Let’s have an analytical look at the optimal size of missiles. It can be easily demonstrated that missile size is a trade-off between two things: The ability to get missiles through enemy anti-missile defences, on the one hand. And, on the other hand the ability to cause internal damage to enemy ships, rather than only damage to armour.
Missile defences can shoot down a given
number of missiles, regardless of their size, so using a large number of small missiles mean that more missiles get through the enemy missile defences. Conversely, using larger missiles means their individual warheads are larger, and damage will be “clustered” more closely together, and reach deeper into enemy armour or ships, if the missiles hit.
The challenge is to determine the quantitative result of these effects. Obviously, the relative magnitude of the effects differs, depending on the likely target, so in fact there is no optimal missile. Regardless, this analysis might still provide some insights.
Some limitations to this analysis: I will ignore several things that would make my life to complicated on the basis that these are not too common for most players: Sensors on missiles, ECCM on missiles, and armoured missiles. Not in this analysis, sorry. [EDIT]Forgot to mention: Shields are not in either. Ignoring them is in favour of large missiles, as shields negate the effect of clustering, and damage-per-second beocmes more relevant[/Edit]
Also we are going to compare equal total missile size scenarios (e.g. two size-1 missiles versus one size-2 missile) on the basis that these result in equal industrial costs, in equal weight of missile launchers, and in equal magazine space requirements, so broadly they reflect the costs-constraints hat players are facing. This is in favour of large missiles, because small missiles have at least two advantages that are not reflected: Small missiles cost less in R&D, and small missiles can be launched more quickly in succession. We are ignoring the effect that this means enemy AMMs have a lot more to deal with at the same time, and that targets could potentially be killed more quickly by this.
The first effect – ability to overcome enemy anti-missile defences – is easy to assess. If we launch X missiles, and Y get intercepted, then X-Y get through. Increasing X (more missiles of smaller size) means more missiles hit the enemy, and a larger total amount of damage is dealt to enemy ships. This is overall quite easy to asses.
The graph is pretty obvious: The smaller the missiles, the less they are relatively affected by PD. The 1 Damage/MSP assumption is just to scale the graph and is otherwise not important. If we only cared about the total damage dealt, and face some anti-missile defences , then we should only ever use the smallest possible missile sizes.
However, we care how this damage is distributed between enemy amour and internal hits. Large missiles have an advantage due to damage clustering, but exactly how large is this advantage? Well, to be honest the math is really yucki, so I decided to run a numerical computer simulation:
A simulation requires a target so I had a look around the ship-design section and thought what might be a “typical” ship in regards to the armour layout. I decided on a design 40 armour tiles wide, with 6 layers of armours. That’s about 10,000 t, with slightly more armour than I saw I most designs, on the basis that we might be slightly more interested in destroying heavily armed enemies. I have now let this ship be hit by a given number warheads with a given size and recorded how much damage was caused. And because there are statistical fluctuations I have done this 10,000 times for each set-up.
The graph shows the resulting probability distribution for internal hits, with a total of 144 WH, which is either delivered as 16 strength-9 hits, 36 strength-4 hits, or 144 strength-1 hits. You can see that the WH1-missiles bombardment causes an expected 4.6 points of internal damage, while larger warheads have a higher probability of causing more internal damage (and a low probability of causing smaller internal damage). Note that the “kinks” in the graphs are
not due to the finite sample size. One can let the situation run many times over and these do not materially change. Rather, these kinks are due to the way that multiple hits that are close to each other result in damage. In other words they are a part of the “real” probability distribution and not a sign of statistical weakness.
So larger warheads are better, but we knew that from the beginning. However, we can of course run the simulation with other set-ups as well. So we can use both effects at the same time and make a plot similar to the first one, but not with the total caused damage, but with the expected internal damage, given the remaining number of missiles and their respective warheads. As a simplifying assumption, we will consider every missile that penetrates the missile-defences as a “hit”, i.e. we assume that our missiles have a 100% hit chance.
And now we are talking. You can see that when the enemy has no capacity to destroy our missiles (0 on the x-axis), larger missiles are certainly better, as they are expected to cause more internal damage. However you can see that the blue line falls of much quicker than the other lines. At around 4 destroyed missiles, strength-9 and strength-4 missiles cause the same amount of internal damage (i.e. through 36-4=32 strength-4 explosions, vs. 16-4=12 strength-9 explosions).
Of course by comparing the blue and the red graphs we can nicely identify in what areas what missile size is better. Of course it depends on the target, and the total of launched WHs, but it still might be a nice pointer.
And there is a very interesting aspect when observing the green strength-6 warhead line. 6 is not a square number (unlike 4 and 9), and therefore has a slightly different damage profile. You can immediately see how inefficient this is! Even without any enemy missile defences, the advantage over a strength-4 warhead is minimal, and this small advantage erodes away very quickly. More importantly, a strength-6 warhead design is never optimal – either strength-9 is better, or strength-4 is better. And strength-6 is not even a good all-rounder. Strength-4 is much better suited to deal a good amount of damage across the entire spectrum. Note that the fact that the strength-6 warhead is not optimal anywhere is not only because it lies between the larger and the smaller number, but only because it’s a non-square number. If we plot the same graph with only square numbers you can see that every square-numbered WH size is optimal
somewhere. Initially, strength-16 is best, then strength-9, followed by strength-4, and finally strength-1.
So, if you take anything away from this its don’t use warheads that are not a square number. They are almost certainly worse than the closest a squared-numbered warhead.