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Developing New Gun Effectiveness Formula
 
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Do you guys like my formula?
Yes, its perfect
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No, the base values are better
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Yes, but there should be adjustments
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MiyabeEienNoZero

 

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Post subject: Developing New Gun Effectiveness Formula  Reply with quote   (Liked by:0)  Like this post
Hello, this is my first time posting and hopefully no one else has discussed this already.

For several months I've tinkered with various formulas to try to determine how a gun's effectiveness is calculated in War at Sea. At face value it seems the number of dice rolled is tied to gun caliber, ex: Yamato at Range 0 hits with 18 dice, and of course her main gun caliber is 18.1in. Nagato at Range 0 hits with 16 dice and her caliber is 16.1in. But I feel like this is far too much of a simplification. Take for example Kongo and Fuso. Both have a main battery caliber of 14inches, and this is reflected in their respective cards, but Kongo has a total of 8 guns vs Fuso's 12, meaning 50% greater output in theory. Yet Fuso only gets one more dice at range 3 than does Kongo (12 vs 11).

Therefore, I came up with a formula that hopefully gives a more accurate representation of gun performance. This comes with a major problem though, you will note that the dice rolls for ships like the Iowa and Yamato are higher than in the base game, which means armor will also have to be recalculated to take this into account.

The formula is this : No. of Guns x Penetration at Point Blank (in inches) / 15.

Penetration was calculated using this page http://www.navweaps.com/index_nathan/Penetration_index.htm
I simply averaged the penetration values against different armors at point blank to get my final number for each ship.

Using the Yamato, Nagato, Fuso, Kongo, Atago, Yukikaze, Iowa, North Carolina, Arizona, Nevada, Baltimore, and Fletcher as my controls, I calculated the theoretical new dice rolls for each ship.

I assumed the basic reload for battleships to be 2 rounds a minute, cruisers about 3-4 rounds a minute. No calculation of RoF is done for battleships, but for cruisers and destroyers the RoF is taken into account. Seeing as 2 rounds a minute is considered to be base value, then for a cruiser that fires 4 rounds a minute the determinant is x2, as it is twice the average fire rate of a battleship.

To balance the buff given for reload, I'm giving several ships an ability akin to "split fire" on Fuso. Atago for example, has a base value of 22 with my formula, so instead Atago rolls 11 but can roll two separate main gun attacks.

**I removed the old method of balancing high reload thanks to the issue being brought to my attention by some commentators, thank you for helping me discover a much more effective method of balancing this out!**

Armor penetration values are sadly missing for the 5in Type 3 gun that armed Japan's destroyers but can be assumed to be almost 6 inches based on the average penetration of the 5.5in/50 cal Mark 1 and 4.7in/45 cal Mark 1 .

Yamato = 22 dice (was 18)
Nagato = 18 dice (was 16)
Fuso = 14 dice (was 14)

Reading Fuso's card I discovered its "split fire" ability which allows it to re roll a main gunnery while losing 4 dice per attack. This is the one ship in this list that actually gets a slight nerf as it loses 6 dice per attack instead. Its base value is 22, so it can roll 2 attacks the first being 14 then the second being 8.
**Edit - Below I came up with a method of shifting dice to secondaries and instead using secondaries twice. I will likely do this with the Fuso instead of the current method.

Kongo = 15 dice (was 14)
Atago = 11 (was 10) As mentioned above, it can do a second main gunnery attack.
Yukikaze = 5 (was 5) Can re-roll its main gunnery attack with a 1 die penalty.

Iowa = 22 (was 18)
North Carolina = 20 (was 15)
Nevada = 16 (was 14) Explanation below for Nevada and Arizona
Arizona = 18 (was 15)

I'm having trouble trying to see how to balance Nevada and Arizona without the loss of any die. Clearly despite having 12x14 inch guns Arizona should not be nearly on par with Iowa.
I'm currently thinking of transferring 2 dice from the main gunnery and adding to the secondaries.

