in this guide we’ll try to explain the hard math behind Combat Power (CP), the base values each Pokemon entails inside the game and some other concepts like Individual Values (IVs). If you played the Gameboy versions or any other previous Pokemon game, you could be familiar with the terminology and some of the calculations.
Pokemon GO introduced Combat Power as a new concept in order to provide a more streamlined and simpler solution to relative Pokemon power, and in order to facilitate that we got a set of new formulas for calculation.
This guide contains a lot of formulas, references and links for further exploration. If you’re not afraid of that, dig in.
Pokemon in Pokémon GO have 3 core stats:
Every species of Pokémon has a base value for each of these stats, roughly approximated as such using values for Attack, Defense, HP, Special Attack, and Special Defense from the games:
- Base Attack = 2.6 * (Atk^0.46)(SpAtk^0.46)(Sp^0.04) + 3
- Base Defense = 2.6 * (Def^0.46)(SpDef^0.46)(Sp^0.04) + 3
- Base Stamina = 2 * HP
Individual Values (IVs)
Pokémon also have additional stats called Individual Values or IVs much like in the games. These stats are random for each individual specimen and range from 0-15 and are added directly on to the Pokémon’s base stats. Think about IVs like height and weight are for humans – these simple modifiers help differentiate multiple instances of the same Pokemon.
Using Total_CP_Multiplier (a constant value explained below), we get a Pokémon’s core stats:
- Attack = (Base Attack + Individual Attack) * Total_CP_Multiplier
- Defense = (Base Defense + Individual Defense) * Total_CP_Multiplier
- Stamina = (Base Stamina + Individual Stamina) * Total_CP_Multiplier
Stamina here is shown to the player in the form of HP!
A Pokémon’s minimum level is 1, and its maximum level is equal to your trainer level. Every time you power up, your Pokémon gains half a level. You can roughly estimate a Pokémon’s level by seeing how far the white dot is along the white semicircle above the Pokémon on their stats page where the leftmost tip is level 1 and the rightmost tip is your trainer level.
Combat Power Multiplier
Credits here and here for figuring out the secrets of CP!
Every level also has a CP Multiplier for that level. For every level your Pokémon has, all your stats get amplified by a set amount depending on the CP Multiplier. When you first catch a Pokémon, it will have a CP Multiplier value that corresponds to that level and an Additional CP Multiplier value of 0.
As it levels up from powering up, Additional CP Multiplier increases by a constant amount depending on the new Pokémon level and gets added to CP Multiplier to get your Total CP Multiplier:
- Total_CP_Multiplier = CP_Multiplier + Additional_CP_Multiplier
You can view the table of level to CP_Multiplier conversions here.
Calculating Combat Power
Now that we have values for Attack, Defense, and Stamina, we can determine CP:
- CP = (Attack * Defense^0.5 * Stamina^0.5 * Total_CP_Multiplier ^ 2) / 10
Using this information, we can conclude that the maximum CP at the level 40 cap and 15/15 in all IVs is:
- Max CP = ((Base_Attack + 15) * ((Base_Defense + 15)^0.5 * (Base_Stamina + 15)^0.5 * 0.7903001^2) / 10
We can also determine CP per power up (power up costs here):
|1-10||(Attack * Defense^0.5 * Stamina^0.5 * 0.009426125469^2) / 10|
|11-20||(Attack * Defense^0.5 * Stamina^0.5 * 0.008919025675^2) / 10|
|21-30||(Attack * Defense^0.5 * Stamina^0.5 * 0.008924905903^2) / 10|
|31-40||(Attack * Defense^0.5 * Stamina^0.5 * 0.00445946079^2) / 10|