Aura Kingdom Crit vs Dmg Stat Analysis



Aura Kingdom Crit vs Dmg Stat Analysis by imakebirdiescry

Hi, welcome to my guide to CRIT vs DMG. Hopefully this will be part of a series that will include HP/DEF/EVA, ACC/CRITDMG, and possibly more (if anyone can think of a comparison they would like, please let me know).

Since I want this guide to be accessible and useful for everyone, I will start off with the conclusions of my math.
IF YOU DON’T WANT TO READ A WALL OF MATH, JUST READ THE FIRST PART. HOWEVER, PLEASE DON’T TRY TO ARGUE MY MATH WITHOUT READING IT, THANKS.

How should I build?

If you’re focusing on dealing the most damage possible, build for crit and crit damage. If you’re focusing more on defense (like guardian and bard), build for damage and ignore crit, because crit damage takes up alot of stat option slots that you would rather use for damage reduction, and crit without crit damage does not give you as much damage as DMG does.

In general, if you have over 200% crit damage, building more crit chance will give you more damage. If you have less than that, building more DMG will give you more damage. BUILDING CRIT AND CRIT DAMAGE WILL GIVE YOU MORE DAMAGE THAN BUILDING PURE DAMAGE WILL EVER GET YOU.

In particular, if you are going crit, you should try to get crit damage anywhere you can. This includes Envoy path, Ultimate skill (Callousness), Secret stones (go for the +6% crit dmg ones, even if they don’t affect any of your skills), trophies (aka Fia’s Fairy dust – this item was made for crit builds), and any other crit damage bonuses you can find. If you have to choose between crit chance and crit damage, and are around 200% crit damage already, 1% crit damage is worth about 0.25% crit chance. Obviously the more crit chance you already have, the more useful crit damage is, and the more crit damage you already have, the more useful crit chance is.

Calculations Intro

Since crit runs on RNG, we will use the law of large number averages to calculate an average damage. The simple formula for average damage is therefore as follows:

total damage = DMG * [1 + critrate * (critdmg – 1) ]

ex: You have 15000 DMG, 50% crit chance, and 170% crit damage. Your average damage is therefore 15000 * (1 + 0.5 * (1.7 – 1) ] = 20250.

Now, most of your damage comes from skills. Skills have a base damage and a damage ratio (these can be found here). Say you’re a level 45 wizard and your Meteor skill is level 48. You have a DMG stat of 15000. Then its damage is 1.4 * (9103 +15000).

Now one thing to note here is that increasing your DMG will increase the bonus damage, but not the base damage. A crit, however, will increase the damage of both the base and the bonus components. We can thus give the damage formula for a skill as:

skill damage = skillbonus * (base + DMG) * [1 + critrate * (critdmg – 1) ]

Now that we have a formula for skill damage, let’s take a look at how adding points to crit or damage will affect your overall damage.

Stats

Title bonuses and Eidolon bonuses are always applied at the end. They are not affected by any % increases.

DMG

Each stat point in damage increases your damage by 0.35%. This applies to both your base damage, weapon damage, and any bonus damage from gear. Other percentage increases in damage (from Envoys and from %DMG stats on gear) stack additively, not multiplicatively, with this. For example, say you have 10 points in damage (3.5% increase) and a full set of damage gear (8% increase). This is an 11.5% increase (3.5+8=11.5).

So the overall formula for damage stat is:

DMG = [(base + weapon + gear) * (stat% + gear% + envoy%)] + title + eidolon

This is the damage stat listed in your character window. The only difference between your primary and secondary weapons is the main damage stat listed on the respective weapons. All other % bonuses are applied the same way.

CRIT

When dealing with crit, I will refer to crit stat and crit chance. These are different. Gear/stats dealing with crit are generally added to your crit stat (some exceptions exist). Crit chance is your percentage chance to land a crit derived from your crit stat relative to the target’s level. Crit stat is linearly related to crit chance – that is, increasing your crit stat by 10 gives you the same increase in crit chance whether your crit stat is going from 100->110 or 3500->3510.

