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Warning: this a long post, if you are not interested in what’s going on, just read the calculations in Step 1-6 and ignore everything else.
I’ve heard recently a lot of rumours regarding the damage dealt by sylphs, and things that may influence it, so I decided to give it a try and make a thorough scientific experiment and reveal the damage calculations (or at least some parts of them).
To establish an easily reproducible environment, I took off all my astrals (especially the non-stat astrals), set troop count to 0, got rid of all my equipped items, medallions, wings and resistance crystals.
In all of the battles I fought against Iris sylphs on the 1st level of the atoll, and my equipped sylph was mostly a fully enhanced lv80 orange Apollo.
In a few other battles I used a newly created (lv28) white Amazon Queen.
After analyzing hundreds of battles and documenting my damage otuput, I came up with a formula that is capable of reproducing all the exact damage values I observed during my test.
Thus the following process calculates the sylph’s (awakened) non-critical auto-attack damage.
**Step 1:** calculate d = (hero\_primary\_atk + sylph\_primary\_atk – opponent\_defense) / 2.0,
/for example Iris’ defense on sylph atoll lv1 is 1000/
**Step 2:** calculate the resistance bonus/malus r = (100.0 – opponent\_effective\_resistance \* 0.12) / 100.0
(r = 1.12 if your opponent has -100 effective resistance, r = 0.88 if opponent has 100 effective resistance)
/effective resistance = opponent\_resistance\_vs\_your\_sylph\_type – your\_resist\_reduction/
If opponent\_effective\_resistance \< -166.7, it has to be limited to -166.7
**Step 3:** calculate the final average damage D = (d – 1.0) \* r \* sylph\_bonus,
where my white amazon has sylph\_bonus = 1.0, orange apollo has a bonus factor 1.1 (no idea about others)
**Step 4:** generate a random integer k in the interval [-10.0, 10.0]
**Step 5:** the final damage dealt by your sylph (auto attack) is D + D / 100.0 \* k
**Step 6:** with 20% probabilty increase this number by min(opponent\_def, 250.0 \* fate\_level) / 2.0,
due the “20% chance to ignore 250.0 \* fate\_level points of target’s defense” passive effect
If the formula above seems too complicated, we can try to interpret the consequences of each step.
**Remarks and consequences regarding Step 1:** your hero’s primary attack is obviously your own PATK if you are a knight or archer, and MATK if you are a mage. /I tested everything with my archer/
So if you are an archer, there is no point to increase your MATK, it won’t increase your Apollo’s or Gaia’s damage output.
Secondly, it is worth increasing your sylph’s primary attack. For example Apollo’s MATK = 0.0018 \* Apollo\_INT \* Apollo\_INT\_Aptitude, thus you can either increase its INT by rearranging your skill points into
intelligence (a lv80 apollo has 395 skill points to set, each reset costs 100 balens), or increase its INT\_Aptitude by giving sepulcrum to the sylph.
However, weaker/medium players should rather set skill points into Endurance to get more HP, because the difference in the total MATK is very low at low level/low colour sylphs (their Aptitude is very low).
**Remarks and consequences regarding Step 2:** when you look at your resistances at Battle Protection window, you see the effects of them by hovering the mouse over the numbers.
For example 410 electro resistance is displayed as ‘49% damage reduction to oneself’. You can simply get these numbers by multiplying the resistance value by 0.12 /i.e every 10 points of resistance gives a 1.2% damage reduction/.
Since 410\*0.12 = 49.2, it is displayed as 49% reduction. (From the formula you can see that these numbers are actually valid.) Another interesting thing is that the effective resistance is bounded from below.
