Damage Calculation

## Different damages

 Damage is modified several times by stats, it is interesting to know
when does each damage stat impact DPS in order to know what buff is the best.

 We have to start from the beginnig :

 the unupgraded weapon, and slowly add each buff, until we reach the one hit critical and balanced value, and the damage/second value.

### **Unupgraded weapon damage (UnWD)**

This is the damage of the weapon without upgrades.

* STR applies there :

1 str gives + 2% unupgraded weapon dmg

* Upgrades from smithy apply there :

1 upg gives + 8% unupgraded weapon dmg if purple

(+7% if blue, +6% if yellow, +5% if grey)

 bonus value from upgrades is added to the bonus value from str and the result will be the **base damage**.

 Even if the weapon is already upgraded 15 times, the str bonus will be based on its unupgraded stats (that you can not see anymore)

*if we give it 10 upg with 50 str, we will have (10\*8) + (50\*2) = +180% bonus damage*
 *we can calculate its base damage :*
 *(1+1.80) \* 500 = **1400 min dmg** and (1+1.80) \* 1000 = **2800 max dmg***

### **Base damage (BD)**

This is the damage that shows on the main stat screen. Buffs apply there

* Min dmg bonus is added to the min base dmg
* Max dmg bonus is added do the max base dmg
* Damage bonus is added to the min base dmg and the max base dmg
* damage potion buff apply there and is also based on the BD.

--> these buffs are added at the same time and are based on the BD, the result will be the **final damage**

(damage that you deal when you do not crit)

*min damage bonus will be : (10 + 20 + 90) = +120%*
*max damage bonus will be : (15 + 20 + 90) = +125%*

*final min dmg = 1400 \* (1.20 + 1) = 3080*
*final max dmg = 2800 \* (1.25 + 1) = 6300*

### **Final damage (FD)**

Balance apply there : game generates a decimal number between 0 and 2, and multiplies it by balance rate.

If the result "R" is above 1 max dmg will hit.

Else the game will calculate the difference between min and max dmg, and multiply it by "R", then add it to min dmg.

--> The result will be your next **hit damage**.

*we can calculate R : 1.72 \* 0.75 = 1.29*
*--> 1.29 is above 1, hit damage will be max damage = 6300*

*we can calculate R : 1.15 \* 0.75 = 0.8625*
*--> hit damage will be : [(6300 - 3080) \* 0.8625] + 3080 = 2777 + 3080 = 5857 dmg*

Average hit damage can be calculated from this:

Max damage is achieved if Bn > 1, thus the probability of max damage is:
Pm = 1-(1/2B)
And the probability for non-max damage is: Pn = 1/2B
Non-max damage increases from Min to Max linearly, so average non-max damage is:
Dn = (Max + Min) / 2
The average overall damage is just the (already normalized) probabilities times the damages:
Davg = (Pm \* Max) + (Pn \* Dn)
This simplifies to the formula:
Davg = Max - (Max/4B) + (Min/4B)

### **Hit damage (HD)**

This is the damage used for the crit hit damage calculations.

critical base damage apply there (200%).

Critical damage bonus is added to critical damage.

if you have 5% crit damage bonus, you will have 205% critical total damage bonus

Crit hit damage will be : HD \* crit total damage bonus.

*critical hit damage will be : 6300 \* 2.10 = 13230 dmg*

*critical hit damage will be 5857 \* 2.20 = 12885 dmg*

### **Attack Speed (AS)**

If attack speed is 2, you hit 2 times every second, if it is 0.5 you hit 1 time every 2 seconds.

by multiplying your average damage with your attack speed, you will get the holy **Damage / second value (DPS)**

it is a simple multiplicator that impacts the weapon attack speed value. Strangely, the displayed value is 1 point under the real value of the attack speed buff on items. If you have a ring that gives +4.8% attack speed, the real buff is +5.8% attack speed...

*1.49 \* (1.01+0.08) (1.01+0.048) = 1.72*
*for our weapon 5495 average dmg weapon, with 10% crit dmg buff,  average DPS with this attack speed will be :*
*5495 \* 2.10 \* 1.72 = 19848 dmg / second*

## Impact of stats on DPS

### Strength

Strength bonus is interesting because it is also buffed by the other min/max and damage bonuses. Even if its value is low, it should not be neglected.

