Gun Effectiveness Analysis

[dbs1701]

How exactly do you choose which guns are the best to use? This is probably one of the first things you think about when starting your design! This will be a pretty long post, but I've spent a couple of days (slowly) gathering the data and darn it if I'm not going to share! If this has already been done, my apologies! I'm going to split this into a few parts on this post, so feel free to jump around. 

CONTENTS:

1. What are the stats that affect gun effectiveness?
2. Which of those are the best guide for a designer?
3. How can one test this?
4. Conclusions and Suggestions for Game Improvement
5. Further Research or Information needed

PART 1: Elements of gun effectiveness

I am neither a programmer, a mathematician, or a developer, or even a particularly skilled player in terms of datamining or minmaxing stats. However, there are some interesting coincidences and game design elements that made me want to crunch some numbers and do a few tests! First, it is boring game design to just make the biggest guns the best, or the most guns the best. So is there a "sweet spot" where, all things being equal, you should start a new build? On the flip side, as a game with so many scenarios and possibilities, if you have an obvious "sweet spot" that is objectively the best way to build, you lose a lot of creativity in the designer as the player thinks they MUST do certain things! I will argue in this post that, yes, there is a sweet spot, and also, yes, there is an element of maximizing is better, but also there is a remarkable flexibility, so you won't be failing too much if you get this wrong, either! I would say overall this is pretty well set up. With that out of the way, here we go!

1. Accuracy: Obviously, we want the ships we shoot at to kindly sink or explode or not shoot at us anymore, so one would think accuracy is the most important thing. It is certainly important, but focusing on it exclusively is not ideal either and leads to some...weird builds (see videos of players maxing kill rate with single 18" guns for example. This will be debunked in this analysis). There are two caveats to this number:
   • Note that in the game, accuracy is percent of shots that are on target at a given range BEFORE bonuses are added. You can see changes to BASE accuracy if you add equipment like towers, but weather, speed, aiming progress, and other bonuses won't show up on the gun info screen.
   • It is given per single shell. So when you look at the penalty of using triple or quadruple mounts, you aren't getting a less accurate weapon overall, it's just each individual shell will scatter more. The real question is does the extra shell downrange make up for the loss in accuracy?
2. Rate of Fire: This is the other interesting one, and the same caveats apply. We want to send as much explosives down range as quickly as possible to make the red ships go away, preferably in spectacular explosions. Rate of fire isn't really affected (yet) by in-battle conditions as far as I can tell, so what you see after applying your technologies and mods is what you are going to get.
   • Note that once again, the reload time is per barrel. So even though a dual turret might reload in 30 seconds and a triple might reload in 35 seconds, the dual turret is firing at 4 shells per minute (2 barrels x 2 rounds per minute), while the "slower" triple turret is firing a bit over 5 shells per minute (3 barrels x 1.71/min) This analysis is thus going to focus on how rate of fire, barrel number, and accuracy come together to create guidance for you beleaguered designers!
3. Penetration: This is a very interesting one. Generally bigger is better, but knowing when and where "plunging fire" happens is important. I haven't looked into this yet, and remember that while penetration is based on range (how much horizontal armor vs how much vertical armor it will defeat), the armor schemes in game are a bit convoluted and as I said, I'm not a dataminer! Penetration is the MOST affected by little things like range and angle of armor, so it's quite difficult to explore without tightly controlled experiments or digging around in the code. It does apply, and I'll explain at the end, but for now we'll leave it behind.
4. Damage Dealt: This is assuming a full penetration. Partial pens and fires do not count here for this number. It is affected by shell weight and technologies as well, and those numbers do pop up on the information card.
5. Modifiers: Towers, Propellant (Explosives), and Shell Weight all affect the gun barrels stats. Aiming time is affected by towers, turret techs, and reloading buffs, but once the guns are dialed in, the shells will hit with the same accuracy, penetration, and damage. Therefore, I'm not too concerned about aiming time here.
   • Note that things like aiming time, 3 and 4-barrel accuracy and reload penalties are applied EQUALLY regardless of gun size. So all we're interested in here to choose your gun type and layout is really just accuracy vs. rate of fire. The rest will make it better or worse, but it won't change you your gun decisions stack up against each other, all things being equal

Picture Break! (figure 1.1)

!

Here we see a graph of the 9" mk 5 gun in terms of accuracy and penetration. Note how quickly accuracy really falls off. Finding the best range to fight at depends on how well the penetration values match up with actually being able to hit anything. Note that larger weapons (15"+) actually do reach a point where the vertical pen will exceed horizontal penetration. If you aren't clear about what "plunging fire is", that's what it is. The tables also might help you determine how much deck armor your ship will need.

 

PART 2: Which Elements should figure into weapon choice?