I found this when I noticed that my apollo deals the same damage againstIris RES\_Reduction = 100 and with RES\_Reduction = 80.
Since Iris has a natural -100 resistance vs Apollo, and both -100-100 = -200 and -100-80 = -180 are smaller than -166.7, they behave the same way.
The magic number -166.7 was found by applying the final formula on my test data.
**Remarks and consequences regarding Step 3:** this was the hardest thing to find in my test, and I’m not even sure that this is the right way to interpret the different behaviour I experienced when changed from my orange Apollo to
my white Amazon. Since Amazon has a 1.0 bonus factor (i.e. no bonus), all the hidden calculations were easier to reveal in that case; but they didn’t work when I tried to apply them for the case of Apollo.
This bonus factor is a possible explanation for this phenomenon. However, I haven’t tested this with other (colour/type) sylphs, I’d appreciate any further feedbacks regarding this question. I don’t know whether my orange Apollo
has that bonus, because it is orange, or because it is Apollo (casher sylph). I admit the formula would look much nicer with D = d \* r \* sylph\_bonus, I just put that -1 there to make the fitting even better, the difference is very small.
**Remarks and consequences regarding Step 4 and 5:** the important thing here is that k is an _integer_, thus when you analyze your damage values, the large variation can be filtered out, because only 21 different numbers may
appear (or a bit more, see Step 6). I am pretty sure that this is the way, how the ‘floating damage’ calculations are implemented in the game, so if you have 17% floating damage, then k is an integer from the interval [-17,17],
and you can observe 35 different random damage values. If you understand this thing deeply, you will never ever calculate your average damage from your test fights by simply taking the mean value of the numbers.
The standard averaging method is very inaccurate and you would need a very large sample size to distinguish small differences reliably. However, finding these 21 values by using the formula requires less test fights and gives a very
accurate answer (+-1 absolute error due to some roundings/truncations).
**Remarks and consequences regarding Step 6:** very bad news for those who thought that ‘20% chance to ignore 250 \* fate\_lvl defense’ was very useful. It seems that the formula calculates the defense points ignored,
halves it, and simply increment the damage by this value. It means that this value doesn’t get mulitplied by the sylph\_bonus, or resistance bonus.
I haven’t tested it with different skills, so I don’t know if it gets multiplied by any other factors, but my guess that it is not. For example Iris on atoll has 1000 defense, so I may ignore 1k defense points only, increasing my final
damage by 500 with 20% probability.
I encourage everyone to try and test my formula, I’d appreciate every feedback, even if you think this is rubbish, and has no connection to reality (if anyone needs, I can provide the spreadsheet where I documented the fights).
These battles very excusively done in PvE battles, I don’t know if same formula governs the damage in PvP battles, too, and of course it doesn’t cover the case when block, crit or other damage enhancing/reducing sources are present,
I’d be glad if anonye had some time to extend my results to these cases. Furthermore I hope the idea behind Step 4 and 5 makes a lot of tests easier in the future, since they were the crucial steps in my investigations to reduce the number of test battles.
Finally, I’d like to thank Holo from s13 (US-West) for his work (with Step 2) and his valuable ideas and suggestions that helped me to move on when I was seriously stuck.
Hhit (s13-US West) a.k.a Tihh (s9-EU)

