Formulas

Room Reload Formula

Formula

$\text{Boosted Reload} = \frac{\text{Base Reload Time}}{\left( \frac{100 ~ + ~ \text{Sum of Crew Stat in Room}}{100} \right)}$

$\text{Powered Reload} = \frac{\text{Boosted Reload} \times \text{Max Power of Room}}{\text{Current Power of Room}}$

Online Room Reload Calculator

Guide

Whenever a Crew member enters a reloadable room and has the room's corresponding stat, the 1^st formula is applied. If the room is not running at full power, the 2^nd formula is applied. If there are multiple Crews, their applicable stats are combined for the 1^st formula.

Examples

• Example 1: A Crew member with a Science stat of 15 enters a Shield Generator that has 12s left before it fully reloads. The formula becomes ${\textstyle \frac{12}{\frac{100 ~ + ~ 15}{100}} = 10.4}$, which sets the Shield Generator's current reload time to 10.4s.

• Example 2: A Crew member with a Science stat of 2 enters a Shield Generator that has 12s left before it fully reloads. The formula becomes ${\textstyle \frac{12}{\frac{100 ~ + ~ 2}{100}} = 11.8}$, which sets the Shield Generator's current reload time to 11.8s.

• Example 3: Two Crew members with a combined Science stat of 125 enter a Shield Generator that has 12s left before it fully reloads. The formula becomes ${\textstyle \frac{12}{\frac{100 ~ + ~ 125}{100}} = 5.3}$, which sets the Shield Generator's current reload time to 5.3s.

• Example 4: A Crew member with a Science stat of 0 and a Weapon stat of 100 enters a Shield Generator. Since the Crew member lacks the room's corresponding stat, the formula will not be applied.

• Example 5: A Crew member with a Science stat of 15 enters a Shield Generator that has 12s left before it fully reloads. The formula becomes ${\textstyle \frac{12}{\frac{100 ~ + ~ 15}{100}} = 10.4}$, which would set the Shield Generator's current reload time to 10.4 seconds. Since the Shield Generator is only running at 2 of 3 power, the 2nd formula becomes ${\textstyle \frac{10.4 ~ \times ~ 3}{2} = 15.6}$, setting the Shield Generator's current reload time to 15.6s.

Crew Stat Buff Formula

Formula

The exact formula depends on the stat to be calculated. The formulas for the Ability stat and the Stamina stat differ from those for the other stats.

${\text{Ability Stat Value}}={\text{Base Stat}}\times {\frac {100+{\text{Training Buff}}}{100}}\times {\frac {100+{\text{Equipment Buff}}}{100}}$

${\text{Stat Value}}={\text{Base Stat}}\times {\frac {100+{\text{Training Buff}}}{100}}+{\text{Equipment Buff}}$

${\text{Stamina Stat Value}}={\text{Training Buff}}+{\text{Equipment Buff}}$

Guide

When a Crew member equips a piece of equipment or gains a buff by training in the Gym/Academy, a formula is applied that'll determine how the Crew member's buffed stat is affected. Buff variables should only be the number, discarding the percentage if they have one. For example, 98% will be included in the formula as 98.

Examples

• Example 1: A Crew member with a base Ability stat of 50 trains to get a 60% Ability stat buff. In addition, they are wearing two pieces of equipment that have a combined Ability stat buff of 25%. The formula becomes ${\textstyle 50 \times \frac{100 ~ + ~ 60}{100} \times \frac{100 ~ + ~ 25}{100} = 100}$, which sets the Crew member's Ability stat to 100.

• Example 2: A Crew member with a base HP stat of 9 trains to get a 110% HP stat buff. In addition, he/she is wearing one piece of equipment that has a HP stat buff of 6. The formula becomes ${\textstyle 9 \times \frac{100 ~ + ~ 110}{100} + 6 ~ = 24.9}$, which sets the Crew member's HP stat to 25 in Ship Battles and 24.9 in Ground Battles.

• Example 3: A Crew member with a base Stamina stat of 0 trains to get a Stamina stat buff of 10. In addition, he/she is wearing three pieces of equipment that have a combined Stamina stat buff of 40. The formula becomes ${\textstyle 0 + 10 + 40 = 50}$, which sets the Crew member's Stamina stat to 50.

