Fr05ty's emporium of formulas and implementation knowledge, reborn

[disa_destroyer]

Hello, I'm disa_destroyer, a slightly above average player from ASIA who always wants to learn more about the game. I recently stumbled across Fr0sty's thread on the NA forums detailing many formulae that he derived from for the game, as well as additional knowledge on other mechanics. https://forum.worldofwarships.com/topic/241266-fr05tys-emporium-of-formulas-and-implementation-knowledge/ However, with the old forums being completely shut down by the end of this month and none of the formulae found being anywhere else. I've decided to try and preserve them by posting them here. The original credit goes entirely to Fr0sty for deriving the formulae, they have proved very useful for seeing how they affect the game.

 Fr0sty derived formulas for pretty much everything that makes a ship tick in World of Warships, except for detectability and fire range (though I can tell you what's meant to affect them). Throughout this post I'm going to try and explain how everything from a ship is calculated, the formulas for it and generally provide what knowledge I have for translating real-life ships into World of Warships numbers. Let's begin!

DISCLAIMER: Fr0sty wrote the general formulas and values that most ships conform to, in many cases you will find disparities with in-game values which often mean that WG has fiddled with values for some reason or another (national flavours often result in these things). After I explain how to calculate "generic ships", I will write down what Fr0sty knew about these modifications so you can apply them to ships you propose for those lines.

NOTE: All calculations use kg, m/s or metric tons.

HITPOINTS

Spoiler

The hitpoint pool for a ship is defined in most cases by just 2 variables: the ship's class & its displacement (use standard displacement for A hulls and full load displacement for upgraded hulls and premiums). Aircraft carriers are the only class that also use their tier to determine their hitpoint pool. Use displacement (dt) in metric tons for these calculations for better accuracy.

BATTLESHIPS: 10,470 + (displacement X 1.19)

SUPERCRUISERS: 11,900 + (displacement X 1.43)

CRUISERS: 9,565 + (displacement X 1.91)

DESTROYERS: 3,670 + (displacement X 4.4)

AIRCRAFT CARRIERS:
T4: 28,373 + (displacement X 0.352)
T6: 34,967 + (displacement X 0.338)
T8: 41,652 + (displacement X 0.328)
T10: 48,446 + (displacement X 0.319)

 

EXAMPLE: I want to see just how much hitpoints the Almirante Brown class of heavy cruisers would have. I know that their full displacement is 9,000t and they're a cruiser, therefore their hitpoint pool would be: 9,565 + (9000 x 1.91) = 26,755 hitpoints which can be rounded up to 26,800 hitpoints.

ARMOUR PIERCING (AP) AMMUNITION

Spoiler

Damage for AP ammunition depends on two things: projectile mass and muzzle velocity.

AP SHELL DAMAGE: 18.59 X ( ( Shell Mass X Muzzle Velocity ) ^ 0.4788 )

 

NOTE: The formula for AP bomb damage is the same as the AP shell damage, but with the speed set to 400m/s. Don't know why, but that seems to be what WG has done.

AP BOMB DAMAGE: 18.59 X ( ( Bomb Mass X 400 ) ^ 0.4788 )

 

AP ROCKET DAMAGE: 19 X ( ( Rocket Mass X Velocity ) ^ 0.528 )

 

EXAMPLE: I want to see just how powerful the 190mm guns from the Almirante Brown class are so I will calculate the AP damage. They fire a 90.7kg shell at 950m/s. Their damage would thus be: 18.59 x ( ( 90.7 x 950 ) ^ 0.4788 ) = 4288 damage which can be rounded up to 4300.

SEMI-ARMOUR PIERCING (SAP) AMMUNITION

Spoiler

Damage for SAP ammunition depends on two things: projectile mass and muzzle velocity. A SAP projectile's penetration is dependent on its caliber.

DISCLAIMER: The SAP damage formula is not very accurate as WG itself doesn't seem to know just how powerful SAP shells should be. Fr0sty has tried to eliminate the weird outliers and use the best values he could find from among all the changes WG did. It will give you a decent figure for most cases, it just isn't as accurate as he'd have liked.

 

SAP SHELL DAMAGE: 45.3 X ( ( Shell Mass X Muzzle Velocity ) ^ 0.416 )

SAP SHELL PENETRATION (mm): 5.6 + ( Shell Caliber (mm) X 0.24 )

HIGH EXPLOSIVE (HE) AMMUNITION

Spoiler

Damage for HE ammunition (including rockets and bombs) depends on two things: projectile mass and bursting charge mass (or warhead's explosive mass in the case of rockets and bombs). HE ammunition's chance to cause a fire however only depends on the bursting charge mass or warhead's explosive mass. The HE penetration of shells is normally 1/6 the caliber of the weapon, whereas for rockets their penetration seems to be closely related to the rocket or bomb's mass. I have few proper data points for rocket & bomb HE penetration, so take the resulting formula only as an approximation.

