PD Gauss Turret comparison

[Garfunkel]

Yes, especially since tracking bonus is now fixed. I'll personally try that approach in my first C# game.

[Jorgen_CAB]

This is entirely situational because target speed is factored in before the cap.  It works if the turret and fire control are as fast or faster than the target, but the 100's still give better PD performance against faster ASMs due to reduced leakage.

Sorry for taking so long to reply.

The thing is that missiles are almost always faster than the fire-controls of point defence even at slightly lower missile versus PD tech. So whether you use a 100% or 50% from that perspective might matter somewhat.

Although, in practice it does not really matter if you have a smaller gun or a larger one from a leakage point of view, the difference is so small and depend more on how many fire-controls you have rather than size of the gun so you don't waste shots as much on overkill on salvos. Putting large 100% Gauss in quad turret might be a waste against low salvo numbers, such as from fighters for example. You also presume scenarios that almost never exist such as one salvo of the PD will be able to take out all the missiles on one salvo, this scenario will rarely happen in practice.

Smaller guns also can get some additional effect from having more barrels per turret and are cheaper to research, both the gun and the turrets. Smaller turrets also give you more leeway of designing stuff in the same sense that smaller engines does. I think that turrets will be even more effective in terms of efficiency in C# too. The tracking bonus might also make smaller Gauss way more effective if you can increase the tracking of the weapon closer to the speed of the missiles.

So over all there are many benefits to using smaller Gauss guns that has nothing to do with the minuscule lower efficiency of a 100% or a 50% gun. The combination with ASM being both slightly larger and slower will probably also effect PD choices to some extent.

Also... you should consider that having missiles leak through the PD can also be a strategy in and of itself. So having some missiles leak through and hitting your shields is a good way to know you are being effective with your use of AMM and PD efforts. If the extremely small difference in leakage between a 100% gun and 50% is noticeable then you PD fire are so effective it does not matter anyway.

[SpikeTheHobbitMage (OP)]

This is entirely situational because target speed is factored in before the cap.  It works if the turret and fire control are as fast or faster than the target, but the 100's still give better PD performance against faster ASMs due to reduced leakage.

Sorry for taking so long to reply.

The thing is that missiles are almost always faster than the fire-controls of point defence even at slightly lower missile versus PD tech. So whether you use a 100% or 50% from that perspective might matter somewhat.

Although, in practice it does not really matter if you have a smaller gun or a larger one from a leakage point of view, the difference is so small and depend more on how many fire-controls you have rather than size of the gun so you don't waste shots as much on overkill on salvos. Putting large 100% Gauss in quad turret might be a waste against low salvo numbers, such as from fighters for example. You also presume scenarios that almost never exist such as one salvo of the PD will be able to take out all the missiles on one salvo, this scenario will rarely happen in practice.

Smaller guns also can get some additional effect from having more barrels per turret and are cheaper to research, both the gun and the turrets. Smaller turrets also give you more leeway of designing stuff in the same sense that smaller engines does. I think that turrets will be even more effective in terms of efficiency in C# too. The tracking bonus might also make smaller Gauss way more effective if you can increase the tracking of the weapon closer to the speed of the missiles.

So over all there are many benefits to using smaller Gauss guns that has nothing to do with the minuscule lower efficiency of a 100% or a 50% gun. The combination with ASM being both slightly larger and slower will probably also effect PD choices to some extent.

Also... you should consider that having missiles leak through the PD can also be a strategy in and of itself. So having some missiles leak through and hitting your shields is a good way to know you are being effective with your use of AMM and PD efforts. If the extremely small difference in leakage between a 100% gun and 50% is noticeable then you PD fire are so effective it does not matter anyway.

I am factoring per fire control so fire control count is irrelevant.

Two shots at 50% cth has the same average hit rate as one shot at 100%.  Against one incoming missile the single will kill it every time while the twins will both miss it 1/4 of the time.  Against two incoming missiles the single will kill one and miss one every time while the double will kill both 1/4 of the time, one 1/2 of the time, and will miss both 1/4 of the time.  In both cases the twin has a 25% chance of missing completely and a 6.25% of doing it twice in a row.  In the two missile case that means more than doubling the minimum shield requirements, while in the single missile case it means needing shields at all.  This is not a 'minuscule' loss of efficiency.