Each stat point you invest in crit will give you enough crit stat to raise your crit chance by 0.25%. That means the stat points you invest in crit give you a constant crit chance as you level, but their crit stat value increases as you level.

Most things that give CRIT+X% just add directly to your crit chance without affecting your crit stat. These incluce costumes, envoy path, and secret stones (?unsure, I don’t have any crit chance stones to test). However, a few gear bonuses will actually add a % of your crit stat. These % crit stat bonuses will ignore any crit stat you get from adding stat points, but include all crit stat gained from gear as well as your base crit stat.

The overall formula for CRIT% is:

CRIT% = %CRITBonus + (0.25 * statpoints) + {K * [ %CRITStat * (base + gear) + title + eidolon] }.

statpoints is the number of attack points you have invested into crit. %CRITBonus is the total sum of all your %CRIT bonuses that apply directly to your crit chance (envoy, costume, secret stone, gear). %CRITStat is the total sum of the %CRIT bonuses that apply to your crit stat instead of directly to your crit chance (ultimate skill, some gear). K is a constant of proportionality between your crit stat and your crit chance. This changes based on level. At level 53 my value of K is around 0.007, which means every point of crit stat gives me 0.007% crit chance.

A nice explanation of K by Mythyc:

Mythyc wrote:

I was actually compiling statistics on K (or in my case, 1/K [how many points does it take to get a 1% increase in a stat]and with my preliminary results (had to start a character from scratch to get these):

  • LVL 1 – 1.55
  • LVL 2 – 1.70
  • LVL 3 – 1.95
  • LVL 4 – 2.30
  • LVL 5 – 2.75
  • LVL 6 – 3.30
  • LVL 7 – 3.95
  • LVL 8 – 4.70
  • LVL 9 – 5.55
  • LVL 10 – 6.50
  • LVL 11 – 7.55
  • LVL 12 – 8.70
  • LVL 13 – 9.95
  • LVL 14 – 11.30
  • LVL 15 – 12.75
  • LVL 16 – 14.30
  • LVL 17 – 15.95
  • LVL 18 – 17.70
  • LVL 19 – 19.55
  • LVL 20 – 21.95
  • LVL 21 – 23.55
  • LVL 22 – 25.70
  • LVL 23 – 27.95
  • LVL 24 – 30.30
  • LVL 25 – 32.75
  • LVL 26 – 35.30
  • LVL 27 – 37.95
  • LVL 28 – 40.70
  • LVL 29 – 43.55
  • LVL 30 – 46.50
  • LVL 31 – 49.55
  • LVL 32 – 52.70

etc…

In other words, the difference in points between each successive level is increased by 0.1. 1/K describes the amount of points required to increase a given stat by 1%.
Applies to CRIT, EVA, SPD and DEF.

I found that the formula to find 1/K is:

(N (N+1) / 2) * 0.1 + (1.5 – [N * 0.05])

Where N is your current level.

In your case, 1/K would be:

53(54)/2 * 0.1 + (1.5 – (53 * 0.05)) = 141.95

or

K = 0.00704 (which coincides with your results)

Hope that helps

A more simplified version of the crit formula if you just want to check values quickly:

CRIT% = %CRITBonus + (K * critstat).

Maths on total damage

Using level 48 Meteor as an example, we have:
skill damage = 1.4 * (9103 + DMG) * [1 + critrate * (critdmg – 1) ]
Sample starting stats are 15000 DMG and 20% crit chance. I plotted a change of 50 stat points’ worth in crit (red line) and indamage (blue line) at different levels of crit damage (130%, 190%, 200%, 210%, 300%). The following plot is what results:

Here we see that at low crit damage, adding points to DMG will increase your damage more. However, once you go over 200% crit damage, adding points to crit will add more to your damage. Also, we can see that you will get more out of building crit+crit damage than you could ever get out of going pure damage. Also, a 10% increase in crit damage is worth a good 10 stat points’ worth of crit chance.

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