HE SHELL DAMAGE: 886.3 X ( ( Shell Mass X Bursting Charge Mass ) ^ 0.1658 )

HE SHELL FIRE CHANCE (%): 5.0447 X ( ( Bursting Charge Mass ) ^ 0.4612 )

 

HE ROCKET DAMAGE: 770 X ( ( Rocket Mass X Warhead Explosive Charge Mass ) ^ 0.193 )

HE ROCKET FIRE CHANCE (%): 3.67 X ( ( Warhead Explosive Charge Mass ) ^ 0.52 )

HE ROCKET PENETRATION (mm): 8.81 X ( Rocket Mass ) ^ 0.323

 

HE BOMB DAMAGE: 1164 X ( ( Bomb Mass X Warhead Explosive Charge Mass ) ^ 0.176 )

HE BOMB FIRE CHANCE (%): 6.54 X ( ( Warhead Explosive Charge Mass ) ^ 0.38 )

HE BOMB PENETRATION (mm): 7.07 X ( Bomb Mass ) ^ 0.329

 

EXAMPLE: I want to find out just how strong the 7.2" Demolition rocket would be if fired from a plane. I know it has a mass of 28kg and a 15kg explosive warhead. I can thus calculate its damage: 770 x ( ( 28 x 15) ^ 0.193 ) = 2470 damage which we can round down to 2450. The chance for it to cause a fire would be: 3.67 x ( ( 15 ) ^ 0.52 ) = 15 % and the penetration would be 8.81 x ( 28 ) ^ 0.323 = 25.84mm which we round to 25.8mm.

TORPEDOES

Spoiler

Damage and flooding chance for torpedoes is determined solely by the torpedo's warhead mass. A torpedo's range is the same as it was historically, with the speed for ship-launched torpedoes being the historical one buffed by approximately 20kts.

 

TORPEDO DAMAGE: 207.18 X ( ( Warhead Explosive Charge Mass ) ^ 0.7444 )

TORPEDO FLOODING CHANCE (%): 2.52 X ( ( Warhead Explosive Charge Mass ) ^ 0.7985 )

 

DISCLAIMER: The aircraft torpedo formulas only work for baseline torpedoes. WG has fudged with MANY of the torpedo parameters to the point where many nations just have gimped performance in one way or another (like the Japanese air-dropped torpedoes having drastically reduced flooding chance, high-tier British torpedoes having nerfed damage and flooding chance or German torpedoes which are thoroughly nerfed throughout)

AIRCRAFT TORPEDO DAMAGE: 394 X ( ( Warhead Explosive Charge Mass ) ^ 0.525 )

AIRCRAFT TORPEDO FLOODING CHANCE (%): 1.84 X ( ( Warhead Explosive Charge Mass ) ^ 0.642 )

ANTI-AIRCRAFT (AA) WEAPONRY

Spoiler

Disappointment starts here. Neither I nor Fr0sty nor anyone else I know has a way to calculate the continuous DPS values for AA. The only thing I can say is that before the AA rework, we had found out that the effectiveness of adding more weapons to a mount had an effect equal to SQRT(new barrel amount/old barrel amount), so that doubling the number of barrels on a mount (so going from a single 40mm Bofors to a double 40mm Bofors) would effectively multiply the DPS by 1.414, and quadrupling the number of barrels would multiply the DPS by 2.

The current AA workings mean that the Continuous DPS has a certain accuracy rate which is determined by 2 things: ship class and which area it is meant to contribute to. Weapons firing in the short range aura suffer a -5% accuracy penalty when compared to weapons firing in the other auras. AA weapons are thus grouped in 3 auras: short range guns (30mm>), medium range guns (30.1mm-85mm) and long range guns (>85mm). Only the long range guns can generate flak and it is only until the mid-range guns start firing.

BASE CONTINUOUS AA ACCURACY:
Battleships: 75%
Cruisers: 90%
Destroyers: 100%
Aircraft Carriers: 100%

FIRING RANGE

Spoiler

Once upon a time, WG told us that the height of the rangefinders on a ship determined the firing range. We know that this is not really true, but it should mean that if a ship couldn't fire beyond X km in real life due to rangefinders/turret elevation, then neither should it in World of Warships. Still, the higher mounted the rangefinder is, the better the range the ship would have in-game.