If that was all there was to it there would be little point in ever fielding the smaller cannons, but cth modifiers exist and must be taken into account.  As I have not yet tested the Fighter Combat Bonus, I will focus on capital ship defence.  Crew grade improves cth without affecting tonnage, and better than 100% effective cth is wasted.  Grade is subject to a training cap at 35% so anything more requires taking combat damage.  All other modifiers are penalties.

Taking into account modifiers against a given target, a smaller weapon with an effective 100% cth will always be superior to a larger weapon due to higher hits/tonne, and a weapon with less than 100% cth will always be superior to a smaller weapon due to less leakage.  There is a tradeoff between a weapon with a greater than 100% cth and a smaller weapon with less as the smaller weapon will have a higher base average hits/tonne but will also leak.

With a 0% grade bonus and a 95% fire control, a Gauss-100 will not exceed 95% acc against any target and will leak slightly.  Smaller weapons will leak more with no benefit.
With a 35% grade bonus and a 95% fire control, a Gauss-67 will have 83% cth against same speed and slower targets, an Gauss-85 will have a 100% cth against targets with a 9% speed advantage, and a Gauss-100 can match a 28% speed advantage.  Against anything faster the Gauss-100 will always give the best performance but will still leak.
With a 35% grade and a 74% fire control, a Gauss-100 will have just under 100% cth against same speed and slower targets.

For C# Aurora and assuming the tracking bonus is a multiplier like grade is, a 40% tracking bonus, 35% grade bonus, and 95% fire control, would let a Gauss-100 match a 79% speed advantage, a Gauss-85 match a 52% speed advantage, and a Gauss-67 match a 20% speed advantage.

[misanthropope]

if both weapons are less than 100%, large isn't better because of less _average_ leakage, large is better because of less _uncertainty_ in leakage.  10 shots at 90% can be relied upon to get 7 hits; 20 shots at 45% at the same level of confidence only can be depended upon for 5.  also, 1000 shots at .9% generate a ton of annoying log entries, screw that.

disregarding the occasionally obsolete enemy, there is a range of plausible speeds of missiles you might find headed in your way.  you want your point defense in the hands of properly trained crew to have exactly 100% chance against a speed near the bottom of that range.  that's all.  imho, ymmv, dyodd, etc

the quote from charlie beeler way back in 2012 makes it sound like the tracking bonus is a percentage of the _missile speed_, i dunno how he would know, but it matches other allegations i can remember reading.  if true, that's going to make all this moot because rail guns will be the only point defense worth using.

if you have shields, you should use them.  but it doesn't follow that installing shields is intrinsically a good decision.  maybe you, jorgen_cab, are only experiencing the ubiquity of leakers because you are spending resources on passive defenses that would have been sufficient to make your active defenses airtight.  im not expressing certainty that such is the case, but the possibility of having reversed cause and effect is clearly present in your argument.

[Jorgen_CAB]

I am factoring per fire control so fire control count is irrelevant.

Two shots at 50% cth has the same average hit rate as one shot at 100%.  Against one incoming missile the single will kill it every time while the twins will both miss it 1/4 of the time.  Against two incoming missiles the single will kill one and miss one every time while the double will kill both 1/4 of the time, one 1/2 of the time, and will miss both 1/4 of the time.  In both cases the twin has a 25% chance of missing completely and a 6.25% of doing it twice in a row.  In the two missile case that means more than doubling the minimum shield requirements, while in the single missile case it means needing shields at all.  This is not a 'minuscule' loss of efficiency.

If that was all there was to it there would be little point in ever fielding the smaller cannons, but cth modifiers exist and must be taken into account.  As I have not yet tested the Fighter Combat Bonus, I will focus on capital ship defence.  Crew grade improves cth without affecting tonnage, and better than 100% effective cth is wasted.  Grade is subject to a training cap at 35% so anything more requires taking combat damage.  All other modifiers are penalties.

