Thank you. I will try my best to find what happen to it. (Still have no idea )
I think so. I think next target should be âlower defense against specific elementâ. I really want to see how the graph look like
I recommend you to try x5 stack color and play S1 1-1 map. You will find that it doesnât fit with the exponential formula.
In fact, the data mostly fit the exponential formula since it have large variance in the formula. For example, at 10.52342488 ratio (your data), the exponential formula give 813.127924 to 3141.005654 damage. The actual damage is never more than 1500. So, actual damage do fit the exponential formula but the exponential formula isnât very useful in this case.
Total attack of 4791, defense is 153, actual damage is 925, 918 and 929.
The exponential formula gives
(100*(.606x31.3137)^1.35)/3 = 3484 for the average value that you would expect to get most of the times
boundaries are
(100*(.606x31.3137)^1.35)/3 = 1171 for the minimum
and
(100*(1.649x31.3137)^1.35)/3 = 6844 for the maximum
=> this deviates significantly from the actual damage values
For practical use you want a formula that gives a good fit or at least a reasonable fit. The average value should already be close to the actual damage. Ranges where the maximum is 3.9 times the minimum value are not practical at all - it is nearly impossible to NOT be in this range! But here we are and did it
A diagram might give a better overview of this situation. Iâm using my previously collected tile damage data without any buffs, debuffs and bonuses and see how the exponential formula does with its boundaries:
As you can clearly see, the range is ridiculously large and makes the calculation kind of meaningless. For example, do you have to expect 100 damage with the tiles or 386? That makes a tremendous difference.
In addition, the exponential formula doesnât get the bend right at approx 0.94, and from something like 5 onwards the average values is getting further and further away from the actual damage values. Yes, at 5 it is still kind of ok, but the higher you go, the worse it gets and the more players will refuse to even consider the exponential formula. Would you agree, if we set the practical limit to 5.5 or 6?
The complete tile damage curve does not resemble an exponential curve (only part of it is similar), so the exponential formula can only give an approximation.
We believe that we found a different formula that is more accurate for raid battle tile damage and looks promising for other damage types. At some point we want to check missions/quests and titans as well.
no exponent, yes, just a linear formula with different curves for different defense values
Iâm more interested right now in the actual variance at 4929 ATK. Itâs simple, each battle is very fast to do and after some time it should give us more insight into the variance.
Will carry on with the elemental defense down afterwards
Ok, so, current target is âvarianceâ. âvarianceâ is relate to âaverage damageâ not ADR. âvarianceâ is 1 for damage <= 39. The point that âvarianceâ change from 2 to 3 is in between 52 and 71 âaverage damageâ.
Could it be that the original formula is actually correct but with variation smaller than 0.606 and 1.649 and limited to certain Attack/def ratio?
Why do you only divide it to <= 0.94 and >0.94? Could there be more attack/defense bracket?
In your formula, I didnât see defenderâs attack bonus or defenderâs defense bonus, did you forget to incluce that when researching? This bonus is only on defender in PvP such as raid or war, not on PvE if I recall correctly.
EXCELLLENT!!!
THANK YOU!!!
Finally we have evidence we can discuss.
SO lets look at your math:
First there are 2 issues with your math. Thatâs ok, you are human and we all make mistakes.
The first mistake is that this is PVP and you must add in the 20% making the actual defense 183.6.
Also we do not know if they have adjusted this value. it was announced in the last update they are adjusting this 20% on HIGH END raids. I do not think this value would be adjusted here but since this is a total mismatch and the attacking team would be considered high end, it is possible that the 20% is not 20% any more
The second issue is you have
and
Same formula with two different answers.
Regardless I did the math myself using the 20% bonus and I concede that these data points do not line up with the original formula.
Now we can discuss that.
It has been discussed in multiple places there are soft caps built into the game. For example this thread
These caps are an unknown and easily explain this discrepancy. Soft caps have been observed and recorded multiple times and for me are a reasonable explanation to this discrepancy
Letâ s look at how you obtained this discrepancy. You are using a fairly powerful teams against a basic beginner team. This is not normal. In fact getting to a ratio of 4791/183.6=26.09477124 is not something most players are going to see often unless they are trying to do it. That is not normal game play, even if using such a team on low level Season 1 maps is normal, you are at a point that the discrepancy does not matter and you are killing mobs and bosses with 1 or 2 tiles, making the discrepancy a non issue for actual game play purposes.
Now lets look at this graph because I think it illustrates one of your main points wonderfully.
Looking at this explains some of the confusion I am having. Multiple times after I started posting the ratio of 5 was given as where the original formula fails. This graph puts it at least at 10 and actually closer to 15. My evidence showed up to 10.52342488 was still within the ranges of the formula.
Perhaps stating that after a ratio of 15 the formula starts to fail is a more accurate statement based on your own data.
Now i did some tests above 15 and had mixed results. Some data points matched yours and some data points worked perfectly with the original formula.
