User blog:Shadow27X/Artillery Spotting Rate Formula

Preface
A model for an Artillery Spotting formula, which is based on data taken from KanColle Kai.

Formula
$$F_{los} = \sum^{\text{All Ships}} \left ( B_{s} + \sum^{\text{All Slots}} L_{sp} \left \lfloor \sqrt{N} \right \rfloor \right )$$


 * $$B_{s}$$ is the ship's unmodified LoS, without including equipment
 * $$L_{sp}$$ is the LoS value of a given Seaplane or Seaplane Bomber
 * $$N$$ is the slot size of a Seaplane (Bomber)-carrying slot

$$A_{los} = \left \lfloor \sqrt{F_{los}} \right \rfloor + \frac{F_{los}}{10}$$

$$L_{los} = \left \lfloor \sqrt{L_{s}} + 10 \right \rfloor$$


 * $$L_{s}$$ is the ship's luck

$$E_{los} = \sum^{\text{All Slots}} L_{eq}$$


 * $$L_{eq}$$ is the LoS value of a given equipment.

$$\text{Base Rate} = \begin{cases} L_{los} + 0.7 \left ( A_{los} + 1.6 E_{los} \right ) + 10 & \text{ if Air Supremacy} \\ L_{los} + 0.6 \left ( A_{los} + 1.2 E_{los} \right ) & \text{ if Air Superiority} \end{cases}$$

$$\text{Spotting Chance} = \frac{\left \lfloor \text{Base Rate} \right \rfloor + F}{\text{Type Factor}}$$


 * $$F$$ is the flagship bonus; 15 if the ship is in the flagship position, 0 otherwise.

$$\text{Type Factor} = \begin{cases} 150, & \text{ for Double Attack} \\ 140, & \text{ for AP Cut-In (Main)} \\ 130, & \text{ for Secondary Cut-In (Radar)} \\ 120, & \text{ for Secondary Cut-In} \\ 130, & \text{ for AP Cut-In (Secondary)} \end{cases}$$