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Posted by: Arwyn
« on: May 31, 2012, 01:52:23 PM »

I think that is an excellent point, and along with that, comes the rate of fire component as well.

At reload 4, your size 1 launchers are running at 10 seconds per volley. Size 4 launchers are running at 30. So, the ship with size one launchers is running 6 salvos to the 2 salvos from the size 4 ship. Assuming similar warhead sizes and range, the damage ratio is clearly in the favor of the smaller launchers. As the reload rate comes up, their is a noticeable shift in the favor of the larger missiles.

(For illustrations sake, this is using the following for baselines. Cobalt warheads (10pts) and Magnetic Confinement drive tech, compressed carbon armor. Range is identical, speeds are identical, hit chance is identical.)

Size 1 missile
Code: [Select]
Missile Size: 1 MSP  (0.05 HS)     Warhead: 4    Armour: 0     Manoeuvre Rating: 20
Speed: 31200 km/s    Endurance: 34 minutes   Range: 64.2m km
Cost Per Missile: 1.7708
Chance to Hit: 1k km/s 624%   3k km/s 200%   5k km/s 124.8%   10k km/s 62.4%
Materials Required:    1x Tritanium   0.5208x Gallicite   Fuel x625
Size 4 missile
Code: [Select]
Missile Size: 4 MSP  (0.2 HS)     Warhead: 12    Armour: 0.2     Manoeuvre Rating: 20
Speed: 31200 km/s    Endurance: 34 minutes   Range: 64.2m km
Active Sensor Strength: 0.28   Sensitivity Modifier: 140%
Resolution: 30    Maximum Range vs 1500 ton object (or larger): 210,000 km
Cost Per Missile: 5.6633
Chance to Hit: 1k km/s 624%   3k km/s 200%   5k km/s 124.8%   10k km/s 62.4%
Materials Required:    3.05x Tritanium   0.28x Uridium   2.8333x Gallicite   Fuel x2500
At reload 6, the size 1 launchers drop to 5 seconds, for 12 salvos a minute. With a damage of 4, thats 48 pts of damage output per launcher.

At reload 6 the size 4 launchers drop to 20 seconds, for 3 salvos a minute. With a damage of 12, thats 36 pts of damage per launcher.

At reload 8 the size 1 launchers are still 5 seconds, for 12 salvos a minute. With a damage of 4, thats 48 pts of damage output per launcher.

At reload 8 the size 1 launchers are now 15 seconds, for 4 salvos a minute. With a damage of 12, thats 48 pts of damage per launcher.


So, at Reload 8, from a total damage perspective, the missile sizes are a wash. The advantages of the smaller missiles are still there (numbers) and with the hit % being identical, the chances are that the smaller missiles are still going to get things through to do damage.

As the tech goes up, missile intercepts go up as well as anti-missile defenses improve, more missiles are intercepted. This would argue strongly for the numbers approach with more numerous but smaller missiles.

Arguably though, the larger missiles are becoming MORE capable as the tech goes up. In the size 4 design above, the missile includes some armor and sensors, which the size 1 lacks. In the case of the size 4, its relatively easy to modify the missile further to improve survival, or speed, or range while maintaining the same warhead yield. Thats not possible with the size 1 missile. The larger missile also has improved penetration vs. the size 1.

So, the question at middle and later tech is smaller + numbers vs. larger + damage/penetration/flexibility.

I think that the smaller missiles have a significant number of advantages, especially so early in the game. In fact, they are probably game breakingly advantageous early on. By middle tech levels, there are some advantages to the bigger missiles that start to become apparent. In terms of flexibility, the advantage goes to the bigger missiles, since its easier to modify the fuel/speed parameters of the design without losing damage. This flexibility is ESPECIALLY pronounced if sensors/ecm are part of the mixture.
Posted by: sloanjh
« on: May 29, 2012, 11:38:02 PM »

Quote from: Brian on May 25, 2012, 11:33:17 AM
Another important factor is how big the crater is vs how large the target.  When you start getting craters that are around 1/3 of the total columns on the ship the chances of getting an early internal hit go up much faster than what the sandblasting will get you.  A quick example with a smaller ship (17 columns and 6 points of armor each) and size 16 warheads.  (Size 16 gets a maximum of 4 levels of penetration and damages at least 7 columns.)  By the fourth hit you will already have some damage overlaping.  On that fourth hit you have a small chance to get internals.  If you didn't then by the fifth you are pretty much garrunteed hitting somewhere that has already lost enough armor to have that hit get through.  In comparison the same total damage (64 or 80 points for 4 or 5 missiles respectivly.) from size 1 warheads will probably have penetrated the first 3-4 rows with about half of the next row being down as well.  You still need about 20 more hits before you are likely to get any internal.  Of course by the point that a sandplasting attack is getting internals the target is pretty much dead.  Flip this example around and have a much bigger target with 40 columns and it takes a lot more hits to start getting your clustering.  In effect you are having to partially sandblast the ship anyway before you get to the point that the larger warheads are actually helpfull.