Taking into account modifiers against a given target, a smaller weapon with an effective 100% cth will always be superior to a larger weapon due to higher hits/tonne, and a weapon with less than 100% cth will always be superior to a smaller weapon due to less leakage.  There is a tradeoff between a weapon with a greater than 100% cth and a smaller weapon with less as the smaller weapon will have a higher base average hits/tonne but will also leak.

With a 0% grade bonus and a 95% fire control, a Gauss-100 will not exceed 95% acc against any target and will leak slightly.  Smaller weapons will leak more with no benefit.
With a 35% grade bonus and a 95% fire control, a Gauss-67 will have 83% cth against same speed and slower targets, an Gauss-85 will have a 100% cth against targets with a 9% speed advantage, and a Gauss-100 can match a 28% speed advantage.  Against anything faster the Gauss-100 will always give the best performance but will still leak.
With a 35% grade and a 74% fire control, a Gauss-100 will have just under 100% cth against same speed and slower targets.

For C# Aurora and assuming the tracking bonus is a multiplier like grade is, a 40% tracking bonus, 35% grade bonus, and 95% fire control, would let a Gauss-100 match a 79% speed advantage, a Gauss-85 match a 52% speed advantage, and a Gauss-67 match a 20% speed advantage.

I know and understand the math just fine... the problem is that you assume that salvo size and number of shot will be exact... it almost never will be. One fire control only shoot at one salvo. If you destroy all missiles in the salvo any additional shots is wasted.

Not talking about fire-controls in this equation is also a bit misleading as it is very important. If you only have five fire-controls and seven incoming salvos then two of them will not be engaged at all no matter how many guns you have. Fire-controls are also allot more expensive than the guns (in general) and also compete with sensor costs on other ships as well.

So, lets say you shoot 8 shots at 100% against an 10 missile salvos you will need more fire-controls to finish them of than if you have 16 shots at 50% based on that you will waste less shots and quite often you will kill a single salvo in one shot... far more often than you will need three salvos to finish of all the missiles. If you fire at missile salvos less than 8 you will get the occasional leaking missile but in those instances the leak are generally so small it is insignificant anyway.

So... the problem is that is all depends and in practice using 100% will not always produce the best result. That is almost only true if the missile salvo you shoot against are equally dividable with the shot made at 100% (or smaller). If you need three salvos from PD to kill incoming salvos the leaking difference become extremely small.

Designing PD to shoot down incoming salvos with one fire-control per salvo is really difficult because missile salvos can vary allot in size. Depending on the ship who launches them and the intensity of AMM used against them. This means you often will need more fire-controls than often is required for a single salvo or you can be overwhelmed by really small missile salvos, such as from fighters for example.

If you want to be effective you will expect leaking missiles anyway otherwise you need to invest quite extensively in very expensive PD fire-controls. Fire controls are more expensive than the weapon so overkill missile salvos is not a bad strategy either, but shields and armour are good equalisers as well.

In C# Aurora we will see slower, larger missiles which means more likely for PD to get closer to missile speed with its tracking speed. When you also add tracking bonus (which are suppose to be a bonus to the tracking speed of the weapon not like grade bonus). This obviously mean that small Gauss guns can become mathematically quite effective. In VB6 Aurora they rarely manage to reach the same speed as incoming missiles at same tech levels.

[Jorgen_CAB]

if you have shields, you should use them.  but it doesn't follow that installing shields is intrinsically a good decision.  maybe you, jorgen_cab, are only experiencing the ubiquity of leakers because you are spending resources on passive defenses that would have been sufficient to make your active defenses airtight.  im not expressing certainty that such is the case, but the possibility of having reversed cause and effect is clearly present in your argument.

You have to look at shields as something that is not only useful for catching the occasional leakers, it is also quite useful against large missile salvos from box launchers penetrating your defences and very useful in beam combat. So the shields are not used for only one purpose. Shields and armour is part of layered defence system together with PD, AMM and other Beam weapon systems.

