Edit: On July 25th Team Rocket returned and has higher stats. Our current hunch is that now defense and stamina are also boosted. A 2.5x multiplier seems to fit the tier 1 invasions. We can use your help for research! Please post videos of your invasions along with your Pokemon stats in the comments section.

On July 22nd, Team GO Rocket snuck onto the scene to steal Pokestops and challenge players to Trainer Battles! With them, they brought mysterious Shadow Pokemon – spooky, evil-eyed, and with Combat Power far higher than we’ve seen previously in Trainer Battles. Before Team GO Rocket could blast off again, celandro and I got hot on the trail to crunch numbers and solve the CP formula behind Shadow Pokemon.

Shadow Pokemon that appear in Team GO Rocket invasions have a few key features that we’ll detail below:

A x1, x2, or x3 multiplier to base Attack

Pokemon level of 25, 27, 30, or 40

An additional factor to base Attack related to trainer level

Random IV’s between 5-15, unique per species and trainer level

Introduction to the CP Formula

Before we dive into Shadow Pokemon, let’s have a quick refresher on how stats work for regular Pokemon. Each Pokemon has three base stats (Attack, Defense, Stamina/HP), three individual values (IV’s) that add a small bonus to the corresponding stat, and a CP multiplier (CPM) determined by Pokemon level.

A Pokemon’s CP is calculated with the following formula:

CP = ( (Base Attack + Attack IV) * (Base Defense + Defense IV)^0.5 * (Base Stamina + Stamina IV)^0.5 * CPM^2) ) / 10

A Pokemon’s effective stats are calculated with the following:

Effective Stat = (Base Stat + IV) * CPM

Note that a Pokemon’s CP and Stamina values are rounded down to the next whole number, while Attack and Defense are not.

Let’s look at an example! Swampert’s base stats are 208 Attack, 175 Defense, and 225 Stamina. At level 40, this Swampert has a CPM of .7903, and because we’re lucky, let’s say it has the maximum of 15 IV’s for each stat. (Hope we got Hydro Cannon!) Here’s how to calculate Swampert’s CP:

CP = ( (208 Base Attack + 15 Attack IV) * (175 Base Defense + 15 Defense IV)^0.5 * (225 Base Stamina + 15 Stamina IV)^0.5 * .7903 CPM^2 ) / 10 = 2974

Likewise, this Swampert’s Attack stat at level 40 would be:

Attack = (208 Base Attack + 15 Attack) * .7903 = 176.2

Now that we’ve covered how regular Pokemon work, let’s take a look at what makes these mysterious Shadow Pokemon different!

Shadow Pokemon Tiers

Shadow Pokemon belong to 4 observable tiers, which determine their Pokemon level and a base Attack multiplier. The table below shows the different tiers and their corresponding values.

Boss Tier Pokemon Level Base Attack Multiplier 1 25 x3 2 27 x1 3 30 x1 4 40 x2

For example, Swampert is considered a Tier 4 Shadow Pokemon, so it appears at level 40 with a base Attack multiplier of x2. We’ll take a look at its final stats in a bit, but there are a few other things we have to take into account!

Shadow Pokemon & Trainer Level

A Shadow Pokemon’s Attack stat is also affected by trainer level. Lower level trainers will encounter weaker Shadow Pokemon than higher level trainers. This factor appears to be calculated by the following:

Trainer Level Factor = (Trainer Level - 15) / (40 - 15)

For example, this means a Level 40 trainer will encounter Shadow Pokemon at full strength (x1), while a Level 35 trainer will encounter Shadow Pokemon with weaker Attack (x0.8).

We’ve observed that Level 39 trainers encounter Pokemon just as strong as the ones Level 40 trainers encounter. When Team GO Rocket returns, we’ll need your help to further reasearch this phenomon!

Shadow Pokemon IV’s

Shadow Pokemon appear to have randomized IV’s between 5 and 15. Pokemon appear to have a set IV combination per species and per trainer level. For example, all Level 40 trainers should encounter the same Snorlax, and all Level 38 trainers should encounter the same Snorlax. We’ve seen instances where level 40 players have encountered the same Pokemon with different CP, so multiple combinations may be involved.

This was one of the tougher nuts to crack when trying to establish a formula that fit all known Shadow Pokemon. We’re eagerly looking forward to Team Rocket’s return to gather more field research!

Shadow Pokemon Formula & Examples

Now let’s put it all together! Once we know a Pokemon’s level, base Attack multiplier, IV’s, and the trainer level, we can reproduce Shadow Pokemon CP like this:

Shadow Pokemon CP = ( (Base Attack + Attack IV) * Base Attack Multiplier * Trainer Level Factor * (Base Defense + Defense IV)^0.5 * (Base Stamina + Stamina IV)^0.5 * CPM^2) ) / 10

Let’s take our Shadow Swampert, level 40 with a x2 Base Attack Multiplier and a 14/12/5 IV combination, and plug it into this formula:

CP = ( (208 Base Attack + 14 Attack IV) * 2 Base Attack Multiplier * 1 Trainer Level Factor * (175 Base Defense + 12 Defense IV)^0.5 * (225 Base Stamina + 5 Stamina IV)^0.5 * .7903 CPM^2 ) / 10 = 5751

How much effective Attack does Shadow Swampert have? Watch out!

Attack = (208 Base Attack + 14 Attack IV) * 2 Base Attack Multiplier * 1 Trainer Level Factor * .7903 CPM = 350.9

Below is a table of other Shadow Pokemon players have encountered, their in-game CP, and associated Pokemon level and IV’s.

Pokemon CP Tier Level Attack

Multiplier IVs Bulbasaur 2258 1 25 x3 10/14/11 Ivysaur 3432 1 25 x3 10/8/13 Charmander 1985 1 25 x3 11/12/12 Snorlax 2356 2 27 x1 12/5/7 Crobat 1931 2 27 x1 11/6/6 Dragonite 2762 3 30 x1 9/5/11 Charizard 1925 3 30 x1 8/5/6 Swampert 5751 4 40 x2 14/12/5

Here are some Shadow Pokemon that have been encountered by players with different trainer levels:

Pokemon CP Trainer Level Trainer Level

Factor IVs Snorlax 2356 40 x1 12/5/7 Snorlax 2151 38 x0.92 8/6/14 Rattata 1487 40 x1 14/12/8 Rattata 1128 34 x0.76 15/9/10

These Shadow Pokemon are more mathematically unique than other boss Pokemon we’ve encountered in the game so far, so we’re excited to see what lies ahead when Team GO Rocket makes their mischevious return!