As we've seen, there are so many possibilities, and the developers have really done a great job of making them all viable. But, how can you tell if some are "more viable" than others? What is the "best" design? 

First, let's focus on accuracy, rate of fire, and equipment. Spoiler alert: All things being equal, there is a best gun to use and a best turret size. However, most will work well. So you want to get the best firepower you can before you start to make compromises on rate of fire or barrel number. Triples are indeed better than duals, so if you can fit triples up to 16", but need to switch to duals to fit 17" on your ship, better to stick with the triple 16's! The same goes for auto reloading. If you can fit auto reloading on 15" turrets but can't on 16" turrets, stick with the ones you can get auto reloaders for. The "Why" gets a bit interesting, and here is our experiment!

Because some equipment works across all gun sizes, to control for that we'll need to ensure that our test ship will have the same equipment fit regardless of weapon choices. If you were to look at French triple turrets, with no modifiers (no tower installed, no auto reloading, same propellant), and compare the accuracy across all ranges, you end up with a chart that looks like this:

(Figure 2.1)

Accuracy for main battery weapons from point blank to 25,000 yds. Note that to spread out the results at effective battle ranges, we are looking at a logarithmic scale for the vertical axis. Takeaways: "Mk" number may refer to an in-battle bonus, it does NOT affect accuracy on the info card. You can see that the smaller guns run out of range before reaching 25Kyds, while some have better accuracy at longer ranges.

You can see there is actually quite a lot of variance, but some weapons are clearly more accurate than others. I was surprised to be honest that there wasn't more "grouping" between the different patterns (ex. all Mk 4's ALL being better than the Mk. 3's; which does not actually happen - more datamining required; is this the "guns grade" bonus in game?). I also expected to see each weapon have a point where it's accuracy was better than others. This does not seem to be happening, so the idea of building around a SPECIFIC range seems to be out the window. There are obviously differences between close and long range weapons, though!

However, this is only HALF of the story. The other thing that matters is how quickly shells are sent downrange. The more shots you can take, the sooner you will score a hit, especially at longer ranges. So, I plugged the accuracy percentage into a "drop calculator" (because I don't math) to figure out how many shots must be taken to guarantee a hit (I call 99% a guaranteed hit for these charts, by the way - the math holds for lower thresholds too, so it doesn't matter here). So I plugged in the number of shots needed, divided by the rate of fire (remembering these are all triple turrets) to come up with "effective" accuracy. That number, to me, is how long you can expect to fire at a target at a given range to guarantee a hit. Basically, If you have half the accuracy, but twice the rate of fire, you are still going to score hits at the same rate.

And here it is! (figure 2.2)

This is the TIME taken to reach 99% chance of a hit for each gun size, using triple turrets. IMPORTANT - lower is better here, because more time taken is bad. This is to GUARANTEE a hit, not "get lucky". Of course you will score hits sooner on average, but your second hit might take a while. This does NOT count ladder aiming or radar aiming progress, target lock, etc. This is ONLY the stock guns with the same equipment. Imagine a turret on a firing range with no technology to assist the aiming. 

Notice that the time taken really flares up beyond 15KYD. This is basically the inverse of your accuracy curve. As long as your armor can take it, you need to get within a certain range to be hitting ships consistently. We all know this already, but it's kind of neat to see on a graph in real time!

As a Log chart, we can expand the closer range and actually see what's happening here: (figure 2.3)

This is the TIME taken to reach 99% chance of a hit for each gun size, using triple turrets. The log scale opens up the closer ranges so you can see that some weapons are consistently "better" at scoring hits over some ranges. Again, lower lines are better, because the less time taken to get hits the more damage you'll be dealing!

So, we can start to see some winners here. Notice that the 12" gun in INCREDIBLE at getting shots on target inside of 10KYDs. At greater ranges, you see that the 9" gun takes over, until it runs out of reach, anyway! The problem, is how much damage are you doing to your targets with such light shells? If you want to look at the "heavy" weapons, you can draw conclusions as well: Note that the 13" and 15" guns are very similar. You are going to get a similar number of hits over time (at closer ranges, the 13" is a little better, at longer ranges, the 15" is slightly better) However, the 15" shell is going to hit a lot harder. Interestingly, the 14" gun is consistently worse than both! There is also a "Pack" of guns around 15KYDs. 14", 16", 17", 18", 19", and 20" are all getting hits at about the same rate. So at that range, bigger really is better. 

BUT - all things being equal, and assuming all shots can do damage, you can still see the 9", 12", 13" and 15" guns ahead of the pack. Against small ships, the light guns seem to indeed be better. Against medium ships, 15" is looking like the best balance of accuracy and hitting power. Against the big baddies, heavier is probably better, as long as you can control the range (and SURVIVE at 15K Yards!)

 

PART 3: Testing Time!