[SpikeTheHobbitMage (OP)]

if both weapons are less than 100%, large isn't better because of less _average_ leakage, large is better because of less _uncertainty_ in leakage.  10 shots at 90% can be relied upon to get 7 hits; 20 shots at 45% at the same level of confidence only can be depended upon for 5.  also, 1000 shots at .9% generate a ton of annoying log entries, screw that.

disregarding the occasionally obsolete enemy, there is a range of plausible speeds of missiles you might find headed in your way.  you want your point defense in the hands of properly trained crew to have exactly 100% chance against a speed near the bottom of that range.  that's all.  imho, ymmv, dyodd, etc

the quote from charlie beeler way back in 2012 makes it sound like the tracking bonus is a percentage of the _missile speed_, i dunno how he would know, but it matches other allegations i can remember reading.  if true, that's going to make all this moot because rail guns will be the only point defense worth using.

if you have shields, you should use them.  but it doesn't follow that installing shields is intrinsically a good decision.  maybe you, jorgen_cab, are only experiencing the ubiquity of leakers because you are spending resources on passive defenses that would have been sufficient to make your active defenses airtight.  im not expressing certainty that such is the case, but the possibility of having reversed cause and effect is clearly present in your argument.

It is actually both.  You need enough shield points to soak the largest leaks and a high enough recharge rate to soak the average.  Failing at either means taking armour damage.  I will refer to the chart attached to this post to demonstrate.  All Gauss cannons have the same rated average (yellow line), but smaller guns experience worse leakage spikes (green line).  Unless your PD is saturated so that the hit spikes (red line) balance them out, they reduce your actual average hit rate below the rated value.  Your only choices are higher hit rate weapons or to increase tonnage.  Unless you have a stupidly* high crew grade, if you are expecting incoming missiles more than 28% faster than your tracking speed then Gauss-100s are the only viable choice.

*Ten thousand HPMs firing at once to train crews lags the game like you wouldn't believe.  Screw that. 

If Charlie's post is correct then with a Missile Tracking Bonus of 100% a fixed-mount Gauss-100 with a firing rate of 8 would slightly outperform two Railguns due to not needing a reactor, and PD turrets would be rendered obsolete.  I really hope that isn't how it works. 

I know and understand the math just fine... the problem is that you assume that salvo size and number of shot will be exact... it almost never will be. One fire control only shoot at one salvo. If you destroy all missiles in the salvo any additional shots is wasted.

Not talking about fire-controls in this equation is also a bit misleading as it is very important. If you only have five fire-controls and seven incoming salvos then two of them will not be engaged at all no matter how many guns you have. Fire-controls are also allot more expensive than the guns (in general) and also compete with sensor costs on other ships as well.

So, lets say you shoot 8 shots at 100% against an 10 missile salvos you will need more fire-controls to finish them of than if you have 16 shots at 50% based on that you will waste less shots and quite often you will kill a single salvo in one shot... far more often than you will need three salvos to finish of all the missiles. If you fire at missile salvos less than 8 you will get the occasional leaking missile but in those instances the leak are generally so small it is insignificant anyway.

So... the problem is that is all depends and in practice using 100% will not always produce the best result. That is almost only true if the missile salvo you shoot against are equally dividable with the shot made at 100% (or smaller). If you need three salvos from PD to kill incoming salvos the leaking difference become extremely small.

Designing PD to shoot down incoming salvos with one fire-control per salvo is really difficult because missile salvos can vary allot in size. Depending on the ship who launches them and the intensity of AMM used against them. This means you often will need more fire-controls than often is required for a single salvo or you can be overwhelmed by really small missile salvos, such as from fighters for example.

If you want to be effective you will expect leaking missiles anyway otherwise you need to invest quite extensively in very expensive PD fire-controls. Fire controls are more expensive than the weapon so overkill missile salvos is not a bad strategy either, but shields and armour are good equalisers as well.

In C# Aurora we will see slower, larger missiles which means more likely for PD to get closer to missile speed with its tracking speed. When you also add tracking bonus (which are suppose to be a bonus to the tracking speed of the weapon not like grade bonus). This obviously mean that small Gauss guns can become mathematically quite effective. In VB6 Aurora they rarely manage to reach the same speed as incoming missiles at same tech levels.

It is clear that you do not understand the math as well as you think you do.  The entire point of testing with equal shots per target is to eliminate such assumptions from the analysis.  This allows hit rates for any shots per target ratio to be calculated accurately and from that the minimum effective weapon tonnage per incoming missile.  The number of fire controls needed is also entirely unrelated to weapon effectiveness per tonne and thus was deliberately factored out so I wouldn't need to make any assumptions about it.

