March 31, 2024

Aurora - Beam PD Allocation and Weapons

First, a mea culpa. I misread the patch notes when putting the last post together, and it turns out that allocation is on a per-missile basis, not a per-salvo basis. This had surprisingly little impact on the overall number of leakers to be expected,1 but quickly led me down a rather interesting rabbit hole that conclusively resolved a long-running question.

Figuring out how to most efficiently allocate beam weapons to avoid overkill has long been an issue in Aurora, although often masked in my experience by gross overkill in available PD systems. Back in the VB6 days, each fire control would only target one salvo, so you needed lots of fire controls. For the pre-2.2 C# versions, this was per-weapon/turret, which was better, but still meant that sizing turrets took some thought. The current system gets rid of all that, but also gets rid of the ability to just make sure there are no leakers by having enough systems available, or at least makes that a lot less desirable as a solution.

After the last post went out, I started messing around with models of single-missile engagements, particularly seeing what happened as I investigated the tradeoff between rate of fire and chance to hit, and I got a very clear result. If you, say, replace full-size gauss guns with an equivalent HS of smaller gauss guns, you get worse performance against missiles without decoys. This is because even if the average number of expected hits stays the same, the increase in variability means you're failing to get even one hit more of the time, while the fact that there's only one missile means that you can't capture any overkill.2 This is particularly stark if the initial Ph is high, when the chance of a leaker might triple if you quadruple the number of shots.

Base Ph0.67
Base Shots3
Base Leaks3.59%
2x Leaks8.65%
4x Leaks11.08%
Base Ph0.34
Base Shots5
Base Leaks12.52%
2x Leaks15.52%
4x Leaks16.92%
Base Ph0.25
Base Shots10
Base Leaks5.63%
2x Leaks6.92%
4x Leaks7.57%

But this is all without decoys, and it turns out that decoys, because they offer the chance of capturing some of the overkill, can even the odds quite a bit. That said, even in the limit case, with enough decoys to absorb all of the overkill, the expected leaker percentage is exactly the same as it is for the full-Ph weapon. So even once we include decoys, you're never going to be worse off with a full-size turreted gauss gun over the alternatives.3

Base Ph0.67
Base Shots3
Base Leaks33.00%
2x Leaks37.05%
4x Leaks38.79%
Base Ph0.67
Base Shots5
Base Leaks8.42%
2x Leaks13.81%
4x Leaks15.97%

The basic conclusion of all this is pretty simple. The way that beam PD allocation is handled now means that it makes sense to prioritize getting the highest reasonable Ph for your weapons, because the higher variance you get when trading Ph for more shots generally works against you and will never benefit you on net. In a lot of ways, the new system has actually made ship design easier. Previously, picking beam PD layout was a matter of figuring out what the best option was to try and minimize overkill without making things too complicated (I suspect that this was a major and overlooked advantage to railgun PD in original C#), whereas now, full-size gauss guns are the way to go if at all possible.

1 It turns out that when I re-ran the numbers, the higher percentage of single-missile saloves with leakers was almost entirely balanced by cases where larger salvoes had multiple leakers, leaving total leaker numbers the same.

2 If this doesn't make sense, consider. I give you the option of flipping two quarters, or one quarter with two heads. If I offer to give you a dollar for every head, the two are equivalent in expected value. If I say "I'll give you a dollar if you get any heads", then the two-headed coin is clearly better because you get only one dollar for two heads, and have the possibility of zero dollars.

3 There are some obvious caveats to this, the biggest relevant to railguns being the assumption that the incoming missile is faster that the tracking speed for the gauss turret/FC, so the railgun is .25 the Ph of the gauss gun. If the missile is slower than that, the railgun is going to have an advantage.

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