# Damage Calculation

Done a few runs at 8.7 defense always 343

26 runs
Atk 595, average damage 54, min 52, max 54, variance ±2.
5% variance 2.7 so seems OK.
Exact numbers average 54.04

82 runs
Atk 761, average damage 72, min 69, max 75, variance ±3.
5% variance 3.6, seems OK
Exact numbers, average damage 72.22 variance + 2.8 / - 3.2

108 runs
Atk 885, average damage 86, min 82, max 90, variance ±4.
5% variance 4.28 seems OK.
Exact numbers, average damage 85.79, variance +4.21 / - 3.79

I’m not sure if that’s what you really want, if not just say what should be different, I’m not always doing 8.7 and I don’t always have the time to record it, but if I have I can probably try other combinations in the future.

Some other funny information, probably not useful for damage calculation, but with 108 stones I had a single crit hit from the 2% class talent. So I would say taking the crit node there is pretty much useless…

These are summary of data against 744 def at low ADR (ADR<k). This will be helpful for 343 def test.

Average Dmg Minimum Atk/Def
5 0.188172043
6 0.22983871
7 0.271505376
8 0.314516129
9 0.345430108
10 0.385752688
11 0.428763441
12 0.471774194
13 0.514784946
14 0.557795699
15 0.586021505
16 0.629032258
17 0.672043011
18 0.715053763
19 0.758064516
20 0.786290323
21 0.829301075
22 0.872311828
23 0.915322581

“Minimum Atk/Def” mean minimum Atk/Def that you need to get that Average Damage.

I also collect data for my new project call “Order of Action” (each action in each turn step by step). So, I don’t have enough time to test this.

All data is welcome.
It might be hard for Aife, but her efforts will be fully appreciated

Same here, although I’m finished with S3. Oh right, I have to do Oni tower now…

Yes. thank you, that is correct.
343DEF/491ASTK/42/2 it is then.

When you get the first damage data for a new ATK value, you can check the 5% (rounded down, but minimum 1) and get a very good impression on the variance that you will find with more data.
For example, you get 47 damage. The 5% give you a variance of ±2. As soon as you get enough data that fits with this range, e.g. 44-48 (=> [44+48]/2=46 as average value), you are finished and can record: “343DEF/XYZATK/46/2”

No worries. It also takes quite some time for me for this data collection (I’m even recording videos for my battles against my alliance member). This is a tedious task, it takes a lot of time to record and analyse and when it’s very stressful at work, it becomes hard to motivate myself for this…

Thank you for the data.
Is the “max 54” correct, or should it be “56”?

@u2371 and I are taking the easy route here and use the average value of the complete damage range as the “average damage”.
For this data point we take 72 as the average damage and ±3 for the variance. For convenience we put all of this in one line:
343DEF/76ATK/72/3

That would great as this data collection goes much faster (and easier) if several players help. It will still take a while.
As a side effect of more players helping with the data collection, the resulting, fine-tuned formula will have been tested much more than just by 1-2 players and is more robust/trustworthy/what-is-the-correct-word?.

Haha, yeah, 2% is really low. I think this makes more sense when this hero also has a crit troop, but minions will profit even from the 2%

Something that will look like the following (purely hypothetical) sequence?

1. attacker specials
2. tile attack
3. minion attack
4. DoT
5. fiend attack
6. equalizer
7. defender specials from left to right
… and so on

Should be 56

OK, so you don’t need a “real” average, just the middle of the damage range? That makes it a lot easier to collect if I just have to look for the maximum and minimum damage.

