PD Gauss Turret comparison

[Jorgen_CAB]

jorgen_cab

your claim is incorrect.  20 shots at .20 has a greater dispersion than 8 shots at .5.  i reckon that you correctly remembered but misconstrued the variance of the binomial-  misconstrued because in this case it is mu, not n that is being held constant.

Yes.. I constructed a program to do some actual statistical tests... since doing it in the game are a bit difficult. Lower size will get a small extra leaking except for the 87% size which actually seem to produce better result in most realistic instances than 100%

From my tests... for example...

Missile salvo size: 5
Missile salvos: 50.000
Missile Speed: 10000 km/s
PD tracking Speed: 5000 km/s
PD to hit modifier from fire-control: 0.9

Size 100, 10 shots, about 45% hit ratio : Average about 4.10 hits per salvo
Size 87, 12 shots, about 39% hit ratio : Average about 4.17 hits per salvo
Size 50, 20 shots, about 22.5% hit ratio : Average about 3.99 hits per salvo
Size 25, 40 shots, about 11.2% hit ratio : Average about 3.92 hits per salvo
Size 17, 60 shots, about 7.6% hit ratio : Average about 3.94 hits per salvo

So... the most effective gun seem to actually be 87% as far as I can tell from a leaking perspective in real terms. The 87% gun are weaker at around 75-100 tracking speed if grade bonus is 100. This interval will then change depending on grade bonus... so it depends... but differences is small and in general the 87% seem better since it get more benefits unless you are in a 25-30% interval.

You can change the numbers above of course but in general the same result will stand and the differences will diminish fast as salvo size go above the turret shot ratio. Although in realistic terms the differences in leaking from a 100% to a 17% gun are so small that other considerations such as fire controls, turret design versus ship design etc should be more important.

If you are often engaging rather small salvos of around 4-8 missiles then having a large 100% quad turret might not be that useful and too big for some ships. You might need more fire-controls and smaller turrets.

To put the above in more real terms... If you are engaging 100 incoming salvos each with 5 missiles the 100% size turret will miss 90 missiles out of 500 while the size 17% turret will miss 106 missiles.


If anyone want to do their own testing you can use this little .NET app if they wish... I provide no support..   https://www.dropbox.com/s/kj1kz6r9aemtpz7/Aurora_PDtest.exe?dl=0

[SpikeTheHobbitMage (OP)]

spike. 

"Targets per FC is independent of the number of FCs by definition"

airball.  it's firing increments per expected hit that's the relevant parameter.  this parameter is not determined by the kind of cannon you use, but is *limited* by the size of the cannon and turrets. 

hypothetical 1500 ton quad-full-gauss turret can engage one salvo.  there is absolutely nothing you can do to improve this.  two 750 ton quad-50%-gauss turrets could, potentially, engage two.  therefore, there are scenarios, common and important scenarios, where two half-size turrets are _twice as good_ as one full size one.

It is hits per FC per increment per tonne.
You can only engage as many salvos per tick as you have PD FCs.  It also takes a minimum number of shots to kill a salvo.  Those are entirely independent questions.
A dual 100 is superior to a quad 50 unless your grade bonus is extremely high.  (100% bonus against same speed or slower, 200% against 2x speed missiles, etc)
A quad mount is superior to a pair of duals or four singles of the same hit rate that share the same fire control.

jorgen_cab

your claim is incorrect.  20 shots at .20 has a greater dispersion than 8 shots at .5.  i reckon that you correctly remembered but misconstrued the variance of the binomial-  misconstrued because in this case it is mu, not n that is being held constant.

Yes.. I constructed a program to do some actual statistical tests... since doing it in the game are a bit difficult. Lower size will get a small extra leaking except for the 87% size which actually seem to produce better result in most realistic instances than 100%

From my tests... for example...

Missile salvo size: 5
Missile salvos: 50.000
Missile Speed: 10000 km/s
PD tracking Speed: 5000 km/s
PD to hit modifier from fire-control: 0.9

Size 100, 10 shots, about 45% hit ratio : Average about 4.10 hits per salvo
Size 87, 12 shots, about 39% hit ratio : Average about 4.17 hits per salvo
Size 50, 20 shots, about 22.5% hit ratio : Average about 3.99 hits per salvo
Size 25, 40 shots, about 11.2% hit ratio : Average about 3.92 hits per salvo
Size 17, 60 shots, about 7.6% hit ratio : Average about 3.94 hits per salvo

So... the most effective gun seem to actually be 87% as far as I can tell from a leaking perspective in real terms. The 87% gun are weaker at around 75-100 tracking speed if grade bonus is 100. This interval will then change depending on grade bonus... so it depends... but differences is small and in general the 87% seem better since it get more benefits unless you are in a 25-30% interval.