I admit there seems to be an issue when the ratio gets high, but i disagree that 5 is where the problem becomes apparent it is much higher and may only occur in circumstances either not anticipated by the designers when the actual code was written, in outside or normal game play anticipated by the designers such as your raid example above, or in new scenarios created by the heroes that have been released since the writing of the original code which can now create unforeseen ratios.
In any case these can all be explained by a soft cap. n my personal opinion the soft cap is likely based on the defense number itself.
and now we get to the heart of the matter, what my original question was all about and why I started posting in the first place.
I agree with you that the ranges are horrible. I do not view the formula as a method to accurately predict the exact damage I can do. The formula serves as an educational tool to new players. It is accurate enough in NORMAL circumstances to show the following:
This is true and factual even if the formula is not perfect.
You have not proven the formula does not work and does not serve as an excellent basic idea for beginners to learn how the game works. The discrepancies you have encounter come at extremely high ratios barely even possible when the original formula was conceived and posted. The discrepancies can be explained away by soft caps, and not the formula being wrong. There is plenty of data in this thread that shows the formula works just fine under normal circumstances. Please stop saying the formula is wrong or doesnât work.
What you are trying to do is make a formula that is more accurate and possibly determines if there are soft caps and what those caps are.
I applaud you for the effort and encourage you to do so. I hope you succeed.
What I disagree with is the disparaging of the original formula given that
it does work under normal circumstances
only ratios previously unavailable when the formula was posted are where the problem seems to arrive
the discrepancies can be attributed to soft caps
This thread is under player guides and has been used as a guide for many years and is established as the best understanding of the damage calculation we have to date
Your new formula is not ready.
All of these posts in the GUIDE make it confusing to use as a guide. If i were new to the game and started reading this guide I would be unsure how damage is calculated because it starts with a formula, the formula is shown to work then a new discussion starts with tons of what can be confusing charts and data to those uncomfortable with math. And now I do not know if the original formula is right or not. When the truth is, the original formula is good enough to get the basics and your new formula when complete could possibly be more accurate and be more useful, but until it is ready and thoroughly tested we just donât know.
and MOST IMPORTANTLY
7. Solemn Wolf is not here to defend their work.
SO once again @moderators
respectfully request that this thread be decluttered.
The original content be left alone
The new discussion of a new formula be moved to itâs own discussion under General Discussion where Zack and others can continue their work.
A link be provided in this thread for others to see Zackâs work and contribute
And when Zack and the others have a workable formula that can be tested and explained clearly to the novices that it be given its own Playerâs Guide and both threads link to each other.
I also came here to defend the exponant formula devised by @SolemnWolf , did some independant testing (posts of the 20th May and 1st June) and came to the conclusion @Zack and @u2371 were right, the true damage calculation does not depend solely on the attack defense ratio, and their formula works much better around ADR 5 and higher.
it does work under normal circumstances
Would you consider mono with any attack bonus or defense down not normal circumstances ? Because thatâs where the bi-linear formula starts being clearly better than the exponent one.
the discrepancies can be attributed to soft caps
You claim the exponent formula is precise at ± 60%, which is preposterous.
The bi-linear one works at ± 5 or 10% which is much better and requires no soft cap.
This thread is under player guides and has been used as a guide for many years and is established as the best understanding of the damage calculation we have to date
No, the best understanding to date, is the bi-linear formula devised by Z&u.
Cracks in the exponent formula had already started to appear years ago, when people tried to understand why bonus to attack and malus to defense did not work as intended. They are working as intended, itâs just the exponent formula is a poor estimate at the ranges you will explore with this.
Your new formula is not ready.
It is already precise at ± 5 or 10%, which is much more âreadyâ than the ± 60% you claim for the exponant formula.
All of these posts in the GUIDE make it confusing to use as a guide.
If the guide is wrong on an important topic (e.g. should I bring both an attack up and defense down with my mono, or am I better doing 3/2 in this configuration because the damage wonât overshoot like predicted) where else to discuss it than on the guideâs page ?
Solemn Wolf is not here to defend their work.
He has been referenced in this topic multiple times recently, and had all the opportunity to âdefendâ his work if he was still playing. This new formula is however not an âattackâ, and given the data analysis skills he has shown, Iâm convinced he would react much better than you on this new analysis.
I am only being aggressive about moving the discussion of the new formula to its own thread. This thread is too confusing at this point. I feel I have been quite polite. I am even encouraging of the effort to make a more precise formula.
quote=âGundar, post:476, topic:29624â]
Would you consider mono with any attack bonus or defense down not normal circumstances ? Because thatâs where the bi-linear formula starts being clearly better than the exponent one.
[/quote]
better doesnât make the original formula wrong
no claim of precision only that it works big difference. and that does not disprove a soft cap
once again precision is not what this is about for me. This is not about the original formula says that something is pink and the new formula says its actually salmon pink.
Apparently I am not making myself clear.
All the data that has been posted in this thread with a few outliers in extreme situations shows the original formula works. That can not be disputed
Is it precise enough for some people? No
All I am saying is the place for this discussion is in its own thread
I do not even know where this new formula is or have any understanding of it. That is part of the problem. in its own thread the formula could be at the top and easily referenced. right now it is lost within nearly 500 posts.