PD layout is complicated, but by breaking it up the problem becomes much easier to deal with.

In VB only x16 fighter-only FCs can match equal tech missile speeds.
When C# comes out I will be interested in analyzing the changes.

if you have shields, you should use them.  but it doesn't follow that installing shields is intrinsically a good decision.  maybe you, jorgen_cab, are only experiencing the ubiquity of leakers because you are spending resources on passive defenses that would have been sufficient to make your active defenses airtight.  im not expressing certainty that such is the case, but the possibility of having reversed cause and effect is clearly present in your argument.

You have to look at shields as something that is not only useful for catching the occasional leakers, it is also quite useful against large missile salvos from box launchers penetrating your defences and very useful in beam combat. So the shields are not used for only one purpose. Shields and armour is part of layered defence system together with PD, AMM and other Beam weapon systems.

Very wide box launcher salvos are best left to AMMs but it is possible to use very wide turret arrays, just very expensive.
Defending against beam attacks is entirely unrelated to PD Gauss Turret design.  Please stay on topic.

[Jorgen_CAB]

It is clear that you do not understand the math as well as you think you do.  The entire point of testing with equal shots per target is to eliminate such assumptions from the analysis.  This allows hit rates for any shots per target ratio to be calculated accurately and from that the minimum effective weapon tonnage per incoming missile.  The number of fire controls needed is also entirely unrelated to weapon effectiveness per tonne and thus was deliberately factored out so I wouldn't need to make any assumptions about it.

PD layout is complicated, but by breaking it up the problem becomes much easier to deal with.

In VB only x16 fighter-only FCs can match equal tech missile speeds.
When C# comes out I will be interested in analyzing the changes.

rol against each salvo. This is not in question... So... yes I understand the math just fine and have done the test myself several times before years ago... that is when I noticed that the tracking speed bonus did not work for example.

I just highlight that this comparison is not the whole picture... I got the feeling from the original post that you should use max size guns because they always are more effective unless you are close to the missile speed in tracking (which you rarely are in VB6). What I pointed out is that number of fire-controls salvos size and ratios do matter in this context in what cannons are more valuable per tonnage too. Leaving it out is not giving you a very good overview on what is most effective in practice given all the variable out there that actually matter.

So the basic maths of probabilities is not in question, just the overall evaluation of the importance of it in relation to how real practical examples can turn out. If you only look at part of a problem you don't get a very good conclusion to the whole problem.

Very wide box launcher salvos are best left to AMMs but it is possible to use very wide turret arrays, just very expensive.
Defending against beam attacks is entirely unrelated to PD Gauss Turret design.  Please stay on topic.

If you completely ignore that some component have other uses then you will assign them too much emphasis in that one calculation, that is just bad evaluation of how effective something really is. If a ship is going to have shields for other uses than for just leaking missiles they will be there no matter what so in that case you could include them for free as well as saying they are to weighty for their use.

I also think that only talking about tonnage as effective use of something is faulty to begin with... it is always a combination of cost, size and distribution of resource usage. If you use one resource too much you get an imbalance in your mining efforts and this is equally important in the entire context. On many occasion have some players complained at the lack of some specific resource only to see they are overly used in their designs over other resources, be it missiles, engines or some other components. I know it is not the topic... but again discussing one specific thing without context will often give the wrong impressions and conclusions.

If we only talk about weight to effective use in a very narrow spectrum then yes I agree that 100% size Gauss is more useful. But if you also add all other factors they do not have to be the best option.

[SpikeTheHobbitMage (OP)]

It is clear that you do not understand the math as well as you think you do.  The entire point of testing with equal shots per target is to eliminate such assumptions from the analysis.  This allows hit rates for any shots per target ratio to be calculated accurately and from that the minimum effective weapon tonnage per incoming missile.  The number of fire controls needed is also entirely unrelated to weapon effectiveness per tonne and thus was deliberately factored out so I wouldn't need to make any assumptions about it.

PD layout is complicated, but by breaking it up the problem becomes much easier to deal with.