You can change the numbers above of course but in general the same result will stand and the differences will diminish fast as salvo size go above the turret shot ratio. Although in realistic terms the differences in leaking from a 100% to a 17% gun are so small that other considerations such as fire controls, turret design versus ship design etc should be more important.

If you are often engaging rather small salvos of around 4-8 missiles then having a large 100% quad turret might not be that useful and too big for some ships. You might need more fire-controls and smaller turrets.

To put the above in more real terms... If you are engaging 100 incoming salvos each with 5 missiles the 100% size turret will miss 90 missiles out of 500 while the size 17% turret will miss 106 missiles.


If anyone want to do their own testing you can use this little .NET app if they wish... I provide no support..   https://www.dropbox.com/s/kj1kz6r9aemtpz7/Aurora_PDtest.exe?dl=0

Jorgen, check your numbers.  There is no Gauss-87.  There is a Gauss-85.

[misanthropope]

spike

are you under the impression that a second fire control will permit one turret to engage two salvos? 

[SpikeTheHobbitMage (OP)]

spike

are you under the impression that a second fire control will permit one turret to engage two salvos?

No, a turret can't be shared or split between controls.

[Jorgen_CAB]

spike. 

"Targets per FC is independent of the number of FCs by definition"

airball.  it's firing increments per expected hit that's the relevant parameter.  this parameter is not determined by the kind of cannon you use, but is *limited* by the size of the cannon and turrets. 

hypothetical 1500 ton quad-full-gauss turret can engage one salvo.  there is absolutely nothing you can do to improve this.  two 750 ton quad-50%-gauss turrets could, potentially, engage two.  therefore, there are scenarios, common and important scenarios, where two half-size turrets are _twice as good_ as one full size one.

It is hits per FC per increment per tonne.
You can only engage as many salvos per tick as you have PD FCs.  It also takes a minimum number of shots to kill a salvo.  Those are entirely independent questions.
A dual 100 is superior to a quad 50 unless your grade bonus is extremely high.  (100% bonus against same speed or slower, 200% against 2x speed missiles, etc)
A quad mount is superior to a pair of duals or four singles of the same hit rate that share the same fire control.

jorgen_cab

your claim is incorrect.  20 shots at .20 has a greater dispersion than 8 shots at .5.  i reckon that you correctly remembered but misconstrued the variance of the binomial-  misconstrued because in this case it is mu, not n that is being held constant.

Yes.. I constructed a program to do some actual statistical tests... since doing it in the game are a bit difficult. Lower size will get a small extra leaking except for the 87% size which actually seem to produce better result in most realistic instances than 100%

From my tests... for example...

Missile salvo size: 5
Missile salvos: 50.000
Missile Speed: 10000 km/s
PD tracking Speed: 5000 km/s
PD to hit modifier from fire-control: 0.9

Size 100, 10 shots, about 45% hit ratio : Average about 4.10 hits per salvo
Size 87, 12 shots, about 39% hit ratio : Average about 4.17 hits per salvo
Size 50, 20 shots, about 22.5% hit ratio : Average about 3.99 hits per salvo
Size 25, 40 shots, about 11.2% hit ratio : Average about 3.92 hits per salvo
Size 17, 60 shots, about 7.6% hit ratio : Average about 3.94 hits per salvo

So... the most effective gun seem to actually be 87% as far as I can tell from a leaking perspective in real terms. The 87% gun are weaker at around 75-100 tracking speed if grade bonus is 100. This interval will then change depending on grade bonus... so it depends... but differences is small and in general the 87% seem better since it get more benefits unless you are in a 25-30% interval.

You can change the numbers above of course but in general the same result will stand and the differences will diminish fast as salvo size go above the turret shot ratio. Although in realistic terms the differences in leaking from a 100% to a 17% gun are so small that other considerations such as fire controls, turret design versus ship design etc should be more important.

If you are often engaging rather small salvos of around 4-8 missiles then having a large 100% quad turret might not be that useful and too big for some ships. You might need more fire-controls and smaller turrets.

To put the above in more real terms... If you are engaging 100 incoming salvos each with 5 missiles the 100% size turret will miss 90 missiles out of 500 while the size 17% turret will miss 106 missiles.


