CP Calculation


#1

It’s bothered me not knowing how the CP values on the hero cards are calculated. Here is some preliminary work on this:

Looking solely at the CPs of fully ascended 4* and 5* heroes, excluding last year’s Spring event, a simple linear regression gives a very good, but not perfect, fit using the formula:

CP = 40.26 * Stars + 5 * SpecialLvl + 0.2030 * Attack + 0.1650 * Defense + 0.080 * Health + 0.845 * Event + 3.62 * HotM

Standard error = 0.7595
Adjusted R-squared = 0.9808

So, 4* heroes start with a base of about 321 points (including the value of 8 levels of special attack) and 5* with a base of about 401. Attack is valued about 20% per point, while defense is about 16.5% per point, and health half of that.

The Event and HotM variables control for an effect I saw scanning the residuals from the simple form of the regression: Event heroes and, particularly, Heroes of the Month had CP values that didn’t line up with their estimated values. Event heroes have a small but statistically significant boost (0.845 points, P-value=0.3%). HotM have large and highly significant boost (3.62 points, P-value=1.7E-15). This suggests that SG just pins the HotM CP at 777 regardless of the underlying stats. I expect they’d rationalize that boost by pointing to the extra power of the special, but that opens a whole can of worms about trying to compare the value of specials across heroes.

BTW, I excluded Master Lepus and Jack O’Hare, specials from the Spring 2017 event, as they were large outliers and, as early one-off heroes, probably don’t tell us a lot about the current CP formula.

I intend to improve this calculation by adding in data from incomplete ascensions and 3* heroes. Anyone who’s got data they’d like to contribute, please throw it my way!


Minor Adjustment to Hero Powers
Team power is misleading across star levels (considerably improved as of version 15.1)
How is Team power calculated?
#2

That’s impressive and convincing stuff. Thanks for sharing.

If you assume that HOTMs are pinned at 777, does excluding them (and their variable) improve your already bloated R-squared?


#3

Putting in two vectors of indicator variables to control for the HotM and Event effects improved the adjusted R^2.


#4

How about if you confine the regression to standard heroes, excluding all special event and HOTM characters? I’m just speculating that if there has been some manual fiddling with CP values for these heroes, then excluding them from the analysis might provide a cleaner formula for the others.

(Mind you, I’m really nit-picking here in an attempt to add some value - what you’ve found already looks pretty clean. Feel free to shoot me down.)


#5

So with a little more data (added Avalon heroes and the January–April HotM), the regression results are highly stable. Here are the updated values:

CP = 39.9 * Stars + 5 * SpecialLvl + 0.2043 * Att + 0.1651 * Def + 0.081 * Health + 0.614 * Event + 3.93 * HotM.

Standard error = 0.8125
Adjusted R-squared = 0.9833
N=66

Excluding the event heroes and HotM as @Brobb suggested doesn’t change the values much, as one would hope.

CP = 40.0 * Stars + 5 * SpecialLvl + 0.2029 * Att + 0.1661 * Def + 0.081 * Health

Standard error = 0.7573
Adjusted R-squared = 0.9730
N=41

No changes to my conclusions in the OP.


#6

Thanks, you helped me a lot


#7

For those of us who don’t know, what is “CP”? :slight_smile:


#8

No idea, but guess is ‘Card Power’


#9

Yes, it’s the “Power” number on the card. Sorry, I borrowed a Pokemon GO acronym.