In VB only x16 fighter-only FCs can match equal tech missile speeds.
When C# comes out I will be interested in analyzing the changes.

rol against each salvo. This is not in question... So... yes I understand the math just fine and have done the test myself several times before years ago... that is when I noticed that the tracking speed bonus did not work for example.

I just highlight that this comparison is not the whole picture... I got the feeling from the original post that you should use max size guns because they always are more effective unless you are close to the missile speed in tracking (which you rarely are in VB6). What I pointed out is that number of fire-controls salvos size and ratios do matter in this context in what cannons are more valuable per tonnage too. Leaving it out is not giving you a very good overview on what is most effective in practice given all the variable out there that actually matter.

So the basic maths of probabilities is not in question, just the overall evaluation of the importance of it in relation to how real practical examples can turn out. If you only look at part of a problem you don't get a very good conclusion to the whole problem.

Very wide box launcher salvos are best left to AMMs but it is possible to use very wide turret arrays, just very expensive.
Defending against beam attacks is entirely unrelated to PD Gauss Turret design.  Please stay on topic.

If you completely ignore that some component have other uses then you will assign them too much emphasis in that one calculation, that is just bad evaluation of how effective something really is. If a ship is going to have shields for other uses than for just leaking missiles they will be there no matter what so in that case you could include them for free as well as saying they are to weighty for their use.

I also think that only talking about tonnage as effective use of something is faulty to begin with... it is always a combination of cost, size and distribution of resource usage. If you use one resource too much you get an imbalance in your mining efforts and this is equally important in the entire context. On many occasion have some players complained at the lack of some specific resource only to see they are overly used in their designs over other resources, be it missiles, engines or some other components. I know it is not the topic... but again discussing one specific thing without context will often give the wrong impressions and conclusions.

If we only talk about weight to effective use in a very narrow spectrum then yes I agree that 100% size Gauss is more useful. But if you also add all other factors they do not have to be the best option.

I never claimed it was the 'whole picture', just that those elements can be factored out so that gun size can be meaningfully considered on its own.  As demonstrated, max size guns are always more effective unless your tracking speed is close to the target speed or you have an unrealistically high grade bonus.

Fire control ratio is a completely independent problem to the choice turret weapon, and therefore not relevant to that choice.  If you want to discuss other topics, start a new thread.

I am going to ask you one last time:  Stop derailing this thread.

[misanthropope]

you've claimed to factor out fire control, but you can't, entirely.  any FC-per-expected-hit ratio that is achievable for full sized turrets is possible for smaller ones, but the reverse is not true.  if you come to the conclusion on the basis of mean and standard deviation that a 100% size 4-cannon turret is optimal, you're going to die like a dog to a many-small-salvos attack.  you've already asserted that dealing with omg box waves isn't in the GC's job description, so in that case in what sense is the 1500 ton turret even useful, let alone optimal?

[Jorgen_CAB]

It is clear that you do not understand the math as well as you think you do.  The entire point of testing with equal shots per target is to eliminate such assumptions from the analysis.  This allows hit rates for any shots per target ratio to be calculated accurately and from that the minimum effective weapon tonnage per incoming missile.  The number of fire controls needed is also entirely unrelated to weapon effectiveness per tonne and thus was deliberately factored out so I wouldn't need to make any assumptions about it.

PD layout is complicated, but by breaking it up the problem becomes much easier to deal with.

In VB only x16 fighter-only FCs can match equal tech missile speeds.
When C# comes out I will be interested in analyzing the changes.

rol against each salvo. This is not in question... So... yes I understand the math just fine and have done the test myself several times before years ago... that is when I noticed that the tracking speed bonus did not work for example.

I just highlight that this comparison is not the whole picture... I got the feeling from the original post that you should use max size guns because they always are more effective unless you are close to the missile speed in tracking (which you rarely are in VB6). What I pointed out is that number of fire-controls salvos size and ratios do matter in this context in what cannons are more valuable per tonnage too. Leaving it out is not giving you a very good overview on what is most effective in practice given all the variable out there that actually matter.

So the basic maths of probabilities is not in question, just the overall evaluation of the importance of it in relation to how real practical examples can turn out. If you only look at part of a problem you don't get a very good conclusion to the whole problem.