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Yes, for now it look like this

Summary - Order of Action

# Turn Start

• (?) Raid overtime damage increase

• (?) Fighter Talent active and revive from Buff on your heroes (E.g. Tyr, Atomos)

• S4’s Biome Effect & Aether Quest’s Buff Effect

• Auto “Special Skill-like” effect (E.g. Mindness Attack, Baldur’s buff, Stonecleave buff) and Spell Slayer (E.g. Hansel’s ailment) on your heroes. (Multiple Check ?)
• “The battle end here”
• Special Skill & Battle Item (Multiple Check)
• Minion & Fiend (on your heroes) attack
• Buff and Ailment on your heroes (E.g. Heal over Turn, Damage over Turn) and (?) second Spell Slayer active
• (?) Counter turn of any status effect that cast by enemy reduce by 1 (Buff on enemy and Ailment on your heroes)
• (?) Starfall Family effect (on your heroes)
• (?) Sorceror Talent from your heroes active

• Fighter Talent active and revive from Buff on Enemy (E.g. Tyr, Atomos)

• Druid, Paladin Talent on Enemy active (Druid summon minion, Paladin get buff)

• War Effect active (Undead Horde, Atteck Boost, Arrow Barrage, War Equaliser)

• ## Enemy (defense team) Turn

• Auto “Special Skill-like” effect (E.g. Mindness Attack, Baldur’s buff, Stonecleave buff) and Spell Slayer (E.g. Hansel’s ailment) on Enemy. (Multiple Check ?)
• Special Skill (Multiple Check)
• Slash Attack
• Mana Regen each turn
• Minion & Fiend (on enemy) attack
• Buff and Ailment on enemy (E.g. Heal over Turn, Damage over Turn) and second Spell Slayer active
• (?) Counter turn of any status effect that cast by your heroes reduce by 1 (Buff on your heroes and Ailment enemy)
• Enemy S4 Gem attack.
• (?) Starfall Family effect (on enemy)
• (?) Sorceror Talent from enemy active
• S2’s Poison Mist and Underwater Effect & Ninja Tower’s Toxic Vapor and some Blessing Effect

# Turn End

The problem for now is there are still some pair that I don’t know the exact position because they are hard to test and I don’t have enough time too add detail since this will be my first “player guide” topic.

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update on the bosses of S1 8-7 with their 343DEF:
Z-U formula now with the following updated 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)

“avg damage” and “variance” are the actual values.

DEF ATK ATK/DEF avg damage variance updated Z-U Z-U variance
343 161 0,469387755102041 11 1 12 1
343 171 0,498542274052478 12 1 12 1
343 190 0,553935860058309 13 1 14 1
343 208 0,606413994169096 15 1 15 1
343 231 0,673469387755102 17 1 17 1
343 249 0,725947521865889 18 1 18 1
343 269 0,784256559766764 19 1 19 1
343 284 0,82798833819242 20 1 20 1
343 300 0,874635568513119 22 1 22 1
343 315 0,918367346938775 23 1 23 1
343 326 0,950437317784257 23 1 24 1
343 344 1,00291545189504 26 1 26 1
343 360 1,04956268221574 27 1 28 1
343 431 1,25655976676385 35 1 36 1
343 491 1,43148688046647 41 1 42 2
343 595 1,73469387755102 54 2 54 2
343 637 1,85714285714286 58 2 59 2
343 761 2,21865889212828 72 3 73 3
343 848 2,47230320699708 82 4 82 4
343 885 2,5801749271137 86 4 86 4
343 917 2,6734693877551 90 4 90 4
343 921 2,68513119533528 90 4 91 4
343 986 2,87463556851312 98 4 98 4
343 1049 3,05830903790087 105 5 105 5
343 1068 3,11370262390671 107 5 107 5
343 1301 3,7930029154519 133 6 133 6
343 1539 4,4868804664723 160 8 160 8
343 1854 5,40524781341108 195 9 195 9
343 2110 6,15160349854227 223 11 224 11
343 2722 7,93586005830904 292 14 292 14
343 2981 8,69096209912536 320 16 321 16
343 4869 14,1953352769679 533 26 533 26

Let’s take look a the diagrams. First, tile damage over ADR (attack/defense ratio) - Z-U formula is only shown for the 343DEF :

All of the collected data here has a 5% variance around the average damage. The first linear part of the damage curves for 343DEF and 744DEF aligns. As soon as the second linear part kicks in they separate and drift apart further and further.
We are very close to the actual tile damage values with our current bi-linear Z-U formula.