I was inspired by the YouTube "Taskmaster" challenges where various gamers tried to kill 10 early battleships as quickly as possible. I've done two levels of test here, so I'll share both. The first test was whether or not the accuracy and reload penalty of more barrels offset the increased fire. My thesis was that more barrels is still going to be faster, even if the guns are less accurate and slower firing. To test, we used the same 5 Turret "Test Hull" (see figure 3.1) with 18" guns, changing only the number of barrels per turret. We used 1940 tech, vs. ten 1900 BB starting at 20,000 Yds. The results were pretty compelling!

 

(Table 1:)

This was my first test, it is not as controlled as the following test and just gives a rough estimate. The results were consistent however, demonstrating the concept that even though larger turrets have reduced rate of fire and accuracy, the extra barrels more than make up for it.

First, against such weak targets, the time to get the first kill was pretty much tied to getting the first hits. I was surprised at how similar the times for that were. The guns do dial in much more quickly (and much more consistently) than my "Effective Accuracy" table would predict. True, we were using the same guns, but the rate of fire was going up very consistently, which WAS reflected in the total time, but was NOT reflected in the first kill time. This suggests a bit of a tweak to the code as far as getting that first hit, maybe there is a little bonus to ensure a quick hit that disappears after that first hit. More research!)

So, if you can afford them, quad barrels are best! However, what about different gun sizes? That was the point of the first bit of analysis, anyway? Well, glad you asked! Here we go for the "BIG TEST"

The Test Ship (Figure 3.1)

The specific stats don't really matter. This is the gun layout all of the test ships for both the preceding and succeeding tests are used. The tonnage was always maxed out (to fit the largest turrets) but armor was changed to allow them to fit.

We always used a 125,000 ton hull so that we could fit quad 18's (and eventually quad 20's) for the purposes of the test. To get the biggest guns, we limited to speed to 25 knots, and cut the armor as much as needed to do so. We always used the same towers, the same explosives (TNT) and standard reloading. Because we know that quad turrets are fastest at getting the kills in this scenario, we only changed the size of the guns - 14", 15", 16", 17", 18", 19", 20". (smaller guns do not allow quads). Because the variance between what the AI builds, RNG, and different starting angles makes a big difference, we ran several tests per weapon loadout. We looked at: Time for first kill, Time to complete mission, and Time from time of first kill to the end ("effective time")

 

Table 2:

Note: The 14" was predicted to perform poorly in the stat analysis above, and after two tests it was clear that that was in fact borne out, so I did not complete the third test.

Looking at this data, I believe the predictions based on the graph of effective accuracy were borne out in the results. As expected from the predictions based on data, the 15 inch gun stands out as the most effectively accurate of the heavy weapons, the 14" is noticeably worse, and at moderate ranges the other heavy weapons are remarkably consistent (but still worse). The 19 and 20-inch guns seemed to overperform, considering that although their raw accuracy is indeed the best, their effective accuracy is hurt by their slow rate of fire and they are EXPECTED to line up with the 16-18" guns in terms of effectiveness. 

My theory is that there is a hidden buff to early "rangefinding" accuracy to get players hits sooner than mathematically should be happening, which then disappears after the aiming process is complete. The 19" and 20" weapons will basically one-shot a 1900 BB, so those "lucky" first salvoes are more effective than would otherwise be expected. It is also important to note that at a range of 15KYD, we should expect the TIMING of hits to be relatively consistent, so the very largest weapons are just showing the point at which the heavier shell does in fact start to overwhelm the other stats! It is also important to note for rangefinding purposes, we are sending 20-shell salvoes downrange, so there is an awful lot of "stuff" to throw at the wall. When some of it invariably sticks, those heavy guns pack a whallop!

 

PART 4: Conclusions and Suggestions

Based on these tests, a few things emerge. Firstly, how effective your fire is depends a lot on the range of engagements. If you get to around 15KYDs, you will find that the heavy guns all perform relatively consistently with each other. If you get closer, accuracy improves a lot over all weapons, and your first hits will be devastating. Also, at the closer ranges, the rate of fire really will make a difference especially if you are crippling targets every salvo. Because penalties for 3- or 4-gun turrets apply to reloading and accuracy, it is fair to ask if they are worth it. As of this patch, they are very much so. The extra shells going downrange compensate for the lower accuracy and rate of fire. It is clear that the more guns in a turret, the better! We also see that unless you are needing very heavy weapons, 15" guns work just fine at least against weaker targets.

My personal conclusion: The quadruple 15" gun is probably the sweet spot for me. Against similar class vessels or less, it is probably the best overall weapon in the game. I would only use heavier weapons if I know I am facing modern or super battleships. 