Very wide box launcher salvos are best left to AMMs but it is possible to use very wide turret arrays, just very expensive.
Defending against beam attacks is entirely unrelated to PD Gauss Turret design.  Please stay on topic.

If you completely ignore that some component have other uses then you will assign them too much emphasis in that one calculation, that is just bad evaluation of how effective something really is. If a ship is going to have shields for other uses than for just leaking missiles they will be there no matter what so in that case you could include them for free as well as saying they are to weighty for their use.

I also think that only talking about tonnage as effective use of something is faulty to begin with... it is always a combination of cost, size and distribution of resource usage. If you use one resource too much you get an imbalance in your mining efforts and this is equally important in the entire context. On many occasion have some players complained at the lack of some specific resource only to see they are overly used in their designs over other resources, be it missiles, engines or some other components. I know it is not the topic... but again discussing one specific thing without context will often give the wrong impressions and conclusions.

If we only talk about weight to effective use in a very narrow spectrum then yes I agree that 100% size Gauss is more useful. But if you also add all other factors they do not have to be the best option.

I never claimed it was the 'whole picture', just that those elements can be factored out so that gun size can be meaningfully considered on its own.  As demonstrated, max size guns are always more effective unless your tracking speed is close to the target speed or you have an unrealistically high grade bonus.

Fire control ratio is a completely independent problem to the choice turret weapon, and therefore not relevant to that choice.  If you want to discuss other topics, start a new thread.

I am going to ask you one last time:  Stop derailing this thread.

If the only thing you want to really say with the topic is that knocking out five missiles with five 100% shots is more optimal than ten 50% shots then I agree with your statement, but that is at least to me rudimentary maths not a revelation. Good to mention it if someone didn't know though. Fact is that 50% reduction of the weapons are basically as bad as it gets (if that is the to hit ratio you finally end up with), really small guns get so many shots that the mean distribution is very tight, to the point it becomes negligible at the very small guns. There might even be a slight case of making 17% reduced canons to be very effective since they also have a 2% higher average efficiency (per tonnage, the same as 85% reduced Gauss) and enough shots to lower the mean distribution to almost negligible.

Another point is actual numbers... the worst leaker is a gun that ends up at a 50% hit chance if I'm not mistaken. Anything below will basically reduce the spread of the mean distribution as will anything above. As you get closer to 0% and 100% you end up at absolutes. This can definitely mean that a large 100% gun can become less reliable after all calculations is done. It all depends on the tracking speed versus missile speed which one will leak more.

Example
A 100% gun with a tracking speed of say 16000km/s shooting at a missile doing 39000km/s have a base to hit ratio of 41%. Let't say you hit at 90% at 10.000km and have a grade bonus of +40% and end at around 51% final to hit. That is worse than four times the 25% reduced size Gauss weapons hitting at around 13% a piece. The 25% reduced sized weapon has less spread and produce less leakers and is more reliable.

In my opinion the above example is more of a realistic scenario... but the problem is that it could just be another missile with another speed making the dice roll different and skew the result in favour of the larger gun. This is the real problem you face in a real game. I do think that this is important to point out so people don't draw the wrong conclusions.

I also believe that having more weapons in a turrets will also have some improvements in C# as well. Having four 100% guns in one turret can in many scenarios be overkill, especially against fighter launched salvos.

To be honest I don't know exactly what the thread is about anymore... I just responded to the replies with information I thought might be interesting to the topic of comparing Gauss turrets and their effect on the game.   

[SpikeTheHobbitMage (OP)]

you've claimed to factor out fire control, but you can't, entirely.  any FC-per-expected-hit ratio that is achievable for full sized turrets is possible for smaller ones, but the reverse is not true.  if you come to the conclusion on the basis of mean and standard deviation that a 100% size 4-cannon turret is optimal, you're going to die like a dog to a many-small-salvos attack.  you've already asserted that dealing with omg box waves isn't in the GC's job description, so in that case in what sense is the 1500 ton turret even useful, let alone optimal?