EG: Nevada will roll a 16 and the two missing dice will be added to the secondary gun value. The base value for secondaries on Nevada is 20. To reflect the fact that the secondaries are of course split on either side of a ship, the value of 20 is divided in 2. This leaves 10, plus the 2 extra dice for a total of 12. However, Nevada and now several other ships will receive "bristling with guns" which allows for 2 secondary attacks meaning no loss of dice.

Arizona will roll 18 but it has a base value of 21. That is a total of 3 dice left over. Arizona's base value for its secondaries would be 18 but as with Nevada I divide this by 2 for 9. The 3 left over dice are added totaling 12 and receiving "bristling with guns".

**Edit - I think this method is what I will stick with from here on out! The math works out pretty well I think!

Baltimore = 14 (was 10). Like Atago, Baltimore gets to reroll its main battery. The base value is 27, which divided by 2 is of course 13.5 which rounded up gives 14. Baltimore therefore gets to reroll with a penalty of 1 die, totaling 27 for range 0.
Fletcher = 7 (was 4) Fletcher gets to reroll its main gunnery attack with a 1 die penalty like Baltimore.

Using these ships as an example I feel like the power of many ships is better represented. Ships with 12 guns like the Nevada for example are comparable to the Nagato due to having a considerably more guns.

Rate of fire also favors heavy cruisers such as Atago and Baltimore. In the case of both the combination of a high rate of fire combined with fairly good penetration mean that they can match battleships like Kongo and Arizona. The effect is very noticeable on destroyers such as Fletcher, which despite having a much lower penetration value than their bigger cousins the incredible rate of fire allows these ships an ability to at least stand to ground with light cruisers.

Remember armor is not being taken into account here, and like mentioned earlier armor would have to be recalculated. The rate of fire of cruisers can at face value equal the fire power of a battleship but not the penetration ability. Baltimore might have a higher attack value than Kongo but the Kongo can theoretically take far more hits than can the Baltimore.

Of course I did the math for only a total of 10 ships, and have only calculated values of secondaries for 2 ships and have not even touched torpedoes but I would still love to hear anyone's opinions on this new attack calculation for primary guns!
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Last edited by MiyabeEienNoZero on Mon Aug 01, 2016 5:23 am; edited 2 times in total
PostWed Jul 20, 2016 2:22 am
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ticat1

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Great research!  And a helluva great first post! Welcome to the forum!

How do you think the new Gunnery stars will interact with the current armour values?  Would those need to be adjusted well?
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PostWed Jul 20, 2016 3:19 am
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MiyabeEienNoZero

 

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ticat1 wrote:
Great research!  And a helluva great first post! Welcome to the forum!

How do you think the new Gunnery stars will interact with the current armour values?  Would those need to be adjusted well?
Yes, armor would have to be readjusted. As I mention a few times, an issue comes up with these new values. Attack is inflated with almost every ship, which means if armor remains unchanged then many ships will suddenly be lacking in armor.

I want the opinion of a few more people on my gunnery calculations first however before I begin coming up with any formulas for armor. But I can think of a basic principle based on the thickness of a ship's armor in inches with a modifier for quality of armor.

Allied armor tended to be of a better quality, especially towards the end of the war, so a Japanese ship with 14 inches of armor might not necessarily have the same protection of, say, an English ship with the same thickness of armor.

I plan to also take into account plunging fire. Yes, hull armor might offer more protection at further distances as shells lose velocity while travelling, but as most people know, ships engaging at long range find it difficult to get shots into a ship's hull due to a shell's arc.

I want to include this to hopefully make long range engagements more interesting as you play a gamble of having better basic protection while also exposing your deck armor.
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PostWed Jul 20, 2016 3:37 am
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LcdrSwizzle

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You are making this much harder than this game needs. I don't know if you have experience with other, more detailed WWII Naval games, and offer that you spend time with those rules to better understand the effects of changes.

Have you downloaded Hap's spreadsheet and studied the gunnery tables? It will help you better understand the dynamics.

Also, not all 14" guns are alike, nor all 16" guns, etc.

The German 15" gun was the best 15" of the war, based on range, dispersion, rate of fire and penetration.

The American 16" on the Iowas was the best of the war, based on the same 3 factors, and it was also the heaviest 16" shell.