I think the salvo size and RoF needs to be looked at here for a good comparison with sandblasting.  Let's pretend that you have a salvo size of 1, with str-16 warheads, and a RoF of 1 (in some units).  This is to be compared with a salvo size of 16, str-1 warheads, with RoF of 16.  In this case, the str-1 missiles can do 256 points of damage to the target for each 16 point salvo of the str-16 missiles.  Since there are only 102 points of armor on the target, sandblasting will have probably annihilated it before the second heavy-warhead salvo is away.  The issue is that you'll have ended up burning more missile volume with the sandblasting than with the heavy missiles (unless the enemy has AM defences, in which case each AM hit is 16x as effective in the heavy warhead case).

That being said, you make a good point that if you can get good internal damage on the target in a single salvo then this is one of the regimes where heavy warheads come out ahead.

John
Posted by: sloanjh
« on: May 29, 2012, 11:22:24 PM »

Quote from: Theokrat on May 25, 2012, 12:22:02 PM
You are very much underestimating the effects of sandblasting. It is extremely unlikely that the small missiles will neatly only touch the outermost undamaged armour layers like you suggest.

I have run 100 simulations on the situation you described: Let an armour layout of 17 (width) by 6 (layers) be hit by 80 strength-1 explosions. The results are very different from your assertion that "You still need about 20 more hits before you are likely to get any internal".

Internal damage was dealt in _all_ 100 simulations. Indeed the most frequent case saw 6 points of internal damage (20 cases), and it went as far up as 13 internal damage (one case). The median was 6.5 internal damage.
Did you try the same experiment with 20 str-4 and 5 str-16 explosions? How about 17x60 with 800 str-1, 200 str-4, or 50 str-16 (i.e. everything 10x)?  My expectation is that you should (on average) always see better effects (in terms of internal damage) from large warheads than from small, because of the larger relative fluctuations in column depth.

The reason that sandblasting wins is because the damage for str-1 warheads is done 4x as fast as for str-4 warheads (assuming same performance).  This just made an interesting idea occur to me - if you're limitted by ammunition stocks, i.e. you're going to run out of ammo before you run out of targets, then large warheads also have an advantage in this case.  Of course this will be offset if the target has any anti-missile defences.

John
Posted by: TheDeadlyShoe
« on: May 27, 2012, 10:34:12 AM »

Data point:  10,000 ton (41 armor column) survey cruiser with 4 layers of armor (and thus 160+points of armor) took 11 hits from strength 6 warheads. This is just 66 points of damage - less than half its total armor strength, and needing 3 hits on the same location to breach - yet it took 4 points of internal damage and has a 5-column wide total breach in its armor. 
Posted by: Bunga
« on: May 26, 2012, 04:38:52 AM »

Quote from: blue emu link=topic=4897. msg50091#msg50091 date=1337967583
I've found that people generally have poor intuition regarding statistics and probabilities. . .  even statisticians themselves often fall prey to this. 
You may be right, statistically speaking of course.
Posted by: blue emu
« on: May 25, 2012, 12:39:43 PM »

I've found that people generally have poor intuition regarding statistics and probabilities... even statisticians themselves often fall prey to this.
Posted by: Theokrat
« on: May 25, 2012, 12:22:02 PM »

Quote from: Brian on May 25, 2012, 11:33:17 AM
Another important factor is how big the crater is vs how large the target.  When you start getting craters that are around 1/3 of the total columns on the ship the chances of getting an early internal hit go up much faster than what the sandblasting will get you.  A quick example with a smaller ship (17 columns and 6 points of armor each) and size 16 warheads.  (Size 16 gets a maximum of 4 levels of penetration and damages at least 7 columns.)  By the fourth hit you will already have some damage overlaping.  On that fourth hit you have a small chance to get internals.  If you didn't then by the fifth you are pretty much garrunteed hitting somewhere that has already lost enough armor to have that hit get through.  In comparison the same total damage (64 or 80 points for 4 or 5 missiles respectivly.) from size 1 warheads will probably have penetrated the first 3-4 rows with about half of the next row being down as well.  You still need about 20 more hits before you are likely to get any internal.  Of course by the point that a sandplasting attack is getting internals the target is pretty much dead.  Flip this example around and have a much bigger target with 40 columns and it takes a lot more hits to start getting your clustering.  In effect you are having to partially sandblast the ship anyway before you get to the point that the larger warheads are actually helpfull.