A different way to show the very same data uses damage over (total) attack:

@u2371 please optimize our bi-linear formula some more with this new data on 343DEF

We are assuming here that this tile damage formula works not just for raid and the S1 8-7 mission, but also for all other missions and quests. If anybody finds evidence to the contrary, please post it here, so we can check and adapt, if necessary.

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So, here’s some data I compiled:

Aife: 343/174/12/1 (21 attacks)
Brienne: 343/276/19/1 (21 attacks)
cHu Tao: 343/627/56.5/1.5 (15 attacks, max 59, min 55)

I happened to have a few numbers for 773 and 833 that i caught on video and they line up with what you have above, but i need to collect a few more maybe. there was one attack each by Hu Tao and cCaedmon, and pretty sure both were from dragon bombs, where all the tiles hit quite a bit harder than in other attacks. is there some kind of bonus for tiles that come from a dragon bomb?

anyway, happy to keep collecting, i’m in 8/7 most days. let me know if you want any specific range for attack. and Aife was actually no problem, if she dies before or during the bosses, the green tiles still count as her attack…

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Thanks!
I’ve added the data in my file.

5% of 59 is 2.95. rounded down it is 2.
5% of 55 is 2.75. rounded down it is 2.
=> that looks good as 343/627/57/2

5% of 96 is 4.8. rounded down it is 4
5% of 100 is 5.
Our current data has the data point 343/986/98/4, so the 989ATK will give either 98±4 or 99±4.
=> we need more data for this 989ATK. Please continue gathering data for this

yes, will do. the attacks were all quite tight in range, all 97-100 with one outlier at 95. i have not seen anything above 100 yet, but the sample size is quite small. for the next couple of days i’ll just collect for this, it will be easy.

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I still have no idea For now, I use table to predict extremely accurate average damage for low ADR (ADR < k). Here is a new pdate table

Average Dmg Min Known Atk/Def Max Known Atk/Def Min Known Atk for 343 Def Max Known Atk for 343 Def
5 0.188172043 0.228494624 64.543 78.374
6 0.22983871 0.27016129 78.835 92.665
7 0.271505376 0.313172043 93.126 107.418
8 0.314516129 0.344086022 107.879 118.022
9 0.345430108 0.384408602 118.483 131.852
10 0.385752688 0.427419355 132.313 146.605
11 0.428763441 0.470430108 147.066 161.358
12 0.471774194 0.51344086 161.819 176.110
13 0.514784946 0.556451613 176.571 190.863
14 0.557795699 0.584677419 191.324 200.544
15 0.586021505 0.627688172 201.005 215.297
16 0.629032258 0.670698925 215.758 230.050
17 0.672043011 0.713709677 230.511 244.802
18 0.715053763 0.75672043 245.263 259.555
19 0.758064516 0.784946237 260.016 269.237
20 0.786290323 0.827988338 269.698 284.000
21 0.829301075 0.870967742 284.450 298.742
22 0.872311828 0.913978495 299.203 313.495
23 0.915322581 N/A 313.956 N/A

The 284 Atk vs 343 Def data is the only data that improve this table. But all new data make we know that “At low ADR (ADR < k), same ADR always give exactly same average damage

The attack that can improve this table and more than 140 are 147, 191, 201, 245, 260 and 299.

I think if we can’t make our formula give 100% correct average damage value at low ADR (ADR < k), we will not be able to improve our formula at high ADR. That is why I focus on only low ADR for now.

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more data:
343DEF/201ATK/15/1
343DEF/245ATK/18/1
343DEF/260ATK/19/1
343DEF/299ATK/22/1

Can’t provide data on 140ATK, 147ATK and 191ATK as I have no matching set of neutral hero+troops for those.

Maybe someone has a purple troop with +12%ATK and an unleveled Silthus 1-1 and some time to help out here?

Doesn’t that mean that we could get an accurate “k” when we investigate several DEF values and get data for the area at k=0.93? The moment the damage values for the same ADR deviate from each other, we are beyond “k”?

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Thank you. This is new update table.

