# The Maths Of Pokémon Go – Calculating Individual Values (IV)

I started Pokémon Go as a bit of a novice.  I knew what Pokémon was to an extent, but had never played it.  Jumping on the bandwagon, I downloaded the game and began to catch them all.  Within not a lot of time at all, I was up to my eye balls in Rattatas, Pidgeys and Drowzees.

I knew there were gyms where you needed strong Pokémon and I knew you could transfer, evolve and power up.  However, I didn’t really know which monster I should be doing what with.  I started by plotting graphs of CP against HP to check the ratios and anything below the line went.  Anything above average was fair game.  I was still left with loads of the little critters though.

That’s when I discovered Individual Values after a Google search but getting to the bottom of how to calculate them appears to be one of those secrets that you need to be part of a special group to know.  People talk about it, but in a way where they expect everyone else to just get it.  Everywhere just says to go online to an IV calculator, but I wanted to know how they work.

So here’s the maths of calculating how good your Pokémon really are.

## Some explanation…

Here’s my Mr Mime.  He’s going to be our example.

Starting at the top…

CP – in this case the CP is 640.  This is the main stat in Pokemon Go and stands for “Combat Power”.  There is a max CP per Pokémon determined by its type and how good it is.

That white semi-circle – that shows how much CP there is still to go to reach the max.  So, as you can see, if I power up Mr Mime using stardust and candies he can get maybe 20% stronger.

HP – this example is 49.  HP stands for Hit Points / Health Points and represents the maximum amount of damage a Pokémon can take in battle before fainting.

Stardust – this isn’t the big number in this instance, it’s the smaller number next to the “Power Up” button.  Stardust is used to power up Pokémon.  The higher the level the Pokémon already is, the more stardust required.

## What other numbers are there?

The CP, HP and Stardust are the only numbers we can get from the Pokémon itself.  However, what we’re trying to calculate are hidden stats called Individual Values, or IV for short.

There are three types of IV – Attack, Defence and Stamina.  Stamina directly links in to HP while Attack and Defense don’t have any direct correlation at all.

To start with these IVs, we first need to know that each species of Pokémon has base stats that have been discovered  by The Silph Road via some clever data mining.  You can find these base stats online, but for our Mr Mime example:

On top of the base stats, each individual Mr Mime has its own stats that we need to work out.  What I wanted to know was “how?”

To start with, it’s really REALLY important to know that this is TRIAL AND ERROR!!!  There are a multitude of IV combinations most of the time that get narrowed down as you power up your Pokémon.

## The Starting Point – Level

The first thing we’re going to do is get our Pokémon’s level.  We do this by finding the amount of stardust needed to power up our Pokémon and putting it in to some more mined game data.  I’ll try to put all this game data in a spreadsheet somewhere for you to download.

Each amount of Stardust corresponds directly to a level.  So 200 stardust to power up starts is at level 1.  400 stardust is level 3.

My Mr Mime requires 1900 stardust which will start me off at level 15.  That puts me in the ballpark, so to speak.

## CP Multiplier

Having the level, we can then find something called a CP multiplier or scalar.  Again, these were all found by data mining and each level has its own number used in the forumlas that we will, eventually, get to.

At this stage you should note that there are such things as half levels.  These happen when a Pokémon has been powered up, so it’s useful to remember when you’ve done this.

Remembering that we’re working with trial and error, I usually go a whole number above and below my stardust defined level (and take the half levels too, if applicable.  My Mime is level 15, so I’ll get multipliers for 14, 15 and 16.

Base stats, levels, multipliers… I’m good to get started with the maths!

## Stamina First

As we said before, stamina directly links to HP so the Stamina IV is the first equation to solve.  Remember that we’re narrowing down to a range rather than, necessarily, finding the exact stats.  I would recommend having a spreadsheet to do your calculations given the number of possible combinations.

This is the forumla:

$HP = (BaseStam + StamIV) \times CPmultiplier$

I create a table using all the possible IVs for all our levels.  I can do this because the minimum possible IV for all characteristics is 0, and the highest is 15. What we’re looking for is the rounded down result of our equation to equal the HP of the Pokémon we’re testing.

We’re looking for 49, and we can see that that is possible if Mr Mime is level 15 and has a Stamina IV of 15, or is level 16 with a Stamina IV of 12 or 13.

We have a start!

## Attack and Defence

The formula here is much more complicated, which is why a spreadsheet is useful.  It’s this:

$CP = \frac{(BaseAtk + AtkIV) \times (BaseDef + DefIV)^{0.5} \times (BaseStam + StamIV)^{0.5} \times CPmultiplier^2}{10}$

Again, we’re going to trial and error to try to get our test subject’s CP out of that formula and this deduce our possible IVs.

I won’t put the entire table because it’s massive, but this is the idea:

Do some filtering to find our magic number (640) and we end up with 11 possible combinations.

I can then narrow this down further, because I know from my Stamina calculation that the Stamina IV at Level 16 cannot be 15 and that it has to be 12 or 13.  I can lose the 6/11/15, 8/6/15 and 10/1/15 combinations, leaving me with 8.

## Percentage Perfection

If you choose to, you can then work out how perfect your Pokémon is.  This is a simple formula! You simply add up all the IVs in a combination and divide by the maximum possible which is 45.

$Perfection = \frac{AtkIV + DefIV + StamIV}{45}$

Obviously you then multiply by 100 for a percentage.

## Appraisals

“That’s great,” I hear you say, “but what do I do with all those combinations?”

Well, as I said, these are indicative.  As you power up, the number of combinations of reduces, but powering up takes stardust which is a scarce resource just to test with.

So maybe you’re looking at your Mr Mime and you’re thinking that there’s some low numbers in there so maybe you’ll transfer him to The Professor.  But then there’s all those 15s at the top… What if you lose a perfect Pokémon?!

Here’s where the Appraisal featureis useful.  You team leader will do the appraisal and give you a number of messages.  They’ll do an initial review, tell you which IV is the best, give a general assessment and then tell you the size of your Pokémon.  Each leader has their own message, but they can be translated.

Each message relates to your Pokémon’s percentage perfection as shown in the screen shot above from IGN.  The other comments to be translated are the general assessment ones:

As you can see, each comment gives you an indication of one IV.  From my research, it does NOT always refer to the strongest one that you’re also told about.

Here’s Candela reviewing my Mr Mime.

We have –

• Amazing – 81-100% perfection.
• HP (stamina) is strongest, but Candela is equally impressed with both attack and defence.  Because of the brackets in the next message, this doesn’t mean that all IVs are the same.
• Blown away by the stats.  This means that we have at least one 15.  But wait… if all three IVs are as strong as each other, they must all be 15!
• It’s also a sizeable Pokémon. (With size there are 5 levels, however they’re phrased – no comment, big, very big, small and very small.)

Not the best example maybe, but you can see how appraisals can be used to further narrow down your IV combinations.

There is more maths, I just haven’t quite worked it out yet.  This is the most useful one though, in my opinion.