This is really impressive work. If this is correct, then we’re probably really close to solving the dmg formula exactly for all known variables.
What kind of distribution did you notice that the PRNG place over the floating damage range? Uniform? Gaussian? The fact that they are generating whole integers within such a small range says quite a bit about how R2 handles “random” events.
“However, weaker/medium players should rather set skill points into Endurance to get more HP, because the difference in the total MATK is very low at low level/low colour sylphs (their Aptitude is very low).”
Doesn’t the HP gain from endurance also suffer from the same drawback? If their INT aptitude is very low, it isn’t a stretch to think that their Endurance aptitude is also just as low. If it’s computed in a similar manner (maybe with a different multiplicative factor), then I don’t see how it wouldn’t.

his point is that the INT-to-dmg bonus for lower sylphs is so low that one might as well get the free HP from higher END sylph. but you are right to point out that low sylphs would also have low END Apt and might not give much hp either. i think this is quite easy to test, since the [Aptitude formulae](http://wartune.wikia.com/wiki/Sylph#Enchanting) are already well known.
* * *
HP = .0060 × (Endurance × END Aptitude) + Base
►1 Endurance gives (0.0060\*END\_Apt) hp.
►for every 1000 END\_Apt, you get 6hp per Endurance stat.
a lv50 sylph with 49\*5=245 adjustable stats & 1000 END\_Apt gets 245\*6 = **1470hp**
a lv70 sylph with 69\*5=345 adjustable stats & 2000 END\_Apt gets 345\*12 = **4140hp**
N.B: these values are bonus hp from just the adjustable stats
* * *
MATK = .0018 × (Intellect × INT Aptitude)
►1 Intellect gives (0.0018\*INT\_Apt) matk.
►for every 1000 INT\_Apt, you get 1.8matk per Intellect Stat.
lv50 sylph, 1000 INT\_Apt: 245\*1.8 = **441matk**
lv70 sylph, 2000 INT\_Apt: 345\*3.6 = **1242matk**
N.B: these values are bonus matk from just the adjustable stats
N.B: INT/STR also grants some mdef/pdef based on INT\_Apt/STR\_Apt; see the link above for the formula.
* * *
some of us would think: yea i’d rather have 1242matk over 4140hp. however, the 1242matk on the sylph only applies to the passive attack (i.e. the pellets while unawakened) then when awakened, it’s added to the player+sylph; whereas the 4140hp is directly added to your player hp once the sylph is equipped. probably some situations where you’d rather have the reliable hp than the less-reliable matk (i.e. when you won’t get to sylph much, or your sylph is used for support/tank rather than damage).
i have some blue sylphs ready for testing if you would like. maybe can shed more light on the “sylph bonus” thing, which is almost completely hidden and not mentioned ANYWHERE at all. if it’s purely a casher sylph thing, then non cashers all around will be vindicated — THAT’S WHY I KEEP LOSING TO CASHERS! haha. cathartic to blame cash/R2 for losing, ain’t it?

> *Originally posted by **[Holosoth](/forums/228/topics/415571?page=1#posts-8212094):***
>
> This is really impressive work. If this is correct, then we’re probably really close to solving the dmg formula exactly for all known variables.
>
> What kind of distribution did you notice that the PRNG place over the floating damage range? Uniform? Gaussian? The fact that they are generating whole integers within such a small range says quite a bit about how R2 handles “random” events.
>
> “However, weaker/medium players should rather set skill points into Endurance to get more HP, because the difference in the total MATK is very low at low level/low colour sylphs (their Aptitude is very low).”
>
> Doesn’t the HP gain from endurance also suffer from the same drawback? If their INT aptitude is very low, it isn’t a stretch to think that their Endurance aptitude is also just as low. If it’s computed in a similar manner (maybe with a different multiplicative factor), then I don’t see how it wouldn’t.
Can you do me a favour please Holo. I lack intelligence or motivation to work any of this stuff out or to be honest read it therefore I want an idiots guide in a simpletons paragraph. I’m an archer with a gaia so what top 5 things should i focus on?