CONCEALMENT

Spoiler

How easy a ship is to detect depends on several weird variables, chief amongst them being WG's balancing. There are two concealment values: one from ships and another from aircraft. Concealment from ships according to WG is determined by how "distinct" the ship's silhouette is and how tall the ship is (although theories abound as to which point of the ship this height is meant to refer to). Personally, I tend to use the side profile's height and area to provide my guesses on concealment against ships, so grab a few ships that are already in-game and compare just how long & tall (even better if you can compare the area of the side profile silhouette) your new ship is compared to them and make an estimate based on it. The concealment against aircraft is another matter just as vague, but it correlates quite well to the deck area of a ship, so you can just look at how much area the ship presents when viewed from above, compare that to other ships in the game and estimate. As usual, concealment is not really something we can calculate easily due to the vagueness of the measurements that WG uses and due to the fact that they've messed with concealment quite a bit for national flavours which leads us to have a really hard time to derive accurate formulas.

TORPEDO PROTECTION

Spoiler

Nobody really knows how WG determines the torpedo protection of ships. It's been a matter of much debate but just as the topic of torpedo protection is so subjective in real life, it is quite as complex when related to WG's implementation. Try to just look at similar ships to estimate.

NATIONAL FLAVOURS

Spoiler

WG has seen fit to modify several ships and tech-tree implementations to apply some extra flavour to them and thus provide more varied and diverse gameplay options. Here are the flavours & modifications that WG has done (I will not go into all the consumable flavours) and that I remember off the top of my head:

GERMANY:
+ Buffed AP damage (for non-battleship weapons)                                                                                                                                                                                          + Buffed AP penetration (destroyer leaders)                                                                                                                                                                                                    + Improved AP autobounce angles (cruisers)                                                                                                                                                                                                  + Unique destroyer leader dispersion formula (approx 50% more accurate at all ranges)
+ Buffed HE penetration (1/4 penetration instead of 1/6)
+ Buffed Hydroacoustic Search consumable (battleships & cruisers)                                                                                                                                                          + Buffed bow and stern armour plating (cruisers)
- Nerfed HE damage
- Nerfed Smoke Generator dispersion time                                                                                                                                                                                                      - Nerfed bow and stern armour plating(battlecruisers)

 

JAPAN:
+ Buffed HE damage
+ Buffed long-range dispersion (battleships)
+ Torpedo Reload Booster consumable (high-tier destroyers)                                                                                                                                                                      + Enhanced Spotter plane with dispersion modifiers (battlecruisers)
- Nerfed short-range dispersion (battleships)
- Nerfed Damage Control Party active duration (battleships)                                                                                                                                                                        - Nerfed bow and stern armour plating(battlecruisers)

USA:
+ Improved AP autobounce angles (cruisers)
+ Improved Repair Party heal (standard battleship line)                                                                                                                                                                                + Reduced Repair Party cooldown(slow battleship line)                                                                                                                                                                                  + Improved acceleration characteristics
+ Buffed Smoke Generator emission time (30s instead of 20s)
+ Buffed Smoke Generator dispersion time (40s more than normal)
+ Buffed Defensive AA consumable (destroyers only)
+ Buffed Surveillance Radar active duration
+ Buffed Damage Control Party active duration (battleships)                                                                                                                                                                      + Buffed bow and stern armour plating(cruisers)

 

UNITED KINGDOM:
+ Buffed HE damage(heavy cruisers and battleships)
+ Buffed Fire chance(heavy cruisers and battleships)
+ Buffed HE penetration(heavy cruisers and standard battleships)
+ Buffed AP autobounce angles (light cruisers)
+ Shortened AP fuse arming time (light cruisers & battleships)
+ Megaheal (high-tier cruisers & battleships)
+ Improved ship turn speed (light cruisers)
+ Improved ship acceleration from stop (light cruisers and battlecruisers)
+ Larger Smoke Generator puffs (0.6km instead of 0.45km for others)
+ Smoke Generator consumable (light cruisers)
+ Short-burst Smoke Generator (shorter emission, dispersion and reload time for destroyers only)                                                                                                        + Engine Boost consumable(battlecruisers)                                                                                                                                                                                                      + Large cruiser dispersion formula(battlecruisers)
- Nerfed Smoke Generator emission time (15s instead of 20s)                                                                                                                                                                      - Nerfed bow and stern armour plating(battlecruisers)