Escape Formula

Formula

$\text{Escape Chance} = \text{Escape Modifier} \times \frac{100 + \text{Sum of Pilot Stat in Room}}{100}$

$\text{Escape Rate} = \frac{\text{Player's Escape Chance}}{\text{Player's Escape Chance} + \text{Enemy's Escape Chance}} \times 100$

Round values. Note, the game rounds five down instead of up.

Guide

When both the player and the enemy have an equipped Bridge, the 2^nd formula is used to determine the player's escape rate. The 1^st formula is applied whenever a Crew member with a Pilot stat of at least 0.01 enters the Bridge. If there are multiple Crew, their Pilot stats are combined for the formula.

Examples

• Example 1: Both the player and the enemy have a level 11 Bridge (60 Modifier) onboard. In the battle, a Crew with a Pilot stat of 23 enters the player's Bridge. The 1^st formula is used and becomes ${\textstyle 60 \times \frac{100 ~ + ~ 23}{100} = 73.8}$, which sets the player's escape chance to 73.8. The 2^nd formula is then used and becomes ${\textstyle \frac{73.8}{73.8 ~ + ~ 60} \times 100 = 55}$, which sets the player's escape rate to 55%.

• Example 2: The player has a level 1 Bridge (11 Modifier), while the enemy has no Bridge equipped (0 Modifier). The 1^st formula is used and becomes ${\textstyle \frac{11}{11 ~ + ~ 0} \times 100 = 100}$, which sets player's escape rate to 100%.

• Example 3: The player has a level 1 Bridge (11 Modifier), and a Crew member with a Weapon stat of 50 enters it. Since the Bridge is not influenced by the Weapon stat, its escape chance remains the same.

Dodge Formula

Formula

$\text{Engine's Dodge Rate} = \text{Base Dodge} \times \frac{100 ~ + ~ \text{Sum of Engine Stat In Room}}{100}$

$\text{Powered Engine's Dodge Rate} = \text{Dodge Rate} \times \frac{\text{Current Power of Engine}}{\text{Max Power of Engine}}$

$\text{Combined Dodge Rate} = \text{Powered Dodge Rate of Engine A} + \text{Powered Dodge Rate of Engine B} + \text{Powered Dodge Rate of Engine C}$

$\text{Ship's Evasion Chance} = 100 \times \left( 1 - \exp\left(\frac{\text{Combined Dodge Rate}}{100} \times \log_e{(0.2)}\right) \right)$ (rounded down)

Note: If the player does not have Engine A, B, or C, replace its dodge rate with 0.

Note: ${\textstyle \exp(\text{stuff})}$ in the 4th formula stands for ${\textstyle e^\text{stuff}}$.

Guide

When a Crew member with an Engine stat of at least 0.01 enters an Engine, the above formulas are applied. If there are multiple Crews, their Engine stats are combined for the formula. If an Engine is not running at full power, the dodge rate goes down for that engine. Engines are given letter codes to help make the formula less confusing, the letter an Engine is given does not matter as long as they’re not repeats. A simpler way to describe the 1^st formula above is that every full engine stat point of a crew in the engine increases the base dodge rate by 1%.

Starting on July 1st, 2023 the 4th formula above is used to determine a ship's evasion chance. The formula has been added to make reaching 100% impossible. Before that date, the calculation of the dodge chance stopped with the result of the 3rd formula.

Examples

• Example 1: A Crew member with an Engine stat of 23 enters Engine A with a dodge of 19. The formula for Engine A becomes ${\textstyle 19 \times \frac{100 ~ + ~ 23}{100} = 23.37 }$, which sets Engine A’s dodge rate to 23.37%.

• Example 2: A Crew member with an Engine stat of 23 enters Engine B with a dodge of 19. The room is utilizing 2 out of 3 power. The formula for Engine B becomes ${\textstyle 19 \times \frac{100 ~ + ~ 23}{100} = 23.37 }$, which then becomes ${\textstyle 23.37 \times \frac{2}{3} = 15.58}$, which in turn sets Engine B’s dodge rate to 15.58%.