> *Originally posted by **[WIGANSTE](/forums/228/topics/415571?page=1#posts-8213143):***
> > *Originally posted by **[Holosoth](/forums/228/topics/415571?page=1#posts-8212094):***
> >
> > This is really impressive work. If this is correct, then we’re probably really close to solving the dmg formula exactly for all known variables.
> >
> > What kind of distribution did you notice that the PRNG place over the floating damage range? Uniform? Gaussian? The fact that they are generating whole integers within such a small range says quite a bit about how R2 handles “random” events.
> >
> > “However, weaker/medium players should rather set skill points into Endurance to get more HP, because the difference in the total MATK is very low at low level/low colour sylphs (their Aptitude is very low).”
> >
> > Doesn’t the HP gain from endurance also suffer from the same drawback? If their INT aptitude is very low, it isn’t a stretch to think that their Endurance aptitude is also just as low. If it’s computed in a similar manner (maybe with a different multiplicative factor), then I don’t see how it wouldn’t.
>
> Can you do me a favour please Holo. I lack intelligence or motivation to work any of this stuff out or to be honest read it therefore I want an idiots guide in a simpletons paragraph. I’m an archer with a gaia so what top 5 things should i focus on?
There are 4 classes in this game: Knight, Archer, Mage, and Sylph
If you are one of the first three, put points in endurance (except if hp is a nonfactor, like in WB). If you are a sylph, put points in your primary attack.
**Reason:** Sylph aptitudes scale the benefit that the sylph’s stat points give you. Its primary atk (sylph patk, matk) doesn’t get involved except in sylph specific things. Its endurance just gives the player more HP.
**Conclusion:** If you _don’t_ rely on the additional attack power of your sylph that much (because it sucks, for example), then keeping your player alive longer is better. If you basically rely on your sylph for everything, then giving it (p/m)atk might as well be as good as giving your player more (p/m)atk.

i didn’t have too much time to do more experiments after I posted these calculations, however, from some fast tests it seems so that every sylph that is at least **blue** quality receives that 1.1 bonus factor, while white and green sylphs get only 1.0.

It turned out that the mysterious sylph bonus factor doesn’t depend on its color or type, it is their _Advanced Awakening_ ability once they reach lv55. The reason why I didn’t notice this was that I didn’t have high lvl white sylphs nor low lvl blue+ sylphs to test with. Thanks, Holo for this observation.
Another thing that might be relevant to people that evolved sylphs have some very high numbers in their skill description: ‘x% + y damage’, for example an evolved Hades can use Awe skill with ‘221% + 3875’ damage. My recent tests suggest an interpretation of these numbers. Simply change the formula in Step 3 to
**D = ( (d-1) \* x + y ) \* r \* sylph\_bonus**
So these numbers get multiplied by resistance and sylph\_bonus factor, which is pretty good if your opponent has a weakness against your elemental attack, not so good if they have high resistance.
Certain sets give damage bonus, like 2 items from lv60 set give +500 dmg, 2pcs from lv70 set give +1000. These numbers don’t get multiplied, they are just simply added to the final damage calculated in Step 6.

Another update: have you ever wondered about the **critical damage**? Now here is the formula that calculates the damage during critical hits:
(By the way I shouldn’t reply to my own posts, but anyway, I think some people are interested in these updates in my calculations, even though they do not reply to the topic)
**D= ((d-1) \* x + y) \*r \* syph\_bonus \* 1.5 + set\_bonus + fate\_bonus(with 20% chance)**
Very very bad news, the +500 and +1000 dmg from lv60-70 sets don’t get multiplied by this 1.5 factor, neither does the fate\_wheel bonus.
Small interesting thing, if you are an archer: archers have a passive skill to get 2% more dmg after each critical hit (lasts for 5 turns, stackable up to 5 times).
Actually when you first crit, this passive already affects your current damage and even your first critical hit is get multiplied by 1.02.
So the formula above for archers (at the first crit hit)
**D= ((d-1) \* x + y) \*r \* syph\_bonus \* 1.5 \* 1.02 + set\_bonus \* 1.02+ fate\_bonus(with 20% chance) \* 1.02**
At least those bonus numbers do get multiplied by this 1.02 factor.
Similar behavior (additional effect is active before your hit, not only after hit) can be observed when Hercules uses his Shock Chain skill: 187% + 1675 dmg and -30% mdef reduction for 3 turns. Actually this skill first decreases your opponent’s mdef by -30%, then deals 187% + 1675 damage and remains active for 3 more turns. Pretty nice.
So here is my current formula: among many other things it does not cover (yet) the following: PvP, block, will destroyer, determination, ruthlessness, critical rate, etc.
All my experiments were done with an archer against sylph atoll monsters.
![](http://i58.tinypic.com/20uejc1.png)

Would you expect that the crit bonus multiplier is 1.5 for everything (with corrections after such with -% crit mitigation) or possibly dependent on the opponent’s lvl, stats, etc?

