In-depth Analysis of Critical Rate

In-depth Analysis of Critical Rate

by Indigna

A lot of people have been asking this very question, is critical worth it? Is it better than pure damage build? Here I will try to explain the mechanics of the critical system and how people are sometimes underrating/overrating it.

Critical is rather interesting in Dragon Nest, in which is ignores monster defense, or armor penetrating if some would prefer. Surprisingly, the damage reduction on Dragon Nest is rather huge in some case; in some cases critical can do more than twice your normal non-critical hits.

This guide is very math intensive, but if you have a basic clue as to how ratios work, it shouldn't come as surprising to you. If you are looking for short answers - well, there is none. Investing in critical is rather situational, to some extent it depends what you want in which area you want to excel.

First of all, a damage formula is important. Chaose5 from mmosite has it listed and I quote:

Skill Damage = 1.25 * Skill Coeff * (%Amp * M.att + Add. Dmg) * (1+% Elemental Att)* (1- % Elemental Resist) * (% Aditional damage)
Reference: http://forum.mmosite.com/thread/2/217/..5af3ca13-1.html

Additional Note: There is a chance critical hit can be resisted, this will be based on the monster innate critical resist stat. When it does happen, your damage is further reduced to 35% of what you would have dealt on a critical. Most monsters have relatively low crit resist, but certain bosses, such as Zxyzzrx in Astral Coven, Electric Ogre in Apocalypse Nest and Lava Golem in Sea Dragon Nest (as mentioned by above link) have really high crit resist. I personally do not think it poses enough threat to forgo the critical route altogether, it's just a minor hindrance. (thanks Light for the suggestion)

This is the formula for critical, for non-critical, you basically replace the 1.25 constant with (1 - monster def/15000)). Chaose5 has told me that a mob with 3000 defense reduces damage by 20%, and that the formula is linear. I am somewhat convinced, of course not backed with hard proofs. But this analysis doesn't really involve this anyway, since I actually look at videos and my own damage to see the difference between critical and non-critical to draw my own conclusions. I will now normalize non-critical damage as the base, and critical as modified damage, or in simplier terms:

critical damage = 1.25/(1 - def/15000) x normal damage

If you look around for minotaur nest solo videos, you'll see that critical damage on regular minos are about 40% higher and on elf arcanist and enchanter and General Ummanba, critical does almost TWICE as much damage. You can actually solve for the monster defense that way but it'll be a fallacy if the formula was incorrect in the first place. It'll be nice if there's a database to confirm these values though. I have checked DNarmory and the values are incorrect, or perhaps there are outside factors not considered, like how critical chance, final damage, are all level dependent. For the sake of comparisons right now, I will use 1.4x and 2x multipliers for critical, for normal mobs and bosses.

Now, to evaluate how much does boosting critical will boost your overall damage, we have to assume that the critical rate, or chance, is (current crit/full-crit - 5%), whereas full-crit is the thresold to achieve 95% crit rate. There had been tests done on various Chinese forums, and Chaose5 has that covered already.
Reference: http://forum.mmosite.com/thread/2/217/..b04f7127f185

Now we have everything that we need, everything else is just linear interpolation and finding the ratio for comparison.

To find out how much effect critical has on you currently, let 'a' be your current critical, 'f' be the full-critical:

(a/f - 5%) x 0.4 + 1 for small mobs or (a/f - 5%) + 1 for big mobs
Note: I have modified the linear interpolation in a simplier way to calculate, basically a(X) + (1-a)M = a(X-M) + M, in this case X is 1.4 for hitting critical on weak mob and 2 for bosses, and M is just 1 for normal non-critical hits.

So let's say you have 2700 critical and you want to know the effect on level 32 mobs (full-crit or f=6000),

(2700/6000 - 0.05) x 0.4 + 1 = 1.16 <- small mobs
(2700/6000 - 0.05) + 1 = 1.4 <- big bosses

These equations tell you that by having that much crit, compared to having no crit at all, nets you 16% more dps on average mobs and 40% on bosses. Just something you might want to know. Now let's see how much 300 more crit will bring:

(3000/6000 - 0.05) x 0.4 + 1 = 1.18
(3000/6000 - 0.05) +1 = 1.45

These are your new multipliers for critical, to find the change or the increase in having 300 more crit, you simply divide the new multiplier by the old, and subtract 1, or:

1.18/1.16 - 1 = 0.01724
1.45/1.4 -1 = 0.03571

These two numbers represent the overall increase in dps by increasing 300 more crit on level 32 mobs, given you already had 2700 to begin with. Okay, now that's fine and dandy, what do we do with that? Simple, this is just like a new multiplier. If you want to compare how much physical or magical range that is, just multiply by those. If you have 1100~1400 range, it'll be equivalent to

1100~1400 x 0.01724 = 18.97 ~ 24.14
1100~1400 x 0.03571 = 39.29 ~ 50

Please keep in mind these are all unmodified values, meaning I did not consider total physical damage/magical damage %, critical % stacking. It shouldn't be that hard to modify it yourself if you understood all my work so far. You can also work yourself backwards and see how much a certain attack range equates to critical.

A few things I want to point out. If you have a solid backgrounds in statistics, or if you don't, you should be aware that damage is the most unstable when you're at half-crit rate, because the variance is at its largest (maximizing Bernoulli variable for critical). Why is that important or why should we care? When you're farming, you have a higher chance of not constantly one-hitting or few-hitting trash mobs, effectively lengthening the killing process. This does not matter when killing bosses with high hp, since overkill variance greatly decreases, or less wasted shots. Critical benefits overall damage, which means if your class utilize duo damage, whether it be physical/magical, or magical/elemental, it might be a better damage boost choice, IF the ratios are favourable. Also, you have seen the numbers differ tremendously between mobs with low and high defenses. Meaning for farming or clearing mobs, focusing on just physical or magical damage may be better to keep your damage spread lower, whereas it'll be beneficial to stack up critical for end dungeon bosses. There are other factors such as archer buffs, priest blessings, force mirror and other skills which I won't get into.

So is it worth to stack critical? Yes, definitely. But would it be better to just build up physical or magical instead. Well, it differs from person to person. You may even want two sets of gears, one for pure damage, and another for critical. Switch them according to the situation and you'll have the best of both worlds. My advice is, stack on your primary stat, but everyone should have a fierce plate on them. Get as much crit as you can without sacrificing too much primary stat, unless you're an archer, since you get the most boost from stacking agi/crit with easy agi hidden ability and spiritual focus. Epic fatal rings are great too but you will have to replace them every new level cap since critical scales with level.

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- dragonnestsource.com/..understanding-critical.html

Posted in: gen1, guides