If anyone want to do their own testing you can use this little .NET app if they wish... I provide no support..   https://www.dropbox.com/s/kj1kz6r9aemtpz7/Aurora_PDtest.exe?dl=0

Jorgen, check your numbers.  There is no Gauss-87.  There is a Gauss-85.

Yes... 87% was wrong (brain fart)... it should be 85% and that is equal with 100% or actually slightly better than 100% in the above case.

As far as I know Steve said something about gearing weight for turrets. So the efficiency of shots per ton actually might be worth it in C# even if a 50% is slightly worse than a 100% gun. So we will have to wait for evidence of this before we know.

In VB6 Aurora there is according to my tests about a 1% difference in performance of the 100% and 50% gun in my test so the saving in weight from a twin to quad turret make that small performance boost extremely small or even no existent in a per tonnage perspective. I have not run the actual numbers on that though.

[SpikeTheHobbitMage (OP)]

Yes... 87% was wrong (brain fart)... it should be 85% and that is equal with 100% or actually slightly better than 100% in the above case.

As far as I know Steve said something about gearing weight for turrets. So the efficiency of shots per ton actually might be worth it in C# even if a 50% is slightly worse than a 100% gun. So we will have to wait for evidence of this before we know.

In VB6 Aurora there is according to my tests about a 1% difference in performance of the 100% and 50% gun in my test so the saving in weight from a twin to quad turret make that small performance boost extremely small or even no existent in a per tonnage perspective. I have not run the actual numbers on that though.

83% would have a rated average exactly equal to a 100%, so giving them 85% cth is arguably a bug.  They still leak more due to greater dispersion.
Gear size is: round(weapon size * weapon count) * (turret speed/turret speed tech) * weapon count factor / 10
WCF for single is 1.0, double is 0.95, triple is 0.925, and quad is 0.9
Rounding only applies to 10% and 8% gauss cannons.

I'll run the numbers later.

[Jorgen_CAB]

Yes... 87% was wrong (brain fart)... it should be 85% and that is equal with 100% or actually slightly better than 100% in the above case.

As far as I know Steve said something about gearing weight for turrets. So the efficiency of shots per ton actually might be worth it in C# even if a 50% is slightly worse than a 100% gun. So we will have to wait for evidence of this before we know.

In VB6 Aurora there is according to my tests about a 1% difference in performance of the 100% and 50% gun in my test so the saving in weight from a twin to quad turret make that small performance boost extremely small or even no existent in a per tonnage perspective. I have not run the actual numbers on that though.

83% would have a rated average exactly equal to a 100%, so giving them 85% cth is arguably a bug.  They still leak more due to greater dispersion.
Gear size is: round(weapon size * weapon count) * (turret speed/turret speed tech) * weapon count factor / 10
WCF for single is 1.0, double is 0.95, triple is 0.925, and quad is 0.9
Rounding only applies to 10% and 8% gauss cannons.

I'll run the numbers later.

Yes.. the dispersion is greater but the slightly higher percentage to weight ratio still in the example above make the 85% slightly better. This will obviously change a bit depending on the actual numbers to both worse and better. I ran about 1.000.000 calculation just to be sure of the result. The 85% destroyed an average of 4.114 missiles while the 100% destroyed an average of 4.107 missiles.

83% add up to 99.6 while 85% add up to 102% for the weight. This is obviously a conscious decision by Steve since the 17% canon also add up to 102% and is exactly five times smaller than the 85% cannon.

A twin 100% turret with a 4x tracking speed in my test have a weight of 15.56HS and a quad has 15.38HS which basically means the average to hit ration per tonnage are almost identical between a twin 100% and quad 50% gun with the number in my test above.

100%
4.107 missile hits with a turret size 15.56HS is 0.267 hits per HS.

50%
3.987 missile hits with a turret size of 15.38HS is  0.259 hits per HS

The difference are less than one percent in efficiency in this particular instance.

In C# the gearing bonus is suppose to be better so it might actually make it more effective with more smaller guns for that single reason.

At least in my opinion the differences are so minuscule that it really does not matter what you do and both have pros and cons.

The guns and turrets you choose to develop probably have more to do with research point and the general design parameters rather than the efficiency since the difference in efficiency is so small and might be way less important than the amount of RP and design choices different types of sizes of gun will give you.