• Example 3: Three Crew members with a combined Engine stat of 236 enters Engine A with a base dodge of 23. In addition, the ship houses Engine B with a base dodge rate of 23. The formula for Engine A becomes ${\textstyle 19 \times \frac{100 ~ + ~ 236}{100} = 77.28 }$, which is then combined with Engine B's dodge rate of 23. The formula now becomes ${\textstyle 77.28 + 23 = 100.28}$, which sets the Combined Dodge Rate to 100.28%. Obviously, 100% is the maximum dodge rate, so there is no need to increase the dodge rate any further.

• Example 4: Starting on July 1st, 2023, the Combined Dodge Rate doesn't represent the ship's overall evasion chance anymore. Plugging the 100.28% from example 3 into the 4th formula yields ${\textstyle 100 \times \left( 1 - \exp\left(\frac{100.28}{100} \times \log_e{(0.2)}\right) \right) \approx 80.09}$, which sets the ship's evasion chance to 80 %.

• Example 5: A Crew member with an Engine stat of 0 and a Pilot stat of 34 enters Engine A. Since the Crew member lacks the Engine stat, the formula will not be applied.

Damage Reduction Formula

Formula

$\text{Damage Reduction} = 100 \times \left( 1 - \frac{100}{100 + \text{Combined Armor Stat}} \right)$

$\begin{align}
  \text{Damage} &= \text{Applicable Damage} \times \left( 1 - \frac{\text{Damage Reduction}}{100} \right)\\ \\
           &= \text{Applicable Damage} \times \frac{100}{100 + \text{Combined Armor Stat}}
  \end{align}$

The result gets truncated to the hundredth.

Online Damage Reduction Calculator

Guide

The Armor value on an Armor block does not directly correlate with damage reduction. In order to avoid a 100% damage reduction, the above formula is designed to give diminishing returns the higher the Armor value is. If multiple blocks of Armor are used to protect a room, their Armor values are combined for the formula.

Examples

• Example 1: A room protected by an Armor stat of 30 takes 3 System Damage. The formula becomes ${\textstyle 3 \times \frac{100}{100 ~ + ~ 30} = 2.30}$, reducing the System Damage the room takes to 2.30.

• Example 2: A room protected by an Armor stat of 300 takes 1 System Damage. The formula becomes ${\textstyle 1 \times \frac{100}{100 ~ + ~ 300} = 0.25}$, reducing the System Damage the room takes to 0.25.

• Example 3: A room protected by an Armor stat of 100 takes 1 Crew Damage. Since Crew Damage is not reduced by Armor, the formula will not be applied.

Fire Damage Formulas

Fire Duration Reductions

$\text{Reduced Fire Duration} = \frac{\text{Base Fire Duration}}{\left( \frac{100 ~ + ~ \text{Sprinkler Stat}}{100} \right)}$

$\text{Reduced Fire Duration} = {\text{Current Fire Duration}} - \text{Crew Repair Stat} \times 50$

Additional Info

The Sprinkler formula is used whenever a Sprinkler activates. This occurs when a fire is ignited or whenever a fire replaces another fire. This is a one-time reduction and does not linger.

• Duration = Total frames of a fire, not seconds.
• One second of fire is 40 frames.
• Decimals are rounded to the 5th decimal place.
• Fire Damage changes depending on what's being damaged.
• f = frames

Examples

• Example 1: A 5s (200f) fire is ignited in a room with 1 Water Sprinkler. For the sake of simplicity, the fire will be lit on a Fire Frame. On ignition, the Sprinkler formula is used and becomes ${\textstyle \frac{200}{\left( \frac{100 ~ + ~ 50}{100} \right)} = 133.\overline{33}}$, reducing the Initial Fire Duration to 133.33 frames. If a Crew member would then repair with a stat of 1.6, ${\textstyle 1.6 \times 50 = 80}$frames are subtracted from 133.33333 to get 53.33333 frames.

Fire Crew Damage Formula

$\text{Gross Crew Damage} = \frac{\text{Current Fire Duration}}{200}$

$\text{Crew Damage} = \text{Gross Crew Damage} \times \frac{100 - \text{Crew's Fire Resistance Stat}}{100}$

Use the 1st formula and then the 2nd.

Examples

• Example 1: A 5s (200f) fire deals damage to a Crew member with a Fire Resistance stat of 50. The 1^st formula is used and becomes ${\textstyle \frac{200}{200} = 1 }$. The 2^nd formula is then used and becomes ${\textstyle 1 \times \frac{100}{100 ~ + ~ 50} = 0.5 }$Crew Damage.

