Damage Calculation

Short story: work got overwhelming during the last weeks and it looks like it will continue like this for a while.

In addition, collecting data for special damage is extremely tedious. Instead of matching 3 suitable tiles you need to match at least 9 suitable tiles. If your hero AND the target survive that long, you get one single data point. Getting relatively complete data for a single defense value seems practically impossible, unless it’s from a popular mission like 8-7, which will still take quite a while to collect.

At least I got a little bit of data for comparing special damage from different special %.
First, Vela with 923ATK and 130% special % giving 1199 attack power compared to
Obakan 1-1 with 370ATK +18%ATK for 436ATK and 275% special % giving 1199 attack power.

Same target with 694 DEF. Both give the exact same damage range

DEF Special ATK ATK/DEF avg damage variance current Z-U Z-U variance actual min actual max
694 1199 1,72766570605187 171 8 175 8 163 179

Next is Berden3-50 with 493ATK +5%ATK for 517ATK with 325% special% giving 1680 attack power compared to
C-Wu4-70 with 728ATK +10%ATK for 800 ATK with 210% special% giving 1680 attack power

Same target with 818 DEF. slight difference for the min damage - probably just very unlucky.

DEF Special ATK ATK/DEF avg damage variance current Z-U Z-U variance actual min actual max
816 1680 2,05882352941176 235,5 11,5 237 11 224 247
816 1680 2,05882352941176 235 12 237 11 223 247

I’m willing to accept that this data is sufficient for our purposes.
=> the same attack power gives the same average damage and damage range

The variance of 12 is a surprise though. With 5% and rounding down we would expect a variance of 11.

new data:

Obakan special versus Little John: 694 DEF / 436 ATK x 275% = 1199 ATK - 28 data points - 174, 176, 179, 173, 165, 173, 169, 165, 169, 169, 165, 163, 169, 164, 173, 166, 173, 179, 168, 178, 167, 163, 175, 178, 176, 177, 163, 178

Berden special versus Tiburtus: 818 DEF / 517 ATK x 325% = 1680 ATK - 51 data points - 238, 231, 238, 240, 224, 244, 227, 233, 235, 237, 235, 229, 227, 240, 238, 229, 234, 236, 242, 227, 232, 227, 233, 237, 226, 226, 242, 242, 243, 228, 242, 233, 237, 226, 241, 228, 239, 243, 230, 244, 235, 238, 230, 239, 241, 225, 235, 229, 247, 234, 242

Costume Wu special versus Tiburtus: 818 DEF / 800 ATK x 210% = 1680 ATK - 48 data points - 226, 244, 225, 237, 232, 228, 230, 232, 242, 224, 232, 229, 234, 229, 227, 223, 244, 233, 234, 244, 238, 234, 240, 237, 235, 236, 229, 223, 245, 234, 227, 226, 223, 228, 230, 226, 242, 242, 226, 236, 226, 247, 229, 225, 235, 235, 239, 239

That’s too much praise for me. It was teamwork with @u2371. :sunglasses:
I wouldn’t have found that formula by myself.

Our current Z-U formula is kind of summed up in this post here.
Since then the parameters have been updated and have slightly changed.
We’ve investigated mostly tile damage so far and started to check on special damage.

Shall we make a summary post with the current status of the formula?

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