the first time and then the second gun tries to get it

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.