The American 5/38 was the best DP gun of the war.

The Japanese 6.1" may have been the best of the war.

Some of the differences you will have to ignore, because they won't matter.

Armor quality for the Allies? Um ... that's a very general statement and not sure I agree.

Oh, without armor adjustments your gunnery adjustments can't really be discussed because it the "effect" that matters, not the technique.

Will gladly discuss by phone or pm.
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PostWed Jul 20, 2016 9:37 am
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MiyabeEienNoZero

 

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I decided to go ahead and make a "card" for the Yamato. Thanks to Swizzle I was directed to a dice probability chart. This allowed me to scale armor relative to the new dice rolls.

Yamato 77
Ship – Battleship 1945
Speed – 2  Flag – 2
Attack 0 1 2 3
M 21 21 19 17
2nd 10 9 8 6
AA 8 - - -
ARMOR:12   VITAL ARMOR:18    HULL POINTS:6

Bristling with Guns – This unit can make
two Secondary Gunnery attacks against
separate targets during your Surface Attack
phase.
Extended Range 6 – While undamaged, this
unit can make range-6 Main Gunnery Attacks
using its range-3 attack value.
Torpedo Defense 2 – Roll a dice. Each
torpedo hit rolled against this unit deals
1 less point of hull damage. If you roll a
6 however, you take no damage.

You will notice Yamato no longer has tertiary guns. For this new rule set I intend to remove tertiary guns from most ships. Yamato loses her tertiary guns as her Type 89 12.7cm guns were not anti-ship. Yamato only had 6 x 6.1 inch guns as her secondary anti-ship armament. However, Yamato does attain "Bristling with guns" to make up for her loss.

The cost of Yamato has also gone up reflecting her new abilities of extended range 6 (based on the 18.1 inch guns' effective range, not maximum range) and the new "torpedo defense 2" to further emphasize the resilience of this ship. Only a number of ships will benefit from this new ability including the Iowa and Montana class.

Cost is calculated by adding the sum of the main gunnery attacks to range 3, in Yamato's case totalling 78, then subtracting by the number of hull points, in this case 6 totalling 72, then adding 1 point per special ability for a total of 77 up from the original 70 point cost.
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PostSun Jul 31, 2016 9:08 am
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Syzmo

 

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Why does Arizona have a lower gunnery value than Nevada and Fuso when all have the same 14 inchers? She has two more barrels than Nevada but throws 4 less dice and has the same amount as Fuso but in a more advantageous layout yet she throws 2 less?
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PostSun Jul 31, 2016 1:09 pm
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I like where you are going with this.  Yes it makes the game more complex and that's all fun and stuff.  I however am having a harder time dealing with guns newer and larger than the 14" on New York and Kongo.  I have my game World of Warships and it has its own table of guns and armor value, but I may be off too on those. would you be able to guide me as to how you came up with your stats on the Nevada (my next ship is the New Mexico and Fuso)
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PostSun Jul 31, 2016 2:00 pm
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MiyabeEienNoZero

 

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bunyan wrote:
I like where you are going with this.  Yes it makes the game more complex and that's all fun and stuff.  I however am having a harder time dealing with guns newer and larger than the 14" on New York and Kongo.  I have my game World of Warships and it has its own table of guns and armor value, but I may be off too on those. would you be able to guide me as to how you came up with your stats on the Nevada (my next ship is the New Mexico and Fuso)


In response to you and the fellow above, I have absolutely no idea how I got those numbers XD I think I actually switched the values for the Pennsylvania class and Nevada at some point.

Just for the sake of having you guys correct my math if I mess up again I'll calculate the values for both ships right now.

Both Arizona and Nevada had 14"/50 caliber guns. After adding in more averages for various shell types using the same resources as in my first post I came to a value of 30.55" of penetration. However, their reload rate was on average 1.75 rounds per minute. This means I invoke a new variable to reflect this, 1.75/2 or .875.

Indeed, I am going back to rework cruisers and destroyers and use an ability like "split fire" mentioned below to reflect their actual reload rate to not eliminate the RoF buff I mentioned earlier. A quick example will be Atago. Attack will change to 12 with a second main gunnery attack rolling 2 dice less.