I feel there is some error here. if the attack type modifier is 0 for tile damage then A3=0 always regardless of all other variables for tile damage
And with A3=0 the formula gives a value of 0.
I am trying to understand and test this formula but I think I am misunderstanding A3, maybe it is explained better somewhere else in the 450+ posts that it is buried in.
So can A3 be explained in more detail, including what are the possible values for crit bonus,element bonus,combo bonus and tiebreaker bonus? what does x3 x90% mean? 270%? what does x3 x110% mean? 330%?
No, the original formula is âonlyâ an approximation. It does work to some degree, but has its limitations. For practical reasons the boundaries 0.606 and 1.649 must be much narrower. Iâm sure that everybody that uses the exponential function primarily looks at the average result and expects it to happen and simply ignores these min and max values ^^
Addtionally, there seems to be slightly different formulas for tile damage, specials, slash attacks and enemy specials, so there isnât just one formula.
That comes from aligning the two straight lines that compose the damage curve, see for example the following curve for 744DEF:
The 0.94 simply gave the best fit so far.
We now from cheking other defense values that this linear curve changes depending on the defense value. Also, the actual variance is smaller than expected. (collecting enough data for the variance is the time consuming part)
At first such bonuses are included in the formula. As soon as we can compare with the formulas for specials, enemy specials, slash attacks, quests, titans, etc, we should see the differences and the applied bonuses.
I think there is a misunderstanding. May I point you to this here
and refer you to SolemnWolfs post up there?
Especially this figure:
This means that, when you get some data points - or even better: lots of data points - you will find that most of them align close to the average value, you only have a few outliers at the extremes.
You can check this for your damage data that you posted previously and you may want to collect some more data as well. look out for the actual average and the actual extremes.
Now, if at some point your actual damage does not align well or at all with your calculated average damage values anymore, then the formula is not working properly in this range, which for raid tile damage starts lower than an ADR of 10, more like below 6.
Can you give an example of calculation for attacker with 1077 attack (after troop, no buff) dealing special with 512% damage towards raid defender who have 850 defense (after troop, no debuff)? SG is testing reduced defender bonus but we are still not sure how much, for the example, lets just assume it still 20%. Thanks
Although we didnât check special damage in detail yet, I would expect an average special damage of around
(25.5 x 1077 x 5.12 / 850 + 0.04 x (1077 x 5.12 - 850 x 0.94) x 3 x 0.9 = 955
This formula should include the bonuses that applied during the past 2.5 years
No, they donât. I tap on each hero during the raid battles and record their indicted ATK and DEF values (so the troop bonus is already included).
Since I didnât find clear information on which ATK and DEF bonus the defender gets for which damage type, I left hidden bonuses out of the ATK and DEF values. That way, all data is directly comparable and any hidden bonuses that SG applied for this data are therefore included.
It is simple to add any bonuses later or test various bonus values to see where this goes. For example, if you compare the damage curves for tile damage and for slash damage later on, you should be able to make them fit by testing various hidden bonuses and finding the correct values for the bonuses.
Yes. Whatever bonuses apply there, these parameters include them and the formula should/will give you the damage with all bonuses already applied.
Then my currently best fit changes the damage factor from 90% to 110%:
(25.5 x 1077 x 5.12 / 850 + 0.04 x (1077 x 5.12 - 850 x 0.94) x 3 x 1.1 = 1168
These 90% for specials and 110% for enemy specials are based on by previously collected data without any buffs, debuffs, etc. When I compare the actual damage with the damage calculated by these formulas I get a very good fit:
The perfect fit would be to to have all of these data points align with the red curve, because then the actual damage would be exactly the calculated damage.
Due to the variance this is not possible, but the next best fit is having all data points align around the red line (deviating from the red line only due to the variance), which they kind of seem to do.
My current data (mostly tile damage with a little bit of special damage) suggests a variance of approx. ±5% now. Will need more date to confirm this, of course.
New raid defense team, Attack bonus should be solvable using DOT ( see notes about DOT below ).
Raid defense team, Defense bonus has always been an educated guess. But original game was very rushed, so simple was probably better at the time. And the Attack 20%/ Defense 20% bonus seemed to fit with observed data.
SGG changed the damage formula at least once. One of the reasons I stopped my own data collection. So much time, and effort, lost. Bonus rant: and I still do not have any red 4* Guardian Falcon.
Known damage formula change. Caused at least one data collection projects to end. And discouraged some of the players from trying again since SGG could just change it whenever they wanted with zero transparency. Impenetrable, and Opaque, the SGG marketing department/ legal department way.
Awesome Forum
P.S. @Petri and crew, are awesome for keeping the official forum running. This kind of history post / historical research would be impossible on Discord/ Reddit
You cannot eliminate urban legends/ myths, but it is easier to untangle confusing subjects with primary sources like original forum posts available for citation.
So the original damage formula in the OP was correct but then changed?
Yes, I also use the DoT to figure out the attack bonus but they said high level raid without explaining what is high level raid and also it seems to differ for each hero:
)