Notes

• This formula is used for each separate Crew member in a burning room. Do not combine Fire Resistance stats if there are more than 1 Crew.
• This formulas means that any Fire Resistance stat on a crew above 100 will effectively heal the crew in the fire.

Fire AP Damage Formula

$\text{AP Damage} = \frac{\text{Duration}}{500}$

Example

• A 5s (200f) fire deals damage to a room. The formula becomes ${\textstyle \frac{200}{500} = 0.4 }$AP Damage.

Crew Stat by Level

Formula

$\begin{align}
  \text{Current Stat} &= \text{Level 1 Stat} + \text{Stat Difference} \times \left( \frac{\text{Current Level} - 1}{\text{Level Difference}} \right) ^ \text{Ease Type Value}
  
  \\ \\
  
  &= \text{Level 1 Stat} + \text{Stat Difference} \times \left( \frac{\text{Current Level} - 1}{39} \right) ^ \text{Ease Type Value}
  \end{align}$

$\text{Stat Difference} = \text{Max Level Stat} - \text{Level 1 Stat}$

$\text{Level Difference} = \text{Max Level} - 1 = 40 - 1 = 39$

Additional Info

• Level 1 Stat is the value of the stat in question at crew level 1.
• Stat Difference is the difference between the level 1 and level 40 values of the chosen stat.
  • http://pixyship.com/crew is a nice database that lists these values.
• Current Level is the current level of the Crew.
• Ease Type Value depends on the Ease Type of a crew. The Ease Type describes the progression of the respective stat when leveling up a crew. Crews with the Ease Type EaseOut are gaining massive stat increases at the early levels but less at later levels. EaseIn is the opposite and Linear is even distribution.
  • The Ease Type Linear has an Ease Type Value of 1.
  • The Ease Type EaseOut has an Ease Type Value of 0.5.
  • The Ease Type EaseIn has an Ease Type Value of 2.
  • Click here for a file listing the Ease Types of most Crews in the game.
  • If it isn't there, sorry, but you have to find it yourself. I recommend testing it with the level it's at currently and try all EaseTypes.
• Level 1 Stat and Stat Difference will change based on the Crew and the stat you want.
• Round to nearest whole number with HP and tenths for the other stats.

Acknowledgements

Thank you Shoes#9099 (Planet-Express), Eosphoros#5365 (Planet-Express) and Antijive (FleetBreaker) for this and the formula above!

Examples

• Example 1: We want to find the HP stat of Cyber Duck at level 32. It's a Crew with the Ease Type Linear, an initial HP stat of 12 and max of 14. Plugging the values into the formula we get ${\textstyle 12 + (14 - 12) \times \left( \frac{32 ~ - ~ 1}{39} \right) ^ 1 = 12 + 2 \times \left( \frac{31}{39} \right) \approx 13.59}$. After rounding we get the result of 14 HP.
• Example 1: We want to find the Attack stat of Xeon at level 23. It's a Crew with the Ease Type EaseOut, an initial Attack stat of 2 and a max of 3. Plugging the values into the formula we get ${\textstyle 12 + (3 - 2) \times \left( \frac{23 ~ - ~ 1}{39} \right) ^ {0.5} = 12 + 1 \times \left( \frac{22}{39} \right) ^ {0.5} \approx 2.751}$. After rounding we get the result of 2.8 Attack.

Gas Draw Price Formula

Formulas

$\text{Exponent} = Maximum \left( ( \text{Number of all 3/4/5 star Crews} ), ~ Floor \left( \frac{DNA}{100} \right) \right)$

$\text{Base Gas Draw Price} = 500 \times 1.5 ^ {\text{Exponent}} ~~~~~~~~~~ \text{(floored to the two most significant digits)}$

$\text{Final Gas Draw Price} = Minimum \left( \text{Base Gas Draw Price}, ~ \text{2 million} \right)$

Online Gas Draw Price Calculator

Guide

The formula determines the Gas price when purchasing random new Crew members in the shop with the Gas draw option. The maximum price is 2 million Gas.