This leads to a few design principles commanders might consider:

1. For a given number of turrets, the more guns in a turret the better.
   • If you can substitute triples or quads without having to sacrifice a turret, do.
   • If you are limited by weight or costs, consider how you can get the most barrels possible.
2. Invest in technologies to boost rate of fire and accuracy. RoF makes a HUGE difference. If you can invest in autoloaders, do so. 
   • I didn't include it here in a table, but I took out my test ship with a full 15" accuracy and ROF, and it brought down the engagement time to consistently around 20 minutes, with one run having just 16 minutes between the first hits and the last kill. Those boosts in rate of fire directly translate to expected time to sink targets.
3. Assuming your shells can damage the target, and assuming all other things being equal, the 15" gun is the most effective, barrel for barrel.
   • BATTLECRUISER DESIGNERS: This is a HUGE takeaway for you. Since you SHOULDN'T be engaging heavy enemies, based on this, you should probably go no larger than 15" guns. You will get more bang for your buck and slightly less dangerous shells lying around.
   • If you are going more for a "super cruiser", the stats suggest that 12" guns may be best, at least on paper, out of the triple-only mounts.
4. If you need to go for heavier weapons, it won't make the biggest difference as long as you can maximize the technologies. If you can get better tech or more barrels on, say 17" guns but have to sacrifice to get 18"'s, it's better to stay with the biggest weapon you can "max out".

Suggestions for Developers:

1. Based on this study, it seems that gun size balances VERY WELL with rate of fire and accuracy. As long as we choose weapons that are effective against the expected targets, there isn't a "right" or "wrong" answer as long as we consider the applicable elements.
2. Revise how quad turrets are selected for or are possible in designs. The way the stats work right now, all things being equal, quadruple turrets are ALWAYS the best as long as they can fit and be afforded. This probably is something that needs to be addressed because we see in reality only three battleship classes ever used them, (with a few more designed and not laid down) while the vast majority of battleships used dual or triple turrets. 
   • Perhaps the weight penalty should be reexamined, so that you could fit a quad turret to replace two smaller turrets but could not fit two quad turrets in a similar area.
   • Perhaps also turret and hull size should be considered - where guns larger than 16" simply cannot fit in a quadruple turret on anything short of the super battleship hull. That is, unlock different turrets based on hull. I would prefer something like this:
     • Battlecruisers/Super Cruisers: 12/4, 13/4, 14/4, 15/3, 16/2, 17/2, 18/1, 19 or 20 can't fit at all
     • Small/Medium Battleships: 12/4, 13/4, 14/4, 15/4, 16/3, 17/3, 18/2, 19/2, 20/2
     • Modern Battleships: 12/4, 13/4, 14/4, 15/4, 16/4, 17/3, 18/3, 19/2, 20/2
     • Super Battleships under 100K: all quads possible except 19/3 and 20/3
     • Super Battleships over 100K: all quads possible.
   • By the way, quads of all main guns should be possible all the way down to 9".

 

PART 5: Further Research, datamining, and Study:

1. I would love to know how initial accuracy is figured out. It seems that ships consistently get their first hit much earlier than expected, especially on the larger guns where it should take vastly longer time to get that first hit (considering the increased time between salvoes). Is it always a hit on Salvo #2, 3, or 4 and an RNG decides which it will be?
   • If such a system exists, what happens after the first hit? Once the first hit is achieved, performance approaches what is expected for gun size and range.
2. Based on the evidence suggesting that more barrels is better with the same techs, I have not compared, say, quad 15" guns to triple 16" guns. 
3. The penetration vs accuracy over range curves would be interesting to plot or see for all weapons.
4. This has not been done on secondary weapons either.
5. This study has only worked with French pattern guns. How are other nations different?

 

If you made it this far, Cheers! Happy Sailing, please let me know if this borne out or if I am barking up the wrong tree!

-dbs1701

 

 

Edited January 31, 2021 by dbs1701

[SPANISH_AVENGER]

Nice post, great analysis and info! I agree that the 15 inch guns are underrated, most definetly.

[Drenzul]

Just ran into this. 

One minor bit in your conclusion you left out.
While a 4x is always better than a 2x in a out and out comparison.... with the 2x you'd have nearly 50% more weight spare.

So take a mega BB armed with 4x4 20" vs 4x2 20", the later has around 13,000t worth of extra armour e.t.c. as well as more accurate weapons and a greater rate of fire.
Even on the biggest ships that 13,000t is 10% difference in the weight of the ship.

Or 4x4 20" vs 8x2 20". The later has a higher rate of fire and accuracy for a extra 800t approx... only problem is getting all those turrets on one ship  

IMHO Twins are the sweet spot unless you need more barrels than you can fit with twins, then 3x/4x  are perfectly viable.

Would be interesting to compare similar weight turrets of different sizes and barrel arrangements, like 2x20" vs 4x 17".

[Littorio]

Very interesting indeed. I will have to consider this info in my designs.