Because str is the first buff (with weapon upgrade) applied to damage, and is used to set base damage, all the other buffs impact after str. This means that str damage bonus has a direct effect on the DPS, and it can be calculated. For more info about forumulas see Stat distribution

DPS bonus provided from 1 str (it depends of your weapon upgrade and rarity):

Players tend to agree about the fact that luck and agi have to be set to a certain value that guarantee their effect on every hit (never miss and always crit) but after this value is reached, all the points tend to go to str. This mean that a str bonus on a belt is +/- the same as a luck or an agi bonus.

### Damage buffs

there are 3 different damage buff : min, max and (both) damage buff.

**max damage buff**

it is more interesting than min damage bonus, especially if balance is high, because max damage will be reach more often. And even if max dmg isn't reached, the value is still used to calculate the hit damage.

It does not directly add to DPS, because max dmg isn't always hit, so 20% max damage bonus will add between 10 (if balance = 50) to +/-15% (if balance = 100) damage bonus to the DPS, depending of your balance.

#### **min damage buff**

it is interesting on low balance gears, because if max damage is reached often, min damage will not impact the result.

If my balance formula is right (and it might be^^), even with 100 balance only 50% of the hits will be max dmg. For a 75% balance, max damage will happen 33% of the time, this means that min damage bonus will be 33% less effective.

It does not directly add to DPS, because max dmg is often hit, so 20% min damage bonus will add between 10 (if balance = 100) to +/-15%(if balance = 50) damage bonus to the DPS, depending of your balance.

#### **Damage buff (and damage potion)**

It impacts both min and max damage, and is a direct addition to DPS, if you have 20% damage bonus, your DPS will be 20% higher.

### **Balance**

 game generates a random decimal number between 0 and 2, and multiplies it by balance rate.

 If the result "R" is above 1 max dmg will hit.

 Else the game will calculate the difference between min and max dmg, and multiply it by "R", then add it to min dmg.

 --> The result will be your next **hit damage**.

 (this is the only formula that may not be 100% accurate, but the real one should be close anyway.)

 *i.e : game generates the number 1.72, and balance is 75%*

 *we can calculate R : 1.72 \* 0.75 = 1.29*

 *--> 1.29 is above 1, hit damage will be max damage*

 i.e : *game generates the number 1.15 and balance is 75%*

 *we can calculate R : 1.15 \* 0.75 = 0.8625*

 *--> hit damage will be for a 3080-6300 weapon: [(6300 - 3080) \* 0.8625] + 3080 = 2777 + 3080 = 5857 dmg*

 Average hit damage can be approximately calculated : just set the random number value to 1*.*

 i.e : *game generates the number 1 and balance is 75%*

 *we can calculate R : 1 \* 0.75 = 0.75*

 *--> hit damage will be : [(6300 - 3080) \* 0.75] + 3080 = 2415 + 3080 = 5495 dmg*

 *--> this overestimates a bit the real average damage if balance is high because dmg can't go above max dmg value.*

### **Crit damage buff**

Crit damage buff has an indirect impact on DPS because its value is based on hit damage and applies at the same time as the crit bonus.

This means that if you have 10% crit damage bonus, your crits will deal 210% of hit damage (and not 220%) so the DPS bonus provided from crit damage is halved, and is in fact 5% dmg bonus.

### **Attack speed**

Directly impacts DPS. 1% attack speed is 1% DPS, **AND adds +0.15%DPS to all your other attack speed bonus points**. This mean that if you have a lot of attack speed, this stat becomes even better and starts a snowball effect.

### **Crit rate**

Directly impacts DPS. 1% crit rate is +1% DPS. AND makes crit damage usefull. It is caped at 100.

### **Accuracy**

Directly impacts DPS, if you lack 1% acc to get 100% hits, you lose 1% DPS.

This is way more important than a 1% bonus, because if you have +100%damage bonus you deal double damage but if you lose 100% of your DPS you do not deal any damage at all, whatever the other bonus.