Damage Calculation Mechanics: Critical, Pierce and Defence
In this article, i will share the results of my research on the dmg calculation mechanics in Blade and Soul. The exact details on the in-game experiments which i have conducted will not be eloborate here, unless it is necessary or in the case where the conclusions contradict with some other findings by other players.
To make it simple, i will only focus on the conclusion of my research, directly or indirectly answering the following questions:
- How is skill damage being calculated?
- If i have xx of critical and pierce, what's the corresponding % dmg increase of my skills?
- How much Pierce % would i need at lvl45 cap?
- Which is better: Critical rate or Crit dmg?
I hope the understanding in the dmg calculation mechanics would help players to make better decision in gear selection and skill building.
It is recommended, although not necessary, for readers to go through my previous article on skill board damage calculation to have a better understanding of the topics presented in this article.
Damage Calculation Mechanics: Skill Board Damage Calculation
Defence
The skill board damage shown in the skill description is indeed the damage inflicted to a target if the target defence is 0.
However, in most cases, the target has a finite defence value, which translates to a lower damage inflicted. The formula is simply:
Non-crit damage = Skill Board Damage * ( 100% - defence %)
assuming you have 0 pierce, and do not deal crit damage.
As an example, say your skill board damage is 251~298, and the target defence is 25%, your actual non-crit damage would be
Non-crit damage = 251 ~ 298 * (1 - 0.25 ) = 188~223
The defence number shown in the stats, is automatically translated to a certain damage reduction %.
Relationship between the defence number/value and the dmg reduction % for lv45 is given by the curve below:
The equation is obtained by curve fitting with a hyperbolic function:
The accuracy of the equation is up to 1 decimal point (sometimes 2). Take note that this is only true for a lvl45 target/player. The constant of 94.999 and 3220.644 are different if the target or player is at other levels, but the hyperbolic form of the equation should remain true. The effects of level on the defence % will be investigated in the future.
From the graph, it can be observed that the
defence % rises quite fast at low def value but
the rise is rather slow after you have passed a certain defence value.
This
diminishing return is the characteristic of most stats in blade and soul, including crit rate, crit dmg and pierce (to be elaborated later).
Also take note that defence value goes to infinity goes to infinity, defence value tend to 94.999 = approximately 95%.
where Def = defence value.
This means that
95% is the limiting or asymptotic defence you can obtain from defence stats. However, it is possible to exceed this limit with skills which add a fixed defence % to the current defence % obtained from def stats.. \
The defence of the bosses in the big 4 dungeons in BNS CN are all measured to be 25%. As for the mobs in the a typical big 4 dungeon, i have measured the defence of the pig spearman and pig gunman, to be 10%, just to get a rough figure on the % def of the target we are hitting.
For Sea Serpent Base boss,
Pohwaran, Chef and Fish King has 10% defence while
bartender has 0% defence (see Ref 4,5)
The defence % of the mobs and bosses are important because it is closely related to the next stats we will be talking about, Pierce.
Pierce
Pierce reduces the defence % of the target, and increases the damage you deal. It is calculated as follows:
Non-crit damage = Skill Board Damage * [ 100% - ( defence % - pierce %) ]
Here, take note that you will first need to subtract pierce % from defence % before minusing 100% with the outcome.
One of the key condition of pierce calculation is
This means that, pierce % cannot increase the dmg beyond the original skill board damage. At its maximum effect, it will only nullify the defence of the target, making the defence = 0%.
For example, if the target defence = 10%, and your pierce is 15%,
(defence % - pierce %) = 10% - 15% = -5% =adjust to> 0%
-5% will be adjusted to 0% due to the nature of pierce mechanics. In other words, the extra 5% of pierce is WASTED.
See appendix if you want to know how i arrive at this conclusion.
The curve of pierce % - pierce value and its equation for a level 45 player are given below:
Looks familiar?
Yes, the equation for pierce is identical to the defence % equation. It also has a limiting value of 95%. I didn't show the curve for the higher pierce value, simply because it is almost not achieveable at this lvl45 cap.
Pierce also increases the piercing damage on blocking target. However, the effect and equation will only be investigated in the future.
Critical Rate & Critical Damage
Critical mechanics in BNS are almost the same as critical mechanics in other mmorpg's; Crit rate gives the chance to deal crit damage, which is higher than normal damage, which is given by the equation:
Crit damage = Skill Board Damage * [ 100% - ( defence % - pierce %) ] * (Crit damage %)
assuming the target has no crit resist.
The base crit damage is 125% of normal dmg. Adding crit stats will increase both the crit rate and crit damage. However, crit damage can be further added directly through accessories with bonus crit dmg % or skill effect.
The curve and equation of Crit Rate for a lv45 player:
The curve and equation of Crit Damage for a lv45 player:
Although these 2 equations shows that the limiting value of crit rate and crit dmg are 97% and (125%+97%) respectively, crit rate and crit damage can be boosted further with skill effect. For example, Fury of destroyer grants 100% crit rate for 6sec.
How to incooperate crit rate into damage calculation during gear comparison?