You really think the developers put this much thought and intelligence in the game? I mean they can’t even make changes to the game without breaking some other aspect. Such as cross server ranks being bugged for, what, a week?

> *Originally posted by **[Dragu89](/forums/228/topics/415571?page=1#posts-8245625):***
>
> You really think the developers put this much thought and intelligence in the game? I mean they can’t even make changes to the game without breaking some other aspect. Such as cross server ranks being bugged for, what, a week?
That’s not how it works. They likely started with a basic damage formula and spliced in values as they added new features and content (e.g. sylph damage, passive skills, fate).

Hi! This is Miklos from wartune-balens.blogspot.com :)
Sorry for not replying your concerns earlier there, was on a holiday and just noticed your last reply and the link to your forum.
I’m glad to see someone else besides me puts effort into detailed testing and figuring out the exact combat formulaes. I hope together we can get to a more precise result. Earlier on, I did a lot of testing to figure out how combat works, my findings are here:
[http://wartune-balens.blogspot.hu/p/how-combat-works-in-wartune-basic.html](http://wartune-balens.blogspot.hu/p/how-combat-works-in-wartune-basic.html)
I see that there are a few differences in what you have found.
You say that the skill modifier (like a delphic’s 400%) is added after defense is reduced:
(atk – def) / 2 \* skill modifier
I say that all such multipliers are applied to the atk before def is subtracted and the value is halved:
(atk \* skill modifier – def) / 2.
The numbers I found corresponded with the later, looks like we have to do more testings to figure out which is right.
Also you mention that crit multiplier is 1.5.
In my findings, the crit damage was approx. 1.6-1.7 , depending on crit, but I just did hundreds of fights, took the average and compared normal to critical.
You also say that the resist multiplier (ie. will crystal bonus minus resist modifier) can be no more than 120%. You tested this or found it somewhere? I will do a testing on this, it made me curious.
Lastly, the main issue. I did some pretty simple, and long testing, and found that the sylph’s atk is NOT added to yours in awakened form:
[http://wartune-balens.blogspot.hu/2014/06/the-truth-about-sepulcrum.html](http://wartune-balens.blogspot.hu/2014/06/the-truth-about-sepulcrum.html)
And you state the opposite. I would really like to know who is right :)
In my testing, I used the same sylph, first did 50 attack, and when I switched points between hp and int, and also spent 500 sepulcrum, I got the same damage numbers.
You say you just did a test with an orange apollo and a while amazon, how could that help you figure out? The orange dealt more damage, but you can’t know if it was due to higher atk, or just the color bonus… You should have increased the apollo’s attack significantly, and see if the numbers change.

Hi Miklós!
You can see that first I did all my test battles with the simplest possible setup: totally naked hero, no medallions, wings, astrals, PvE against a lv1 atoll Iris, and noted down the
auto attack damage values (after awakening), and considered only crit-free battles (one crit hit increases archer’s dmg by 2% and thus corrupts the data).
Later I put on some more PATK on my hero, and even rearranged ENDU skill points into INT on my apollo (my firt test sylph, and yes, I even used balens to do this), and noticed the increase in the damage.
In the following experiments I added more and more details step by step: changed (low and high lvl) sylphs, tuned my RES RED value, sylph skill points rearranged,
used non-auto skills, added set DMG bonus, ignore DEF bonus, critical hit (with and without determination) with archer crit bonus, QTE dmg bonus, etc…
All my formulae show an almost perfect fitting on the whole data I documented. When I’m speaking about perfect fitting, I mean that only rounding/flooring errors may occur, the relative error is far less than
0.1% (absolute error is less than 6 even during the most complicated fights). As I’ve mentioned, I’m willing to share all my data (currently a spreadsheet with ~30 different worksheets corresponding to different setups)
with anyone who is interested in it.
Considering that 120% limitation in Resistance Reduction, I noticed this (first seemed like a paradox) when I heavily increased my RES RED with will crystals from a relatively high value to another and saw no difference
in the damage I dealt. Turned out that the truth must have been somewhere between -150 and -180. (Iris on atoll has -200 resistance against my electro sylph,
so no difference in damage even with 0 and 210 RES RED from will crystals). When I finished my formula, plugged back these old data and turned out that -166.67 is the lowest possible effective resistance in
the calculations, that corresponds exactly to that 120% dmg bound.
Anyway, I’m open to more discussions about this topic, that I started to examine mainly because I was inspired by your findings on your blog.
Maybe we can continue this conversation in an other form of communication (probably in a more comfortable common language :D )
Üdv,
Tihh