 

U.S.S.R.:
+ Unique cruiser dispersion formula (Tallinn, Riga & Petro)
+ Unique battleship dispersion formula (better at close ranges and worse at long ranges)
+ Improved AP bounce angles (Tallinn, Riga & Petro)
+ Improved AP fuse arming time (Tallinn, Riga & Petro)
+ Fast Damage Control Teams consumable (shorter reload time for battleships)
- Nerfed HE performance (Tallinn, Riga & Petro)
- Fast Damage Control Teams consumable has limited charges (battleships)                                                                                                                                              - Repair Party consumable has one less heal than standard(battleships)

 

FRANCE:
+ Engine Boost consumable (battleships)
+ Buffed Engine Boost consumable (destroyers & cruisers)
+ Main Battery Reload Booster consumable (destroyers & cruisers)                                                                                                                                                            + Improved secondary battery accuracy (large cruisers)                                                                                                                                                                                - Large Cruiser dispersion formula (large cruisers)                                                                                                                                                                                          - Increased fire duration (large cruisers)

 

ITALY:
+ SAP ammunition
+ Exhaust Smoke Generator consumable
- No HE ammunition (cruisers & high-tier battleships)                                                                                                                                                                                      - No AP ammunition (destroyers)

NETHERLANDS:
+ Air Strike weapon
+ Buffed AA continuous DPS                                                                                                                                                                                                                              - Large cruiser dispersion (high tier cruisers)                                                                                                                                                                                                    - Increased fire duration (high tier cruisers)

PAN-EUROPE:
+ Buffed torpedo speed
+ Shortened AP fuse arming time                                                                                                                                                                                                                      + Long range Surveillance Radar consumable(high tier gunboat destroyers)
- Nerfed torpedo damage
- Nerfed torpedo flooding chance                                                                                                                                                                                                                      - No AP ammunition (gunboat destroyers)

 

PAN-ASIA:
+ Deepwater torpedoes (buffed damage & flooding chance)
+ Buffed Smoke Generator emission time (30s instead of 20s)
+ Buffed Smoke Generator reload time (100s instead of 160s)
+ Short-range Surveillance Radar consumable (high-tier destroyers)                                                                                                                                                          + Torpedo Reload Booster consumable (high-tier destroyers and cruisers)
- Deepwater torpedoes (ineffective against certain classes)

 

AIRCRAFT CARRIER FLAVOURS

Spoiler

I was going to include aircraft carrier flavours in their own nations, but since they're all rather weird, I chose to better do a section just for them (make sure to check WoWS wiki for all their flavours):

USA:
+ Durable planes
+ Unmatched payload (high-tier planes can unleash more or harder-hitting ordnance than others nations)
- Poor dispersion on ordnance delivery

 

JAPAN:
+ AP bombs
+ Faster & harder-hitting torpedoes
+ Improved torpedo bomber concealment (7.5km detectability instead of 10km)
+ Improved torpedo bomber & bomber boost speed (40kts instead of 35kts)
+ Improved Aircraft Repair consumable (extra charge & lower reload time)
- Fragile planes

 

UNITED KINGDOM:
+ Extremely durable planes
+ Level bombing instead of dive bombing
+ Highest amount of rockets dropped per plane
- Slow planes

 

GERMANY:
+ AP rockets
+ AP bombs
+ Very fast planes
+ Improved torpedo bomber & bomber boost speed (40kts instead of 35kts)
+ Improved Engine Cooling consumable
+ Aircraft Repair consumable (bombers)
+ Improved secondary battery range
- Very fragile planes

 

U.S.S.R:
+ All planes attack in a single wave
+ Skip HE bombs
+ Long range torpedoes
+ Very fast planes
+ Improved secondary battery range
- Very fragile planes

OUTLIERS

Spoiler

There are several ships & weapons that are just horrible outliers. Some of the most notable are:

Blyskawica: Listed in-game displacement of 3,383t which means she should have a hitpoint pool of roughly 18,500 and yet only has 15,500 in-game. It's the largest disparity for a current DD in-game at almost 20%.

Anchorage: The T8 premium cruiser has the same displacement as the Buffalo at T9, and yet for balance reasons she has 6,000 fewer hitpoints (15%) which is the largest disparity for a current cruiser in-game.

There is only a single non-premium battleship with a strange disparity between expected hitpoint pool and real hitpoint pool: The New Mexico with its A hull has a displacement of 35,406t which means it should have around 52,600 hitpoints instead of the 48,200 hitpoints it currently has. It is quite interesting that the difference between the A and B hull is just 594t and yet the hitpoint pool changes by 5,000.

