# EVE-Online:Formulae

## General

### Skill Training Time

$T=\frac{N}{P+\frac{S}{2}}$

• $P$ is the skill's primary attribute
• $S$ is the skill's secondary attribute
• $N$ is the number of skill pointed needed
• $T$ is the time it will take, in minutes.

### Available Agent Quality

\begin{align} S &= 2L - 2 + \frac{Q}{20}\\ Q &= 20S - 40L + 40\\ L &= \frac{S}{2} + 1 - \frac{Q}{40} \end{align}

• $Q$ is the highest quality agent available for the level
• $S$ is the current total standing you have with the agent's corp
• $L$ is the level of the agent

### Capacitor/Shield Recharge Rate

$\Large R = 5\frac{M}{T}\sqrt{(1-P)^2-(1-P)^4}$

• $R$ is the capacitor/shield recharge rate
• $M$ is the maximum capacitor/shield value
• $T$ is the time required for the capacitor/shield to recharge
• $P$ is the current percentage of capacitor/shield available

#### Peak Cap/Shield Recharge

The formula above yields a curve that rises sharply from 0% to some value, then falls off gradually as it approaches 100%. It is possible to calculate this percentage precisely and then use it to identify the peak recharge rate. See the analysis here. The actual value is $1-\frac{sqrt{2}}{2}$, or about 29.29%. With this in mind, the Peak Recharge Rate value is $R = \frac{5M}{2T}$.

## Modules

### Mass:Thrust Calculations

$I = S\left(\frac{F}{M}\right)$

• $F$ is the thrust of the drive
• $M$ is the mass of the ship
• $S$ is the drive's listed speed increase as a percentage
• $I$ is the effective speed increase as a percentage
Example
An Amarr Maller cruiser has a mass of 12.75 million kg. A standard 1MN Afterburner provides a thrust of 1.5 meganewtons and a max velocity bonus of 105%.

\begin{align} I &= 1.05\times{}\left(\frac{1500000}{12750000}\right)\\ &= 0.124 \end{align}

One therefore receives only a 12.4% speed increase from using a 1MN Afterburner on a Maller. This is normal, since 1MN devices are intended for frigates, not cruisers.

### Range Falloff

$C = 0.5^{\left(\frac{(R-O)}{F}\right)^2}$

• $R$ is the range from the target
• $O$ is the optimal range
• $F$ is the falloff range
• $C$ is the chance of success

These values are further modified by signature radius and tracking speed for guns. The bigger an object's signature radius, the slower the gun needs to track to hit it.

### Turret Damage

There are two components to this formula.

#### Chance To Hit

\LARGE \begin{align} z &= 0.5^{\left(\left(\frac{V_t}{RT}\times{}\frac{S_{res}}{S_{rad}}\right)^{2}+\left(\frac{R-O}{F}\right)^{2}\right)}\\ &= 0.5^{\left(\left(\frac{V_\omega}{T}\times{}\frac{S_{res}}{S_{rad}}\right)^{2}+\left(\frac{R-O}{F}\right)^{2}\right)} \end{align}

• $V_t$ is target's transversal velocity (m/s).
• $R$ is range to target (m/s).
• $T$ is tracking speed of gun (rad/sec).
• $S_{res}$ is gun's signature resolution (m).
• $S_{rad}$ is target's signature radius (m).
• $O$ is gun's optimal range (m).
• $F$ is gun's falloff distance (m).
• For situations where $R-O<0$, use $R-O=0$.

#### Damage

if $x < 0.01$:
$q = 3$
else:
$q = x + 0.5$
if $x < z$:
$d = qd_{max}$
else:
$d = 0$

• $x$ is a random number between 0 and 1, generated for each shot
• $q$ is the "quality" of the shot (1% chance of a "wrecking" shot)
• $d_{max}$ is the total maximum, non-wrecking damage of the shot
• $d$ is the actual damage of the shot

This can be mathematically modeled as $d = 1.025zd_{max}$

A few notes:

• DPS goes down a lot faster than chance to hit does
• Chance to hit is never 100% whenever any angular velocity is involved
• See Modeling Turret Damage for additional information on turret damage.

### Missile Damage

Missile DRF
Light 2.8
Rocket 3.0
Heavy 3.2
HAM 4.5
Cruise 4.5
Torpedo 5.0

$\Large D = D_0\min\left(\min\left(\frac{S_{rad}}{E_r},1\right),\left(\frac{E_v}{v}\times{}\frac{S_{rad}}{E_r}\right)^{\left(\frac{\ln{(f)}}{\ln{(5.5)}}\right)}\right)$

• $D_0$ is base missile damage
• $E_v$ is missile explosion velocity
• $v$ is the target's velocity
• $S_{rad}$ is the target's signature radius
• $E_r$ is the missile explosion radius
• $f$ is the Damage Reduction Factor of the missile (see table to the left)

Note that when $v = 0$, $\frac{E_v}{v} = \infty$, so the left-hand side of the minimum function comes into play instead.

### Stacking Penalty

When you use multiple modules of the same type that confer a bonus, each successive module provides less of a bonus than the original.

#### Stacking Penalty to the Module

$\LARGE S(n) = 0.5^{({\frac{n-1}{2.22292081})^2}$

• $S(n)$ is the stacking penalty applied to the module's bonus
• $n$ is the hierarchical position of the module (i.e. first, second, third). This is always done from highest bonus to lowest (meaning lowest bonus items are penalized the harshest).

#### Total Cumulative Bonus

$\LARGE B_T=\sum{(1-B_{n-1})\times{}(B_{n}S_{n})}$

• $B_T$ = Total bonus
• $B_{n-1}$ = Cumulative bonus of previous module (for $n-1 = 0$, use the base value of the ship/with no modules)
• <Math>B_n[/itex] = Base module bonus value
• $S_n$ = Stacking penalty for module $n$.

## Industry

### True Mineral Requirement

$\Large M_t = M_0\left(1 + 0.05(5-S) + \left(\frac{W_0}{1+L_M}\right)\right)$

• $M_t$ = True mineral requirement
• $M_0$ = Perfect mineral requirement (i.e. perfect recycle value)
• $S$ = Production Efficiency skill level
• $W_0$ = Blueprint base wastage factor (10% for ships)
• $L_M$ = Material Level of the specific blueprint

### Wastage Factor

$\Large W = \frac{W_0}{1+L_M}$

• $W$ = actual wastage factor
• $W_0$ = Blueprint base wastage factor (10% for ships)
• $L_M$ = Material Level of the specific blueprint