> *Originally posted by **[katihi](/forums/228/topics/415571?page=1#posts-8262653):***
> As I’ve mentioned, I’m willing to share all my data (currently a spreadsheet with ~30 different worksheets corresponding to different setups)
> with anyone who is interested in it.
Sure, I’d like to look at it if you can upload it.

> *Originally posted by **[katihi](/forums/228/topics/415571?page=1#posts-8244140):***
>
> ![](http://i58.tinypic.com/20uejc1.png)
My formular was a little simpler:
$$$$$$$ = win

> *Originally posted by **[katihi](/forums/228/topics/415571?page=1#posts-8262653):***
>
> All my formulae show an almost perfect fitting on the whole data I documented. When I’m speaking about perfect fitting, I mean that only rounding/flooring errors may occur, the relative error is far less than
> 0.1% (absolute error is less than 6 even during the most complicated fights).
Though what is the error if we tried to use his model? It’s good that your model matches the data nearly perfectly, but you would have to demonstrate that the data is sufficient to exclude it from other models.

The error grows very very large when you try to use (atk \*skillmod -def)/2 instead of ((atk-def)/ 2 ) \* skillmod, esp at higher atk and def values, it is the same result against 0 def, and the difference is marginal against very low def targets however
For example, ponder 60k atk and 60k def, you’d end up hitting 180k dmg with a 400% skill, instead of the correct 24k(all other factors omitted)

> *Originally posted by **[WIGANSTE](/forums/228/topics/415571?page=1#posts-8263723):***
> > *Originally posted by **[katihi](/forums/228/topics/415571?page=1#posts-8244140):***
>
> My formular was a little simpler:
>
> $$$$$$$ = win
hehehe (y)

katihi: I’m very glad that my curiousity for the truth insipred you, I hope we can discover the exact formulaes eventually. I will do more testings when I have time, sent you my email in priv. would love to see the data you collected.
> *Originally posted by **[gruntarswe](/forums/228/topics/415571?page=1#posts-8264896):***
>
> The error grows very very large when you try to use (atk \*skillmod -def)/2 instead of ((atk-def)/ 2 ) \* skillmod, esp at higher atk and def values,
>
> For example, ponder 60k atk and 60k def, you’d end up hitting 180k dmg with a 400% skill, instead of the correct 24k(all other factors omitted)
ok, lets see an example of class wars finals. Delphic is usually a finish-off, dealing 100-180k damage. Now let’s see the 2 figures, with the examples below (Hades vs hades):
Opponent: approx. 60k MATK
Delhpic: 3.1x skill modifier
my lvl 10 goddess blessing: x 0.7 modifier
intensity (him 40%, me -20%): x 1.2
my pdef: 35K
60 sec modifier: x 1.5
usual resist reduce: 240
my dark resist: 346 (so resist multiplier x 0.9)
sylph growth modifier: 1.5 (?)
will destroyer (maybe crit) 1.5
My formulae: (ATK \* multipliers – DEF) /2 \* resist \* round modifier \* EWD/crit:
(60.000 \* 3.1 \* 0.7 \* 1.2 \* sylph modifier – 35000) / 2 \* 0.9 \* 1.5 \* 1.5 = 201k – seems a bit lot :)
Your formulae: (ATK – DEF)/2 \* modifiers:
(60.000 – 35.000) / 2 \* 3.1 \* 0.7 \* 1.2 \* sylph modifier \* 0.9 \* 1.5 \* 1.5 = 97K – seems a bit low :)
You did testings again Iris in sylph atoll (if I understood correctly) which probably have a neglectable defense. I tested against players in Altar, with significant defense. First I supposed too the formulae is (atk-def)\*multipliers, and the results were very far from the calculated. Then I tried to adjust them to the above, and the numbers jumped in place. Probably truth is somewhere halfway, maybe some multiplier is inside, some outside :)