Another very important part as discussed before is the fire controls because these are way more expensive than the turrets, small but expensive. If you expect incoming salvos to be around 8 missiles (or multiples of it) large then one quad 100% turret might not be enough but two is a great overkill so you opt to build two 85% turrets instead. One 100% turret will on average kill (if each barrel shoots 4 shots) 6.75 missiles while two will destroy on average 7.99 missiles. One 85% quad will kill on average 5.95 and two will kill 7.94 missiles. Even two 67% turrets might be acceptable per fire control with an average kill of 7.65 missiles per salvo since some leakers is acceptable if you have shields and good armour (which might be something you need no matter what). This is where design philosophy comes into the picture, perhaps a quad 67% turret also is small enough that some ship can mount one where two is too large which give you some design leverage to really large turrets of other designs.

[Titanian]

Even two 67% turrets might be acceptable per fire control with an average kill of 7.65 missiles per salvo since some leakers is acceptable if you have shields and good armour

The problem with pd consistently leaving one missile in a salvo alive is that the next fire control will happily target this one missile instead of a fresh salvo, wasting most of its shots.

[Jorgen_CAB]

Even two 67% turrets might be acceptable per fire control with an average kill of 7.65 missiles per salvo since some leakers is acceptable if you have shields and good armour

The problem with pd consistently leaving one missile in a salvo alive is that the next fire control will happily target this one missile instead of a fresh salvo, wasting most of its shots.

To be honest I don't remember exactly how the game target which salvo and in which order they engage.

In my opinion the game should make it so that the largest salvo is always targeted first with the biggest PD batteries even if one salvo have been engaged in order to make fire-controls more affordable. The fire controls are pretty much the most costly of all the components for point defence.

This way the odd laser batteries meant for anti-ship work will always fire last and hopefully targets salvos with only one or a few missiles left.

[SpikeTheHobbitMage (OP)]

Yes.. the dispersion is greater but the slightly higher percentage to weight ratio still in the example above make the 85% slightly better. This will obviously change a bit depending on the actual numbers to both worse and better. I ran about 1.000.000 calculation just to be sure of the result. The 85% destroyed an average of 4.114 missiles while the 100% destroyed an average of 4.107 missiles.

83% add up to 99.6 while 85% add up to 102% for the weight. This is obviously a conscious decision by Steve since the 17% canon also add up to 102% and is exactly five times smaller than the 85% cannon.

A twin 100% turret with a 4x tracking speed in my test have a weight of 15.56HS and a quad has 15.38HS which basically means the average to hit ration per tonnage are almost identical between a twin 100% and quad 50% gun with the number in my test above.

100%
4.107 missile hits with a turret size 15.56HS is 0.267 hits per HS.

50%
3.987 missile hits with a turret size of 15.38HS is  0.259 hits per HS

The difference are less than one percent in efficiency in this particular instance.

In C# the gearing bonus is suppose to be better so it might actually make it more effective with more smaller guns for that single reason.

At least in my opinion the differences are so minuscule that it really does not matter what you do and both have pros and cons.

The guns and turrets you choose to develop probably have more to do with research point and the general design parameters rather than the efficiency since the difference in efficiency is so small and might be way less important than the amount of RP and design choices different types of sizes of gun will give you.

Another very important part as discussed before is the fire controls because these are way more expensive than the turrets, small but expensive. If you expect incoming salvos to be around 8 missiles (or multiples of it) large then one quad 100% turret might not be enough but two is a great overkill so you opt to build two 85% turrets instead. One 100% turret will on average kill (if each barrel shoots 4 shots) 6.75 missiles while two will destroy on average 7.99 missiles. One 85% quad will kill on average 5.95 and two will kill 7.94 missiles. Even two 67% turrets might be acceptable per fire control with an average kill of 7.65 missiles per salvo since some leakers is acceptable if you have shields and good armour (which might be something you need no matter what). This is where design philosophy comes into the picture, perhaps a quad 67% turret also is small enough that some ship can mount one where two is too large which give you some design leverage to really large turrets of other designs.

I ran some numbers.  The 85 has a 2% weight advantage vs baseline, but to achieve 90% confidence vs leaks around a 22% penalty, increasing above 50% against smaller salvos.  At 90% confidence one in ten salvos will leak and there is a 1% chance of two salvos in a row leaking.

cth.py - a Python script to calculate shots needed to kill salvos of various sizes at any cth, to a specified confidence.
cth.dat shots per salvo for salvos from 1-100 at cth from 1-100 with 90% confidence.
85cth.png tonnage per target for 90% success
 X axis is number of missiles
 Y axis is relative tonnage per missile
 lower is better
 1.0 is equal to a gauss 100
 2.0 is double a gauss 100
The line is jagged because you can't fire a partial shot.