Premium battleships are on a league of their own with many of them having vastly lower hitpoint pools than expected:
Slava: 82,149t (same as Kremlin) but with 91,800hp providing a difference of almost 18% (16,500hp) is the worst one
Champagne: 42,544t but with 52,600hp providing a difference of above 16% (8,500hp) of what is expected
Brandenburg: 47,520t but with 58,800hp providing a difference of almost 14% (8,200hp) of what is expected
Kearsarge: 70,630t but with 84,300hp providing a difference of above 12% (10,200hp) of what is expected

Supercruisers & Battlecruisers are remarkably interesting because WG sometimes implements them using the battleship HP formula and sometimes using the supercruiser HP formula. The following ships use the battleship HP formula despite being considered supercruisers at some point: Puerto Rico, Congress, Odin (one of the legacies of Odin being a supercruiser is that her guns benefit from the German Cruiser AP damage buff). The rest (including the new Dutch ships) follow the standard supercruiser HP formula.

 

For weapons:

The Type 93 Mod. 3 has the biggest disparity between expected and in-game damage & flooding chance of a torpedo. Its 780kg warhead would give it 29,500 damage and 514% flooding chance whereas it currently has 23,766 damage and 406% flooding chance.

Here are some interesting notable outliers that show how expected values to in-game values change with WG's national flavours:
The upcoming Dutch Haarlem cruiser uses the same guns and shells that the German Admiral Hipper, Roon & Hindenburg do, but there's are big differences. Haarlem's AP shells deal 4800 damage while the German's AP shells have their damage buffed to 5900. Haarlem's HE shells deal 2850 damage and have 34mm penetration whereas the German's HE shells have their damage nerfed to 2500 but have their penetration buffed to 51mm. They are otherwise the same.
We know that German Cruisers get buffed AP damage and German Battleships do not because Graf Spee uses very similar (in fact they're weaker) 283mm guns compared to Scharnhorst's 283mm guns and yet the Graf Spee's deal 8400 damage and the Scharnhorst's deal 7600 damage. The AP damage buff is larger (percentage-wise) the smaller the gun is; the 88mm guns have roughly 35% additional AP damage, the 203mm guns have roughly 20% additional damage and 283mm guns have roughly 10% additional damage.
Warspite and Queen Elizabeth battleships use the same HE shells, but QE's deal an extra 1,000 damage (5300 vs 6300), have 31mm extra penetration (64mm vs 95mm) and have an extra 1% fire chance (34% vs 35%).

PS: I will update these formulas from time to time if any newer releases are found.

[Wolfswetpaws]

1 hour ago, disa_destroyer said:

I've decided to try and preserve them by posting them here.

👍

[BOBTHEBALL]

This is very good, please keep up the great work archiving these! 

[Project45_Opytny]

I would like to argue that a few of the short comments on national and branch flavors are questionable if not incorrect.

9 hours ago, disa_destroyer said:

+ Improved AP autobounce angles (cruisers)

German "Oceanic" gunboat destroyers, not cruisers.

9 hours ago, disa_destroyer said:

+ Shortened AP fuse arming time (light cruisers & battleships)

For a number of such characteristics it is overgeneralizing to classify them into binary "good" or "bad" ones. Though this one can be considered as "good" overall.

9 hours ago, disa_destroyer said:

+ Unique cruiser dispersion formula (Tallinn, Riga & Petro)
+ Unique battleship dispersion formula (better at close ranges and worse at long ranges)

For battleships mixed, while for cruisers bad.

[Admiral_Karasu]

@I_cant_Swim_ This seems to fall under the retrieval/archival project of ours.

[I_cant_Swim_]

5 minutes ago, Admiral_Karasu said:

This seems to fall under the retrieval/archival project of ours

Yes it does. Fits well in Guides, as stated on the can.

[I_cant_Swim_]

@disa_destroyer Really good stuff, mate! Thank you, and please do carry on!

[disa_destroyer]

On 10/20/2023 at 11:40 PM, Project45_Opytny said:

I would like to argue that a few of the short comments on national and branch flavors are questionable if not incorrect.

German "Oceanic" gunboat destroyers, not cruisers.

For a number of such characteristics it is overgeneralizing to classify them into binary "good" or "bad" ones. Though this one can be considered as "good" overall.

For battleships mixed, while for cruisers bad.

My bad. It seems some mistakes may have slipped.