Targets per FC is independent of the number of FCs by definition.  The data shows that accuracy per shot is more important than the number of shots fired to hit a given number of targets at minimum cost and that larger turrets are cheaper than the equivalent in smaller turrets, though the margins are admittedly small.

During my most recent engagement, the enemy was firing salvos of 9 with a 3x speed advantage.  Defending with Gauss-100s with 95% FCs and 35% crew grade gives 43% cth per shot.  It takes 4 shots to get a ~90% kill probability against one missile.  It takes 28 shots to get a ~90% kill probability against a full salvo of 9.  Pairing a quad with a triple would have been more efficient than two quads.  To do the same thing with -50s would take 60 shots per salvo.

If the only thing you want to really say with the topic is that knocking out five missiles with five 100% shots is more optimal than ten 50% shots then I agree with your statement, but that is at least to me rudimentary maths not a revelation. Good to mention it if someone didn't know though. Fact is that 50% reduction of the weapons are basically as bad as it gets (if that is the to hit ratio you finally end up with), really small guns get so many shots that the mean distribution is very tight, to the point it becomes negligible at the very small guns. There might even be a slight case of making 17% reduced canons to be very effective since they also have a 2% higher average efficiency (per tonnage, the same as 85% reduced Gauss) and enough shots to lower the mean distribution to almost negligible.

Another point is actual numbers... the worst leaker is a gun that ends up at a 50% hit chance if I'm not mistaken. Anything below will basically reduce the spread of the mean distribution as will anything above. As you get closer to 0% and 100% you end up at absolutes. This can definitely mean that a large 100% gun can become less reliable after all calculations is done. It all depends on the tracking speed versus missile speed which one will leak more.

Example
A 100% gun with a tracking speed of say 16000km/s shooting at a missile doing 39000km/s have a base to hit ratio of 41%. Let't say you hit at 90% at 10.000km and have a grade bonus of +40% and end at around 51% final to hit. That is worse than four times the 25% reduced size Gauss weapons hitting at around 13% a piece. The 25% reduced sized weapon has less spread and produce less leakers and is more reliable.

In my opinion the above example is more of a realistic scenario... but the problem is that it could just be another missile with another speed making the dice roll different and skew the result in favour of the larger gun. This is the real problem you face in a real game. I do think that this is important to point out so people don't draw the wrong conclusions.

I also believe that having more weapons in a turrets will also have some improvements in C# as well. Having four 100% guns in one turret can in many scenarios be overkill, especially against fighter launched salvos.

To be honest I don't know exactly what the thread is about anymore... I just responded to the replies with information I thought might be interesting to the topic of comparing Gauss turrets and their effect on the game.   

Using your example, the 100% gun takes 3-4 shots to get a 90% cth one missile and 13-14 shots to have a 90% chance of killing 5 incoming missiles.  The 25% gun takes 16-17 shots for 90% cth against one and 59-60 shots for 90% cth 5.

As it says in the title, this thread was supposed to be a comparison of PD Gauss Turrets.  I apologize for getting snippy.

[misanthropope]

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. 

[Jorgen_CAB]

Using your example, the 100% gun takes 3-4 shots to get a 90% cth one missile and 13-14 shots to have a 90% chance of killing 5 incoming missiles.  The 25% gun takes 16-17 shots for 90% cth against one and 59-60 shots for 90% cth 5.

As it says in the title, this thread was supposed to be a comparison of PD Gauss Turrets.  I apologize for getting snippy.

That is completely irrelevant in this context.

What I meant to prove is the mean distribution of results. the closer the to hit goes to either 0% or 100% the mean distribution of expected results is the same going from 50% if you add and remove dice accordingly.

We was talking about mean distribution not the chance of getting a certain specific number of hits, that is different.

shooting 8 shots at 50% will produce a far more diverse result than rolling 20 dice at 20% which will have roughly the same mean distribution as rolling 5 80% dice even if there is a potential of some results of 6 misses on the 20% dice, but those results become far less common the lower the percentage versus increase on dice. but the mean distribution are practically the same.

Fact is that a gun that fires at close to 50% to hit rate will produce the most leaking missiles as long as you add or remove shots linear to the to hit rate and do a comparison. You can test this if you want, it will be so...

[misanthropope]

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.