> *Originally posted by **[Holosoth](/forums/228/topics/415571?page=1#posts-8263377):***
>
> Sure, I’d like to look at it if you can upload it.
[Here you can find my documented battles](https://www.dropbox.com/s/55m3zxuuo2irk2o/tests.xlsx)
There is a summary worksheet called _full\_stats_, that works like a table of contents to make the navigation through the worksheets easier.
There are also some auxiliary sheets, those were just to verify some of my calculations, you can ignore them.

> *Originally posted by **[KamuR](/forums/228/topics/415571?page=1#posts-8262252):***
>
> In my testing, I used the same sylph, first did 50 attack, and when I switched points between hp and int, and also spent 500 sepulcrum, I got the same damage numbers.
> You say you just did a test with an orange apollo and a while amazon, how could that help you figure out? The orange dealt more damage, but you can’t know if it was due to higher atk, or just the color bonus… You should have increased the apollo’s attack significantly, and see if the numbers change.
I remember doing a test fairly close to solving this “color bonus” that I have heard about. I tested a white level 42 iris against a level 1 white iris, ran through about 20 battles with another player, and at first I saw no damage difference, but I was letting the battles go on into the 200% marks, and at that point there was a very significant damage difference (around 600 if I remember right, excluding fate hits and with damage low enough that floating damage would not change it much). I believe this “color bonus” is a myth due to the huge stat gains of sylphs when growth goes up at the same time as aptitudes, without drawing a huge amount of attention to it. At low color it is very significant, but it is no different then evolving a sylph, which also increases growth and is why those sylphs seem so much stronger.
If your looking for ways of ultimately deciding this, you could test a level 1 purple versus a level 1 white, where the growth would not throw so much havoc into the stats that it looks like a real bonus damage, only aptitudes should change which is negligible except for a couple damage points, not enough to significantly change a person’s attack. more reasonable would maybe be blue against white, if either of you want to farm a blue sylph, though from looking at his data, Katihi might already have one.
Also, just a question on your last bit of math Miklos, As far as I know, factors such medals are not added into the formula that Katihi has provided, yet, but will be interesting when completely put together. Then again his formula seems to calculate almost everything but that, even the random damage, so why not put that to the test, excel sheet it up, get 1 player into altar, remove stuff that does not apply to the formula that Katihi provided, blast your friend with a delphi, and if your damage does not match one of the 42? ( I believe that was the suggested amount) values, Katihi listed by +- lets say 20, then maybe the formula is not right, though I would wager with what I am seeing on a brief overlook of the data, it will be.
For Katihi, something for your formula that you might overlook, though kinda a pointless experiment, but I would love to see at which step minimum damage is decided. We all know it exists from the monsters in void and such, but it would just make your formula more complete. Otherwise, thanks for all the work you put in, and looking forward to seeing a complete version.