Brian

You are very much underestimating the effects of sandblasting. It is extremely unlikely that the small missiles will neatly only touch the outermost undamaged armour layers like you suggest.

I have run 100 simulations on the situation you described: Let an armour layout of 17 (width) by 6 (layers) be hit by 80 strength-1 explosions. The results are very different from your assertion that "You still need about 20 more hits before you are likely to get any internal".

Internal damage was dealt in _all_ 100 simulations. Indeed the most frequent case saw 6 points of internal damage (20 cases), and it went as far up as 13 internal damage (one case). The median was 6.5 internal damage.

Posted by: Brian Neumann
« on: May 25, 2012, 11:33:17 AM »

Quote from: sloanjh on May 24, 2012, 07:17:22 PM
My gut feel is that if your warhead can penetrate with 2 or maybe 3 hits, then you're probably not in the sandblasting regime, i.e. large warheads are better because they penetrate (and cluster) better, but anything more than that and you're in sandblasting mode.

John
Another important factor is how big the crater is vs how large the target.  When you start getting craters that are around 1/3 of the total columns on the ship the chances of getting an early internal hit go up much faster than what the sandblasting will get you.  A quick example with a smaller ship (17 columns and 6 points of armor each) and size 16 warheads.  (Size 16 gets a maximum of 4 levels of penetration and damages at least 7 columns.)  By the fourth hit you will already have some damage overlaping.  On that fourth hit you have a small chance to get internals.  If you didn't then by the fifth you are pretty much garrunteed hitting somewhere that has already lost enough armor to have that hit get through.  In comparison the same total damage (64 or 80 points for 4 or 5 missiles respectivly.) from size 1 warheads will probably have penetrated the first 3-4 rows with about half of the next row being down as well.  You still need about 20 more hits before you are likely to get any internal.  Of course by the point that a sandplasting attack is getting internals the target is pretty much dead.  Flip this example around and have a much bigger target with 40 columns and it takes a lot more hits to start getting your clustering.  In effect you are having to partially sandblast the ship anyway before you get to the point that the larger warheads are actually helpfull.

Brian
Posted by: sloanjh
« on: May 24, 2012, 07:17:22 PM »

Quote from: TheDeadlyShoe on May 24, 2012, 03:41:09 PM
Just for kicks... looking at a 40,000ton freighter being hit by strength 1 warheads.  That's 104 armor columns, but with 20 missile hits you have a 84% chance of having scored internal damage.  

And if those 20 points of damage were instead from 5 strength-4 hits you'd have a 100% chance of doing at least 5 points of internal damage, with even more internal damage done if the str-4 hits overlap.  The intuition here is that the 4th point of damage (on the 29 column warship) has a 100%, rather than 3/29 chance of clustering.

The detailed math is really yuckky, but I'm pretty sure that clustering actually helps big warheads more than it helps small warheads.  The reason for this is that, for a large number of hits, the percentage fluctuation of hits in any one column (i.e. the relative size of the mountains and valleys) will go like 1/sqrt(NHits).  So the damage profile from a large number of big warhead hits should be more jagged than from a set of small warhead hits that do the same amount of total damage.  For example, imagine a ship with 100 columns of armor that is hit with with 10,000 str-1 hits or with 2,500 str-4 hits.  In the str-1 case, each column is likely to get 100 +/- 10 hits; in the str-4 case each will get 25 +/-5 str-4 hits.  The average damage per column is easy for the str-1 case - it's just 100.  For the str-4 case, it's 2*25 for the column being considered + 25 each spillover from each adjacent column, for a total of 100 (this is as it must be, since both cases did the same total damage).  The fluctuations in the str-4 case are very interesting though.  You need to add uncertainties in quadrature, so it sqrt(2^2+1^2+1^2)*5, or sqrt(6)*5, which is sqrt(1.5)*10.  In other words, the fluctuation in the penetration depth for str-4 warheads will be sqrt(1.5) larger than for str-1 warheads.  The reason that str-4 (stronger clustering) doesn't win in this regime is that the str-1 missiles can be fired 4 times as fast, and this affects the central (average) value, not just the fluctuations.

