## 03 December 2017

### WildStar - Calculating Assault Power Rating on Items

As I mentioned in my introduction post. This blog will contain theorycrafting and theorycrafting here we go.

#### A curious mind always seeks for answers

and a game developer playing games while striving to improve their performance in a dungeon or raid might wanna figure out how the developers of the game set the stats on items.

Now, of course, you could assume:
"Hey, let's just give this item... say... hmmm.. I dunno... 340 Assault Power Rating"
However, when Carbine Studios introduced the prime system to the game scalable (scale + able) items were added. If items scale programmers are not going to set every single item. We're talking about programmers, they might be called engineers or developers but in the end, they're humans and they're lazy.
"The computer does it for me."
And so we can conclude that there's some kind of function or system going on in the background determining what stats items have.

#### So how do you figure it out then?

Using theorycrafters best friend Google Sheets (not sponsored) and gathering a sample size. The sample size is the items that have the stats on them. So I've been running the same instances over and over again to get the same item with different item levels. The reason why I've run the same instance getting the same item on different prime levels getting different item levels is simple. It's the same when doing experiments in physic lessons or as a researcher. Keep all variables the same and change one. Thus you can determine the correlation between every single variable. In this case, my variable was the item level.

So now I've inserted all the data into a Google spreadsheet (still not sponsored) and calculated the difference between each item. The range of items I've got was item level 65 to item level 85 with a step of 5 item levels per item. So a sample size of 5 items. Additionally, thanks to a friend, I've got an item level 100 and item level 130 item as well.

#### Now the math begins...

Now we've got our data:

 Item Name Prime Level Item Level Assault Power Rating Stat Increase Gauntlet Gloves 0 65 175 (175.5) N/A Gauntlet Gloves 1 70 189 (189) 13.5 Gauntlet Gloves 2 75 202 (202.5) 13.5 Gauntlet Gloves 3 80 216 (216) 13.5 Gauntlet Gloves 4 85 229 (229.5) 13.5 Gauntlet Gloves 10 100 270 (270) 40.5 Gauntlet Gloves 13 130 351 (351) 81

Looking at the data we notice that every 5 item levels it increases by 13.5.
So it's linear which means it should work for all item levels in between as well as higher and lower.
Small calculation: 13.5 divided by 5 equals 2.7.
Great! So now we know each item level increases the value by 2.7.
We can assume the function to be

f(x): y = 2.7x + t
with y being the assault power rating m being the modifier 2.7 and x being the item level

Now we need the t. By inserting the item level and the assault power rating as y of the item we can solve for t:

175.5 = 2.7 * 65 + t
175.5 = 175.5 + t | - 175.5
t = 0

Thus the function is:

f(x): y = 2.7x + 0
f(x): y = 2.7x
with y being the assault power rating, m being the modifier 2.7 and x being the item level

Non mathematically said:

f(itemLevel): assaultPowerRating = 2.7 * itemLevel

Now, this is a surprise. The item level multiplied by 2.7 equals the assault power rating of the item.

#### Generalizing

Okay. Nice to know it works for this one item but it might not work for every item or does it?
I've tested it on several items and all scalable items, as well as many others, support this correlation.
As long as they're gloves!
Thus there must be a different formula for a different type of item.
Now experience shows it might be the same formula with a different modifier respective to the item and looking at different items shows this.

If we take an item for the leg spot. Assault power rating is 607 and the item level is 135. We divide the assault power rating by the item level the result is 4.49.... rounded up to 4.5. Why can we round here? the assault power rating on the item is rounded too! It's 607.5. You can calculate this by comparing the change in total assault power rating with the item and with no item on the slot.

With this new value of 4.5. Let's try it with different items of the same item type.
The same result always 4.5.
Now we can test all the item types through.

#### The Result

And here's the result after testing everything except the weapon:
Assault Power Rating is calculated:

 Slot Type Formula Head 3.6 * Item Level Shoulders 3.6 * Item Level Breast 4.5 * Item Level Gloves 2.7 * Item Level Pants 4.5 * Item Level Shoes 2.7 * Item Level Weapon Attachment 3.6 * Item Level Support System 3.6 * Item Level Implant 3.6 * Item Level

The weapon is a different story. I'm gonna write about that one once I've done the respective tests and math. I also need a sample size. If anyone has figured that out already please tell me. :)
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