Disclaimer: The formula has been tested for 1-5 star Crew Members and for Special Crew members, but not (yet) for Legendary Crew members. Currently it is therefore not confirmed if Legendary Crew members affect the Gas Draw Price.

Additional Info

• The number of all 3/4/5 star Crew members is the sum of all 3 star Crew members, 4 star Crew and 5 star Crew the account currently has, regardless of whether the Crew members are in active service or are in the inventory. Crew members in the inbox do not count.
• DNA is the amount of DNA the account currently has. See the Bio Recycling page for details.
• Floored to the two most significant digits means taking the left-most 2 digits and replacing the remaining digits with 0. No rounding takes place, so it's floored and not rounded. Example: 9,876,543.21 becomes 9,800,000.00 (with rounding it would have been 9,900,000.00).

Examples

• Example 1: The account has a total of 15 Crew members with 3, 4 or 5 stars. The account has 0 DNA because no Crew members were blended yet. The exponent therefore is ${\textstyle Maximum \left( 15, ~ 0 \right) = 15}$. The Base Gas Draw Price is ${\textstyle 500 \times 1.5 ^ {15} \approx 218,947}$, which gets floored to 210,000. This is below the cap of 2 million, so the Final Gas Draw Price is 210,000 Gas.
• Example 2: After purchasing five more 3 star Crew members the exponent becomes ${\textstyle Maximum \left( 20, ~ 0 \right) = 20}$and the Base Gas Draw Price is ${\textstyle 500 \times 1.5 ^ {20} \approx 1,662,628}$, which gets floored to 1,600,000. This is still below the cap of 2 million, so the Final Gas Draw Price is 1,600,000 Gas.
• Example 3: Purchasing one more 3 star Crew member results in exponent ${\textstyle Maximum \left( 21, ~ 0 \right) = 21}$ and Base Gas Draw Price ${\textstyle 500 \times 1.5 ^ {21} \approx 2,493,942}$, which gets floored to 2,400,000. This is above the cap of 2 million, so the Final Gas Draw Price is 2,000,000 Gas.
• Example 4: After blending 1 Hero, 4 Epic and 1 Unique Crew members the account again has 15 Crew members with 3, 4 or 5 stars - the same as in example 1. The account now has ${\textstyle 800 + 4 \times 200 + 60 = 1,660}$DNA. The floored DNA value (${\textstyle Floor \left( \frac{1,660}{100} \right) = 16}$) exceeds the Crew member count and the exponent becomes 16. The Base Gas Draw Price is ${\textstyle 500 ~ \times ~ 1.5 ^ {16} ~ \approx ~ 328,420}$, which gets floored to 320,000 and is below the cap of 2 million, so the Final Gas Draw Price is 320,000 Gas.

Trophy Gain/Loss Formula

$\text{Trophies Exchanged} = 20 \times \left( \frac{\text{Loser's Trophy Count}}{\text{Winner's Trophy Count}} \right) ^ 4$

Additional Info

Make sure you use Trophy Counts prior to the battle for the formula. Also, you can not gain or lose more than 40 Trophies, so any answer from the formula greater than that should be set to 40. It's the same for any answer under 0.5. Set it to 1 as you cannot exchange 0 Trophies. If you get a decimal, round to the nearest whole number.

If the winning ship's trophy count is 5,000 or more trophies higher than the losing ship's trophy count, the winning ship won't gain any trophies. If a ship in Legend League attacks a ship outside of Legend League (after doing its 12 daily Legend League battles), no trophies will be exchanged either.

Examples

• A player with 5,000 Trophies defeats a player with 7,000 Trophies. Plugging in the values to the formula, ${\textstyle 20 \times \left( \frac{7000}{5000} \right) ^ 4 \approx 76.38}$. Since this is greater than 40, the Trophy Exchange is 40.
• Let's flip the above example and have the loser be the 5,000 and the winner be the 7,000. The formula, ${\textstyle 20 \times \left( \frac{5000}{7000} \right) ^ 4 \approx 5.20}$, which rounds to 5.

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Damage Mechanics

Volley • System Damage • Crew Damage • Shield Damage • AP Damage • Direct Hull Damage • EMP Damage • Fire Damage

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Crew Mechanics

Crew Abilities

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Misc. Mechanics

Formulas

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