My gut feel is that if your warhead can penetrate with 2 or maybe 3 hits, then you're probably not in the sandblasting regime, i.e. large warheads are better because they penetrate (and cluster) better, but anything more than that and you're in sandblasting mode.

John
Posted by: jseah
« on: May 24, 2012, 06:02:38 PM »

Bigger ASMs could get better performance than smaller ones by having less than 1 Warhead per MSP. 
You are also presented with the tradeoff of getting slightly more than 1 warhead per MSP. 

Eg. the Wakizashi could be a size 4 carrying WH:3 (assuming sandblasting is going to happen)
It could also be a size 3 carrying WH:4

These proportions are inaccessible to a size 1 ASM. 
Posted by: Havear
« on: May 24, 2012, 05:54:54 PM »

All good points. I'll admit, I've not used reloadable launchers for some time. Even on box launchers, I've been considering moving from size-6 back to size-4, as I'm not really noticing much more then slightly increased range (pretty useless for fighters) and some ECM, which doesn't seem to match the 50% density tradeoff.
Posted by: TheDeadlyShoe
« on: May 24, 2012, 03:41:09 PM »

Quote
4)  When thinking about damage templates, there are two limiting regimes: the warhead can penetrate the targets armor and do internal damage with a single hit, or it can't.  Consider a ship with thick armor (e.g. 12, or 20, or even 6) and a strength-9 warhead, which has penetration 3 and so needs to hit a patch of armor only 2 units thick in order to do internal damage.  Because of the way statistics of large numbers works, you should assume that you're going to have to grind away essentially all of the armor before you're able to do internal damage.
I think you are underballing damage clustering.   Check this out:

http://en.wikipedia.org/wiki/Birthday_problem

let's assume you have a 6,000 ton warship being attacked by missiles, which is 29 armor columns.  The second missile has a 1/29 chance of landing on the same location. The third missile has a 2/29 chance of landing on either previous location. The fourth has 3/29, and so on. It rapidly becomes more probable to have landed two hits on the same location than not. That's for *direct hits* on previous impact craters.   What this basically means is that battle-damaged ships armor will be mountains and valleys - even on the thickest armor, you're likely to have undamaged columns while other sections have been completely penetrated. 

or to put it another way: if you hit something with 7 missiles, there are 21 distinct chances for hits to cluster. on a 29-column (or 6000 ton) hull that works out to about a 52% chance that 2 missiles will hit directly on top of eachother.  So lets suppose that the hull is armor rating 5, being attacked by strength 9 warheads - you have a 52% chance of internal damage after taking only 63 points of damage out of 148 armor strength.  Bear in mind that this significantly underballs that chance, because it does not take into account damage outside the 'central column' of the pyramid.

If you hit that same ship with 10 missiles, you have about an 80% chance that two of your hits will be on top of eachother. 15 missiles is a 98% chance. 

Just for kicks... looking at a 40,000ton freighter being hit by strength 1 warheads.  That's 104 armor columns, but with 20 missile hits you have a 84% chance of having scored internal damage. 
Quote
EDIT - Ninja!!  (I got pulled away while typing  ).  Theokrat's post is spot on.  One caveat: when you start talking about missile armor the advantage goes to the big missiles.
Yeah - now if only armor scaled up with technology. :(


**EDIT**

I got to thinking. What about strength 12 warheads? The damage shape means that you essentially have 3 chances(one slight off left, one direct, one slightly off right) of scoring a stacking hit on a previous impact rather than 1.  So a strength 12 warhead needs only 4 hits (48 damage) to hit ~50% internal damage chance, and 6 hits (72 damage) to hit ~80%.  Hrm.  Same applies to strength 6 vs armor 3, or strength 20 vs armor 7.
Posted by: sloanjh
« on: May 24, 2012, 11:24:22 AM »

A few comments (many of which many people are already aware of):

1)  I think a lot of people upthread have been using "size" when describing warheads rather than "strength".  When I say "strength 4 warhead" below, I mean a warhead that does 4 points of damage.

2)  If you stick with the basic systems (engine, warhead, agility, fuel) and don't put "dead weight" systems (e.g. armor, sensors) onto your missile designs, then missile capabilities scale exactly.  In other words, a size-4 missile, with a strength-4 warhead will have exactly the same range, speed, and hit probability as a size-1 missile with a strength-1 warhead if you pick the percentages of basic systems to be the same (and the size and cost will be 4x greater).  This means that, in terms of expected damage per (non-intercepted) missile, the size-4 missile and 4x size-1 missiles cost the same and occupy the same amount of magazine space.  I'll assume that missiles of different sizes have been tuned in this way (to have same performance characteristics) in the discussion below.

