Research on the Target Ship Size modifier

[Evil4Zerggin]

I decided to try to determine the formula for the Target Ship Size modifier to accuracy. 

Methodology

• This was done in Alpha 3. Things could change in Alpha 4.
• In 1890, all TBs are exactly 200 tons. Thus I could repeatedly use this to factor out the effect of displacement.
• I looked at several Target Ship Size modifiers for enemy TBs randomly generated in custom battles and compared them to Target Signatures computed from their components.
• I found that the chance to hit them was proportional to (100% + 1.75% * Target Signature), which matches the Ship Detectability modifier in the designer exactly. Another way of putting it is that a ship's chance to be hit is proportional to (1 + Target Signature / 57.1).
• Then I compared ships of several displacements, including two CLs and a BB, divided out the Target Signature factor, and found that the remaining trend was perfectly linear. Specifically, the base chance to be hit is about 14.4% + 1.54% per thousand tons displacement. Another way of putting it is that a ship's chance to be hit is proportional to (1 + displacement / 9350 tons).

Result

The multiplier for a ship's chance to be hit from Target Ship Size modifier is approximately (1 + displacement / 9350 tons) * (1 + Target Signature / 57.1) * 14.4%.

Implications

• For small ships, Target Signature doesn't matter too much because that factor will be dominated by the constant 57.1. Going from 15 to 25 Target Signature makes you only 14% easier to hit.  On the other hand, large BBs can reach hundreds of Target Signature, and in these cases Target Signature is much more important---going from 150 to 250 Target Signature makes you nearly 50% easier to hit.
• Likewise, for small ships displacement doesn't matter that much. A 600 ton TB is only 3.1% easier to hit than a 300 ton TB for equal Target Signature. And again, it matters more for large ships; a 60 000 ton BB is 76% easier to hit than a 30 000 ton BB.

Commentary

• If we figure that ships scale up uniformly in all three dimensions with displacement and that chance to be hit is proportional to surface area, this would rather imply a baseline chance to be hit proportional to displacement in tons^(2/3). I think this is a more realistic starting point. If desired, you could again add an offset in order to simulate near-misses and make TBs a little less hard to hit. Still, the current displacement modifier seems at least serviceable. 
• The effect of Target Signature on chance to be hit seems far too dramatic to me. I would not expect the main battery configuration to make such a dramatic difference in the difficulty of getting a fire solution on a ship; while turrets are large, they are also relatively low to the deck and potentially moving around; I would probably prefer to point my rangefinder at a nice, tall mast instead. Perhaps make this modifier based on the towers only, or nix it entirely. With the current Target Signature mechanics I would expect every player BB to end up like Richelieu in order to maximize firepower-per-Target Signature.

Edited February 9, 2020 by Evil4Zerggin

[arkhangelsk]

1 hour ago, Evil4Zerggin said:

Result

The multiplier for a ship's chance to be hit from Target Ship Size modifier is approximately (displacement in tons + 9350) * (Target Signature + 57.1) / 3.71e6. Multiply by 100 for percent.

Interesting. I have noticed that when the ship is about 15000 tons generally the modifier is close to zero, so if a typical target signature is about 100 with a cruiser, this should be correct. As for player BBs ending up like Richelieu, don't forget that even now the triple penalty is applied quite heavily, so a triple is worth less than 2 singles. A quadruple if it ever shows up will be penalized more heavily.

[Evil4Zerggin]

1 hour ago, arkhangelsk said:

even now the triple penalty is applied quite heavily, so a triple is worth less than 2 singles

In terms of raw firepower, absolutely. It looks like at early tech (1915) triples suffer -20% accuracy, and at end tech -5%. Due to how modifiers stack triples also have less proportional benefit from autoloading than singles---autoloading also being heavily favored by the Target Signature mechanics since it allows you to greatly increase your ratio of firepower-to-Target Signature. Finally, it could be argued that more turrets mean less firepower lost if hit, though I'm unsure how turret hit points work in this game.

However, 2 singles have nearly double the Target Signature of a triple---more than double, if you consider that you could use the saved deck space to replace at least one pair of wing secondaries with a single centerline secondary. For example, 4 single 18" versus 2 triple 18" will increase your Target Signature by 80. Even considering the other sources of Target Signature, that's a huge percentage.  Fewer turrets also means a greater proportion of firepower on your favorite arcs.

As for quads, it's a fair point that we can only speculate on their stats. If it's something like -40% accuracy then maybe I'll stick to doubles or triples. If it's -10% then I'm putting quads on everything without a second thought. I suppose I'm used to the (quite generous) implementation in Rule the Waves.

Edited February 3, 2020 by Evil4Zerggin

[Evil4Zerggin]

It looks like this did indeed change dramatically in Alpha 4. Target Signature values of components, modifier per Target Signature, and base chance to be hit all changed. Small ships seem to be a lot easier to hit than previously.

May do more detailed testing later, but it looks like the Target Signature meta is no more.

[Evil4Zerggin]

Okay, new equation seems to be approximately:

(1 + displacement / 26500 tons) * (1 + min(Target Signature, 200) / 238) * 74%

In addition, the Target Signature of many components was changed. Probably the most significant is that there used to be a large increase in Target Signature for guns above 8", but now larger guns have a more smooth increase.

The Target Signature divider increased from 57.1 to 238, as a result of the Ship Detectability modifier decreasing from 1.75% per point of Target Signature to 0.42%, more than a 4x drop. I'm not sure if there was a cap before, but in any case now Target Signature stops increasing Ship Detectability at 200 Target Signature / +84% Ship Detectability. The upshot is that the effect of Target Signature on chance to be hit has dropped greatly. Going from 100 to 200 Target Signature only makes you 30% easier to hit, and the effect is even smaller for light ships. So now I would consider Target Signature only a side consideration when designing ships. This is a relative boost to:

• Single-gun turrets over triple turrets
• Turret farms
• Funnel farms
• Torpedo farms
• Standard loading rather than autoloading
• Bonus options other than Firepower

The displacement divider also increased, from 9350 to 26500 tons. 

Finally, the minimum chance to be hit (i.e. for a theoretical 0-displacement, 0-Target Signature target) increased from 14.4% to about 74%---about a five-fold increase. This makes it much harder for light torpedo ships to close before being hit (although the apparently stronger Target Speed modifier could help with this).

Conclusions

• Light ships took a huge loss due to being proportionally much easier to hit than in Alpha 3.
• Turret farms are back on the menu.

Edited February 9, 2020 by Evil4Zerggin