Its attack would look like this therefore
M - 12  12  10  8
"Split fire" 10  10  8  6

I'll calculate Nevada first - 10 x 30.55 x .875 =267.3
267.3/15  =  18 dice

Arizona = 21 dice.

Now these values I'm sure make more sense XD. As with Fuso however I have to do some changes to reflect the number of guns. It should be common sense that Arizona did not have near identical power to the Yamato.

Unfortunately I'm getting ready to head out, to visit the USS Iowa ironically enough. I'll get back to everyone after my rather fitting adventure!
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PostSun Jul 31, 2016 5:29 pm
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Have you ever played War Thunder?

Not a criticism.

Smile
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PostSun Jul 31, 2016 6:19 pm
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MiyabeEienNoZero

 

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ticat1 wrote:
Have you ever played War Thunder?

Not a criticism.

Smile


I have played it for several years now. However I slowly started getting more and more frustrated with it. I still play every once in a while but not for very long sessions.
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PostMon Aug 01, 2016 4:30 am
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MiyabeEienNoZero

 

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I went ahead and came up with the stats for all the classes of battleship and heavy cruiser available to Japan in this game (not counting the forumini expansions). You will notice some very interesting changes to the cruisers. On top of all of them getting the new ability "fast reload", long lance torpedoes  have been reworked completely. Now they are deadlier than ever, both to their opponent and owner! Long lances can now be fired up to a range 4 but if you have bad luck you can actually receive damage yourself, reflecting the danger of oxygen torpedoes.



























[/i]
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Last edited by MiyabeEienNoZero on Fri Aug 05, 2016 2:16 am; edited 2 times in total
PostMon Aug 01, 2016 7:44 am
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As I keep working I keep finding new things to improve!

For one, speed of ships is going to be slightly more accurate. Ships with a speed of between 28 and 32 knots will remain unchanged. Ships however moving between 26 and 28 knots will receive Slow 1, which is the same penalty as there already is in the game. Ships moving between 24 and 26 knots will receive Slow 2, which instead of giving -1 speed on a roll of 1 or less, is given on a roll of 2 or less. Ships moving between 22 and 24 knots will receive  Slow 3, which gives -1 speed on a roll of 3 or less.

Armor protection, while already being revamped due to the higher gunnery values across the board, will also be a determination of what SAs a ship has. If you look at my cards you will notice Yamato has Torpedo Protection 2, and all of the cruisers  have Tough Cruiser. Originally I planned to base this simply on whether a battleship would be considered a super-battleship and whether a cruiser was heavy or light. Now, I've come up with a more realistic solution. Ships with an armor belt of at least 14 inches will receive Torpedo Protection 2. Ships with an armor belt of between 12 and 14 inches will receive Torpedo Protection 1.

Ships with an armor belt of between 8 and 12 inches will receive Battlecruiser - which is a new SA that provides +1 armor against gunnery attacks from destroyers and cruisers.

Ships with an armor belt of between 6 and 8 inches will receive Tough Cruiser, the already available SA which provides +1 armor against gunnery attacks from destroyers and fighters.

Ships with an armor belt less than 6 inches will receive no SA.

I understand that this might all seem too much work for War at Sea, but my intention has been to create a more realistic game without jumping to the complexity of games such as GHQ's "Micronauts" rules. In summary I want to add a few more details of realism without the game being overwhelming and losing its casual feel.
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PostWed Aug 03, 2016 12:19 am
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Why do they all have tough cruiser 1?
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PostThu Aug 04, 2016 1:34 pm
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MiyabeEienNoZero

 

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Ryan Da Great wrote:
Why do they all have tough cruiser 1?
Yes, as I mentioned in my most recent post, I went ahead and changed how certain SA's are determined. I wrote up the cards before coming up with the new system, and am currently replacing all of the cards with the current SAs.
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PostFri Aug 05, 2016 12:49 am
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@MiyabeEienNoZero:
You may want to summarize this thread and post it in the other forum so that the discussion can continue.


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