3)  Launch rate is proportional to missile size, and launcher size is inversely proportionaly.  This means that (assuming no interceptions) the expected damage per salvo for size-4 missiles is the same as the damage per salvo for size-1 missile.  It also means that the rate of damage is inversely proportional to missile size, since salvos are launched more quickly for smaller missiles.  Since it costs the same to intercept a size-4 missile as to intercept a size-1 missile, sandblasting with size-1 missiles (which might have warhead strengths greater than 1!) is vastly superior if damage templates are ignored.

4)  When thinking about damage templates, there are two limiting regimes: the warhead can penetrate the targets armor and do internal damage with a single hit, or it can't.  Consider a ship with thick armor (e.g. 12, or 20, or even 6) and a strength-9 warhead, which has penetration 3 and so needs to hit a patch of armor only 2 units thick in order to do internal damage.  Because of the way statistics of large numbers works, you should assume that you're going to have to grind away essentially all of the armor before you're able to do internal damage.  Because of the increased RoF, size-1 sandblasting is most effective here; even in comparison to size-2 missiles it will grind away twice as fast (and that's before the effects of interception are taken into account).  Now consider a really big freighter with armor-1.  In this case, the size-4 missile will have twice the penetration (and an even bigger improvement in the ratio of internal-to-armor damage) of the size-1 missile, and you don't have to wait for a later hit to randomly hit a hole you've made in the armor before you can do internal damage.  So for thinly armored ships (e.g. armor less than  4 or 5) you want big honking warheads.

In my designs, I tend to have two missile sizes: size-4 ASM missiles, which give a good balance between RoF and salvo size vs. penetration in the early game and size-1 missiles.  For the size-1 missiles, I usually have a warhead strength-1 designed optimized for AAM work, and an ASM "slug" design with the biggest warhead size I can manage (typically 2 or 3 in the early game).

John

EDIT - Ninja!!  (I got pulled away while typing :) ).  Theokrat's post is spot on.  One caveat: when you start talking about missile armor the advantage goes to the big missiles.

Posted by: Theokrat
« on: May 24, 2012, 11:09:33 AM »

Quote from: Havear on May 24, 2012, 10:17:35 AM
There's two things I'd like to point out. 1) Agility points are independent of missile size. 2) Warhead strength is independent of size.

Yes, it *is* indeed possible to get a smaller missile with the same speed and range, since those are proportional to size. However, you then have to lower either your warhead or agility ratings, which are not proportional, and thus are flatly lower. It's indeed possible to get missiles with better performance in *very* small packages, but actually doing decent damage when they get there is another story.
At the risk of repeating a bit what TheDeadlyShoe said:

1) The Maneuver rating is, like range and speed, a function of only the proportion of size devoted to agility- but not of the total size. x% of missile space towards agility results in the same maneuver rating, regardless of whether its a size-1 or a size-10 missile. Thus decreasing the size of a missile does not change the agility the tiniest bit.

2) The Warhead is the only component other than sensors and ecm that is propotional to the total size devoted to it (and not to the proportion of the missile).

But of course one should not compare missiles on a per-unit basis. Sure one size-1 missile is worse than one size-2 missile. But that comparison is meaningless, as it does not consider the constraints involved. Players are limited by the industrial costs of producing missiles, by the magazine space on their ships, and by the weight of ships that can be devoted to missile launchers. All of these factors scale proportionally to the size of a missile, thus one size-2 missiles must be compared to two size-1 missiles (or even four when considering missiles per second in non-attrition situations). But therefore "splitting" a missile into a number of smaller ones does not decrease the total sum of warheads, it merely leads to a different damage profile caused by these. And for strongly-armoured ships this is almost certainly a second-order effect at best.

Posted by: TheDeadlyShoe
« on: May 24, 2012, 10:22:24 AM »

Agility ratings are divided by missile size, and thus are proportional.  Warhead strength is completely independent of size; 4 strength 1 warheads are equal to 1 strength 4 warhead, except insofar as damage grouping/cratering is concerned. 

However, damage grouping is irrelevant versus shields, and even strength 4 warheads dont do much clustering to write home about against decent (5+) armor layers.  It takes strength 9 or higher warheads to do meaningful clustering in my experience.

The only things that small missiles cant do are ecm and sensors.  Even armor scales down to some extent, but you're almost always better off with more engine instead of armor.