> *Originally posted by **[simbu95](/forums/228/topics/415571?page=1#posts-8276454):***I believe this “color bonus” is a myth due to the huge stat gains of sylphs when growth goes up at the same time as aptitudes, without drawing a huge amount of attention to it. At low color it is very significant, but it is no different then evolving a sylph, which also increases growth and is why those sylphs seem so much stronger.
As you can see above, I revised my theory about the _color bonus_ and it turned out that this is simply the 10% bonus damage that your sylph gains when it reaches lvl55. You can see this in the description _Advanced Awakening_. Thus this bonus is not color-dependent, but level-dependent.
Concerning the other factors (minimal dmg, goddess blessing, QTE dmg, will destroyer, medallion, dmg reduction talents) I’m missing, finally I’ll do some extensive tests in PvP this week, hopefully more factors will go into their right places. But you can see I prefer to do the simplest experiments first, then change the setup step by step, so this will be a long process, too.

Sorry I didn’t make it clear Katihi, but I was referring to Miklos for the first 3 paragraphs. There is a damage increase however, when sylphs change color, which is stated in your own formula, since the sylphs attack goes up, especially at higher levels due to the growth and attitudes changing. I was just pointing out it is covered in your formula, and providing evidence, as you can see my sylphs were both under level 55, and thus the damage increase in sylph form was justified better by the attack influencing your sylph form damage, rather then a color bonus.
I also completely understand that the process will take a while to complete, and I am sorry for not making clear that I was looking forward to the end result. My last paragraph was mostly a suggestion of something to test, as of all the factors I believe it would be easiest to overlook, though in honesty I could have missed something a bit more obscure. But as a restatement, good work so far, and good luck in your next tests, hope they turn out well.

Here are some updates on my work on the damage formula.
I tried to find the right place for the QTE damage boosts in my formula, and I almost succeeded to do so. 25% damage boost from my archer’s Delphic Sniper and Incendiary Shot work as a 1.25 factor in the formula,
and the same holds for the mage skill Rain of Fire (see more details later). However, it seems that the mage skill Thunderer’s 25% damage boost gives actually less than a 10% increase. I don’t have any explanation for this,
the most likely hypothesis is that devs once nerfed this skill’s QTE and forgot to update the skill description.
Talking about Rain of Fire, it is a skill that does ‘140% + 0 damage’, and it comes in 2 parts. /The same way as knights’ EDD comes in multiple (3-5) parts, or archer’s Lunatic Fire comes in 3 parts/.
According to my experiments, these 2 partial damages are considered as independent ‘70% + 0 damage’ skills, both can independently crit and can be blocked, too.
Thus the opponent’s defense is subtracted twice, however your extra (1000/500) damage from (lv60, lv70, lv80) sets are added twice, too. (Interesting thing, that the Brutal Edge bonus is halved for both, though …)
Another interesting thing I found is about Will Destroyer astrals. You can see my formula that involves Crit damage and Determination astral’s enhancement, for example a lv8 Determination gives a 1.9 factor in the formula.
When you use a WD astral, for example a lv7 EWD, it gives 35% more damage, i.e. a 1.35 factor. However, they don’t act the same way. Crit damage doesn’t affect the extra damage from sets/items, while the WD damage increases
**everything**. (Except Brutal Edge bonus, that is unaffected…)
A simple example to imagine the difference: assume that you deal 10000 damage with your skill (sylph\_bonus, resistance\_bonus and QTE\_bonus included) and you have a full 4-pcs lv70 set, that gives 1000 more damage.
Then with a lv8 determination, your skill deals 10000 \* 1.9 + 1000=20000 average damage, **when it crits** , the other crit values you observe are 20000 + 190 \* k, where k is an integer from [-10,10].
When your skill doesn’t crit, it deals 10000 + 1000 = 11000 average damage, with other values equal to 11000 + k\*100.
If you use a lv8 EWD, your skill deals 10000\*1.4 + 1000\*1.4 = 15400 average damage, and the other observable values are 15400 + k\*140.
As a summary: sylph\_bonus, resistance\_bonus, crit\_bonus, QTE\_bonus all affect the same values, while the 1.02 possible archer crit bonus and the WD bonus affect more values in the formula.
I have updated my spreadsheet with experiments about testing these factors, you can download the current version on the same link I provided in my comment.