Average Dmg Min Known Atk/Def Max Known Atk/Def Min Known Atk for 343 Def Max Known Atk for 343 Def
5 0.188172043 0.228494624 64.543 78.374
6 0.22983871 0.27016129 78.835 92.665
7 0.271505376 0.313172043 93.126 107.418
8 0.314516129 0.344086022 107.879 118.022
9 0.345430108 0.384408602 118.483 131.852
10 0.385752688 0.427419355 132.313 146.605
11 0.428763441 0.470430108 147.066 161.358
12 0.471774194 0.51344086 161.819 176.110
13 0.514784946 0.556451613 176.571 190.863
14 0.557795699 0.584677419 191.324 200.544
15 0.586005831 0.627688172 201.000 215.297
16 0.629032258 0.670698925 215.758 230.050
17 0.672043011 0.713709677 230.511 244.802
18 0.714285714 0.75672043 245.000 259.555
19 0.758017493 0.784946237 260.000 269.237
20 0.786290323 0.827988338 269.698 284.000
21 0.829301075 0.870967742 284.450 298.742
22 0.871720117 0.913978495 299.000 313.495
23 0.915322581 N/A 313.956 N/A

I think no. “k” is in between 23 and 24 average damage. Investigate at the point that change 23 to 24 average damage might able to find accurate “k” but the problem is the bonus damage may have irregular gap like “21 32 32 32 32” at low ADR. Anyway, we have to understand the “21 32 32 32 32” first if we want 100% accurate. But I still have no idea

Could you set up exactlyt 500 or 750 defense for test ?

a quick attempt

first damage recorded is 15. 5% of 15 is 0,75 (rounded down 0, but minimum 1)
17 tiles recorded in the range from 15 to 13. then is correct saying that

343DEF/199ATK/14/1 ?

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I didn’t check that Silthus 1-1 (178 atk) with +12%ATK troop will have 199 atk not 191 attack.

Thank for your test @UroSecondo but sadly it doesn’t improve the table

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Well then… Gan Ju, I choose you!
(Gan Ju level 1.2, ATK 168 + 14% troops)

first damage recorded 13.
32 tiles recorded in the range from 12 to 14.

343DEF/191ATK/13/1

2 Likes

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

1. calculation of average special damage: 511 damage
2. calculation of 5% variance: ±25
3. min damage for this is 486 and max damage is 536
4. 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

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The different between our function’s average damage and actual average damage look like what happen in tile damage but is larger. I think it doesn’t fit with the minimum variance of ±1 in some cases because of %Atk of special skill which make it larger or special skill really have slightly different a,b,c,k value. I think we might have to solve that low ADR problem before go any further. But special ATK is rarely in low ADR range, so we ,might have to go back to tile damage.

About special skill I have a question, is “1000 Atk with 200%Atk” exactly same to “500 Atk with 400%Atk” against any defense ? I remember that you already test they and they are same but I am not sure if I remember right or not.

It seem to be like that.

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I quickly noticed there was a massive +/- gap in the formula posted by the OP when considering current heros.

For example: Krampus vs Gefjon

Where the Defense and Attack stats are rather large.

So, I definitely agree all of this data mining/mapping is needed to get an actual understanding of how the various stats, buffs, etc affect damage.

That being said, since this new formula was presented like 1/2 through the thread, it’s kind of burried.

It would be beneficial to have an OP that you could update as you evolve your formula. Because, as written, I’m pretty lost on where the variable data is being pulled from (IE: What numbers to plug in where).

If such a thread exists and I simply didn’t see it, then I apologize, and a link would be appreciated.

That all being said, I foind this thread because I was trying to determine if Jotts +atk tile modifier would come out to be more or less damage than Alexandrine’s +Crit % tile modifier.

I started using the original formula in this thread and totaling the damage over 100 tiles with the assumption that, at 54% crit , you would see 54 crit tiles in 100.

But, if the original formula is not reliable for this task … No Clue!!!

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@Dudeious.Maximus any idea how to update the outdated formula? @Zack had developed more accurate formula.

Get @Zack to post the new stuff.