By using the mean dmg from skill board damage range,
Average damage = crit rate % * crit dmg + ( 100% - crit rate%) * non-crit dmg
As example, i shall compare the two necklaces:
~~~~
Assume target def = 25%,
skill amp % = 375% (Demolition rank 2 for destroyer)
Case 1: Extreme Flame Emperor Necklace Lv10 (New)
Hit Rate +135
Crit dmg +8.3%
Attack + 12
Additional dmg + 20
My stats:
Att: 362
Additional dmg: 29
Crit rate: 37.13%
Crit dmg: 165.76%
Pierce: 7.28%
Mean Skill board damage = 3.75*362+29 = 1386
Non-crit dmg = 1386 * (1-0.25+0.0728) = 1140
Crit dmg = 1118 * 1.6576 = 1891
Average Damage of Demolition = 1891 * 0.3713 + 1140 * (1-0.3713) = 1419
Case 2: Battle Necklace Lv10
Crit dmg + 6.7%
Crit + 149
Defence + 112
My stats:
Att: 350
Additional dmg: 9
Crit rate: 39.52%
Crit dmg: 165.51%
Pierce: 7.28%
Mean Skill board damage = 3.75*358+17 = 1321
Non-crit dmg = 1321 * (1-0.25+0.0728) = 1087
Crit dmg = 1087 * 1.6551 = 1799
Average Damage of Demolition = 1799 * 0.3952 + 1087 * (1-0.3952) = 1368
~~~~
So, apparently Case 2 is slightly weaker than Case 1 in terms of damage output, but not by much. However, case 2 provides additonal defence, while case 1 provides additional hit rate. You need to sacrifice about 3.7% of damage to gain approximately 2% more defence.
Another necklace which is commonly used is
Case 3: Battle Necklace Lv10
Pierce + 121
Crit + 243
Attack + 4
My stats:
Att: 354
Additional dmg: 9
Crit rate: 40.71%
Crit dmg: 161.05%
Pierce: 10.32%
Mean Skill board damage = 3.75*354+9 = 1337
Non-crit dmg = 1337* (1-0.25+0.1032) = 1140
Crit dmg = 1140 * 1.6105 = 1836
Average Damage of Demolition = 1836 * 0.4071+ 1140 * (1-0.4071) = 1424
Apparently this is better than the necklace in case 1 since my initial pierce is low. In terms of the damage output, it is also 4% better than the battle necklace with defence.
Due to then non-linear nature of pierce and crit, the outcome of dmg comparison between accessories strongly depends on your current stats. In other words, the above results are not absolute. You should compare the accessories based on your own stats to see which one is better.
The effect of crit resist is not studied here, but will be discussed in the future. Crit resist apparently, is a very good stats for PVP.
Conclusion
This is for those who are lazy to go thorugh the whole article:
Non-crit damage = Skill Board Damage * [ 100% - ( defence % - pierce %) ]
Crit damage = Skill Board Damage * [ 100% - ( defence % - pierce %) ] * (Crit damage %)
Condition:
Defence % - Pierce % >= 0%
Average damage which include crit rate:
Average damage = crit rate % * crit dmg + ( 100% - crit rate%) * non-crit dmg
Excel spreadsheet for calculation of average damage:
http://freedom-chaos.webs.com/freedomplays/BNS-AverageDamageCalculator.xlsx
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Acknolwdgement:
I couldn't have completed my research without the help of my fellow guildmates in Freedom, in particular, v2seraph, nureha, lighteyes, harle etc who have aided me in the series of test. Their help in the research is much appreciated.
Appendix:
Interestingly, my finding contradicts with two independant researchs by chinese players, see Ref 1 and 2, who claimed that the pierce % can further increase the damage beyond nullifying the defence %. This means that pierce % can result in a negative defence value.
However, if you go through the 2 articles in ref 1 and 2 carefully, you will realize that their reasoning from the ingame experiment are flawed. I will not go through the reason why they are wrong, but rather i would explain how i arrive at my conclusion.
I have exploited one of the skill of destroyer, called Fury, which reduces his own defence to almost 0%. Then, another player with a finite pierce value, in this experiment, pierce = 419 or 11.25%, attack the 0% defence destroyer with a skill with board damage of 251~298.
IF the pierce can result in negative defence %, the non-crit skill damage should range from
251 ~ 298 * [ 100% - (0% - 11.25%) ] = 251~298 * 111.25% = 279~331
In the chinese findings are true, there shouldn't be any damage lower than 279. However, from my test, numbers which is lower than 279, such as 264 and 266 appear. This simply test shows that their findings are clearly wrong.
Furthermore, the damage number i obtained from the test ALL fell within the original board damage, which is 251~298. In conclusion, you reduce the target defence below 0% with pierce mechanics.
Recently, there are another independant tests which arrive at the same conclusion as mine, see ref 3 & 4. Therefore, the validity of my test result is further strengthen.
Reference:
1.
http://news.4399.com/gonglue/bns/gonglue/zonghe/280831_2.html
2.
http://bns.yzz.cn/gl/201311/708048.shtml
3.
http://bns.17173.com/news/12312013/101620520_all.shtml
4.
http://bns.duowan.com/1401/254138520123.html
5.
http://bbs.duowan.com/thread-37319251-1-1.html