Finally got enough data for the few data points for specials from my blue mono versus my alliance member (friendly raid). Getting the complete min-max range for specials is really taking a long time…

DEF |
Special ATK |
ATK/DEF |
avg damage |
variance |
current Z-U |
Z-U variance |

830 |
1199 |
1,44457831325301 |
139 |
6 |
143 |
7 |

694 |
1199 |
1,72766570605187 |
171 |
8 |
175 |
8 |

818 |
2944 |
3,59902200488998 |
475 |
23 |
474 |
23 |

694 |
3156 |
4,54755043227666 |
572 |
28 |
573 |
28 |

818 |
4191 |
5,12347188264059 |
713 |
35 |
709 |
35 |

Z-U formula still with the following parameters (until further improvement):

a = 25

b = 0.0392

k = 0.93

c = 0.0116 (or 0.29, if c is added directly without multiplying it with a, i.e. 0.29 = 25 x 0.0116)

For special damage, the calculated damage is currently multiplied with “x3 x90%”

=> Not perfect, but quite close to the actual damage.

@u2371, this data should help with finding improved parameters

=> There is not a single outlier to the 5%, so the 5% variance clearly apply to special damage, as well.

Bonus: Grimm special versus Chao (for minor damage = -50% damage): 830 DEF / 1070 ATK x 295% = 3156 ATK

DEF |
Special ATK |
ATK/DEF |
avg damage |
variance |

830 |
3156 |
3,80240963855422 |
255,5 |
12,5 |

This looks like the variance is actually added here before the damage factors kick in, then everything is rounded down.

The numbers fit with the following sequence

- calculation of average special damage: 511 damage
- calculation of 5% variance: ±25
- min damage for this is 486 and max damage is 536
- now the -50% damage reduction for minor damage then gives: min damage = 243 and max damage = 268

which is exactly the range that I found.

Then again, this doesn’t fit with the minimum variance of ±1 in some cases, so there must be more to this.

data:

Vela special versus Chao: 830 DEF / 923 ATK x 130% = 1199 ATK - 67 data points - 135, 143, 144, 143, 142, 135, 135, 134, 136, 145, 138, 141, 134, 143, 140, 141, 138, 137, 141, 136, 138, 138, 142, 139, 139, 140, 139, 137, 140, 140, 139, 140, 142, 137, 145, 136, 141, 135, 133, 138, 139, 136, 139, 133, 137, 134, 135, 145, 143, 139, 133, 139, 142, 145, 134, 145, 145, 140, 145, 138, 144, 141, 135, 140, 133, 141, 136

Vela special versus Little John: 694 DEF / 923 ATK x 130% = 1199 ATK - 66 data points - 166, 166, 178, 170, 173, 171, 171, 164, 178, 173, 170, 178, 175, 176, 169, 169, 176, 168, 176, 173, 169, 177, 176, 171, 174, 166, 179, 167, 169, 165, 173, 163, 175, 176, 164, 177, 168, 165, 165, 164, 164, 172, 164, 175, 176, 173, 174, 169, 179, 171, 178, 176, 165, 175, 169, 177, 174, 178, 171, 167, 164, 177, 168, 169, 172, 176

Grimm special versus Little John: 694 DEF / 1070 ATK x 295% = 3156 ATK - 61 data points - 568, 586, 547, 562, 597, 600, 562, 552, 546, 574, 551, 598, 573, 555, 593, 566, 546, 567, 554, 598, 576, 566, 551, 547, 550, 571, 572, 598, 559, 593, 559, 550, 575, 557, 596, 593, 575, 545, 567, 563, 557, 600, 594, 569, 563, 587, 546, 593, 575, 572, 552, 559, 544, 585, 547, 545, 574, 574, 562, 551, 592

Fenrir special versus Kiril: 818 DEF / 920 ATK x 320% = 2944 ATK - 59 data points - 489, 455, 493, 494, 492, 459, 482, 462, 473, 478, 461, 454, 480, 484, 459, 492, 486, 481, 472, 472, 472, 453, 478, 498, 479, 476, 463, 483, 471, 471, 465, 483, 480, 491, 496, 486, 472, 455, 468, 483, 461, 492, 473, 487, 458, 477, 470, 495, 472, 490, 495, 459, 478, 484, 454, 478, 452, 492, 467

Magni special versus Kiril: 818 DEF / 998 ATK x 420% = 4191 ATK - 65 data points - 693, 736, 705, 721, 737, 694, 742, 705, 708, 734, 736, 718, 704, 722, 748, 707, 679, 687, 688, 728, 697, 693, 735, 678, 731, 748, 721, 746, 720, 684, 710, 708, 708, 744, 714, 695, 692, 688, 715, 685, 741, 747, 691, 742, 692, 746, 699, 741, 715, 706, 724, 703, 740, 725, 742, 709, 684, 685, 730, 687, 701, 714, 735, 684, 748

Grimm special versus Chao (for minor damage = -50% damage): 830 DEF / 1070 ATK x 295% = 3156 ATK - 59 data points - 260, 251, 243, 245, 251, 243, 267, 253, 249, 254, 245, 261, 246, 260, 265, 255, 249, 243, 258, 243, 255, 247, 244, 263, 244, 268, 249, 251, 263, 247, 262, 257, 260, 254, 250, 262, 263, 243, 243, 244, 253, 266, 249, 254, 244, 247, 249, 259, 260, 246, 267, 246, 265, 268, 247, 260, 252, 244, 243