Average damage

Description

This page contains information for calculating the average damage for both auto and (most) non-bleed abilities as well as the average damage for bleed abilities. There are two calculators in total as well as a description for each. The following are the major differences between non-bleeds and bleeds:

• Bleeds have a damage cap of 10,000 as they cannot land critical hits. Autos and non-bleeds can go above this damage cap for critical hits.
• Many bleeds have an unusually high chance to land their minimum hit.
• Bleeds are unaffected by most damage modifying perks as well as many other damage modifiers.

Below are the two buttons that allow usage of both calculators.

This article has a calculator here. Calculators determine experience and costs based on real-time prices from the Grand Exchange Market Watch.

The average damage for most non-bleed abilities and auto-attacks can be calculated by:

• Finding the minimum and maximum hit (Precise and Equilibrium perks included)
• The rank of Biting perk used (and if it is on level 20 gear)
• Whether or not Erethdor's grimoire has been activated
• Whether the attack comes after a critical boosting ability, such as Concentrated Blast, Fury, or Greater Fury

A quick way of finding the minimum and maximum hit of an ability is to use a Training dummy at the Dummy area in War's Retreat under any and all damage modifiers desired, including but not limited to:

• Damage modifying auras, which include the Berserker aura, Maniacal aura, Reckless aura, Mahjarrat aura, and Equilibrium aura
• Use of scrimshaws such as the Scrimshaw of the elements, Scrimshaw of cruelty, or their respective superior versions
• Use of ultimates such as Berserk, Sunshine, Metamorphosis, and Death's Swiftness
• Special attacks that modify damage from weapons such as the Zaros godsword or Dragon battleaxe
• Damage boosting prayers and ancient curses
• Use of potions such as overloads, holy overload potions, supreme overload potions, or elder overload potions
• Use of the vulnerability spell
• Damage boosting abilities, such as Needle Strike

Once the minimum hit and maximum hit are known for a specific hit of an ability (this means, for example, the calculation will be different for the first hit of hurricane as compared to the second), the average damage can be calculated. This calculator assumes the hit chance is 100%. This result of this calculator is meant to be a good approximation due to how the variables are stored (has an effect on the natural critical hit chance as well as the range of the critical hits).

• The same calculator along with documentation can be found at the top of this section.

 template  = Calculator:Template/Combat/Average damage
 form      = avgDmgCalcForm
 result    = avgDmgCalcResult
 param     = dmgType|Is this hit an auto attack?|No|select|Yes,No
 param     = tuska|Is the Tuska's Wrath ability used?|No|select|Yes,No
 param     = minHit|Minimum hit|1000|int|0-32000
 param     = maxHit|Maximum hit|5000|int|0-32000
 param     = eqRank|Equilibrium perk rank|2|select|0,1,2,3,4
 param     = eqAura|Is the Equilibrium aura active?|No|select|Yes,No
 param     = bitingRank|Biting perk rank|4|select|0,1,2,3,4
 param     = level20|Is the Biting perk on level 20 gear?|No|select|Yes,No
 param     = grimoire|Is Erethdor's grimoire active?|No|select|Yes,No
 param     = corbicula|#Corbicula rex farm totems (leave as 0 if not using Meteor Strike)|0|select|0,1,2
 param     = kalg|Is the Crit-i-Kal scroll from the Kal'gerion demon (familiar) active?|No|select|Yes,No
 param     = minMFury|(Optional) Minimum hit of Greater Fury|0|int|0-32000
 param     = maxMFury|(Optional) Maximum hit of Greater Fury|0|int|0-32000
 param     = splitSoul|Is Split Soul active?|No|select|Yes (with Amulet of Souls),Yes (without Amulet of Souls),No|Yes (with Amulet of Souls)=splitSoulGroup,vuln;Yes (without Amulet of Souls)=splitSoulGroup,vuln
 param     = splitSoulGroup|Split Soul effects||group|vuln
 param     = vuln|Is Vulnernabilty applied?|Yes|select|No,Yes||Vulnerability affects the Split Soul damage.
 param     = atLeastX|Find the probability of hitting greater than X damage (Enter value for X)|0|int|0-32000
 param     = debugToggle|Display additional information?|No|select|Yes,No

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Calculations

${\begin{aligned}{\text{avgdmg}}&={\text{p}}_{\text{crit}}^{\text{forced}}\cdot {\bigg [}\max(0,\min(1-{\text{z}}_{1},1))\times {\text{crit}}_{\text{cap}}\\&\qquad \qquad \quad +\min(\max(0,{\text{z}}_{1}),1)\times {\frac {\min({\text{crit}}_{\text{cap}},{\text{crit}}_{\text{min}}^{\text{forced}})+\min({\text{crit}}_{\text{cap}},{\text{crit}}_{\text{max}}^{\text{forced}})}{2}}{\bigg ]}\\&\quad +(1-{\text{p}}_{\text{crit}}^{\text{forced}})\cdot {\bigg \{}{\text{p}}_{\text{crit}}^{\text{nat}}\cdot {\bigg [}\max(0,\min(1-{\text{z}}_{2},1))\times {\text{crit}}_{\text{cap}}\\&\qquad \qquad \qquad \qquad \qquad \quad +\min(\max(0,{\text{z}}_{2}),1)\times {\frac {\min({\text{crit}}_{\text{cap}},{\text{crit}}_{\text{min}}^{\text{nat}})+\min({\text{crit}}_{\text{cap}},{\text{hit}}_{\text{max}})}{2}}{\bigg ]}\\&\qquad \qquad \qquad \qquad +(1-{\text{p}}_{\text{crit}}^{\text{nat}})\cdot {\bigg [}\max(0,\min(1-{\text{y}},1))\times {\text{dmg}}_{\text{cap}}\\&\qquad \qquad \qquad \qquad \qquad \qquad \qquad +\min(\max(0,{\text{y}}),1)\times {\frac {\min({\text{dmg}}_{\text{cap}},{\text{hit}}_{\text{min}})+\min({\text{dmg}}_{\text{cap}},{\text{crit}}_{\text{min}}^{\text{nat}})}{2}}{\bigg ]}{\bigg \}}\end{aligned}}$

Notes

• The damage range is defined by $[{\text{hit}}_{\text{min}},{\text{hit}}_{\text{max}}]$ with the condition that the ${\text{hit}}_{\text{min}}\leq {\text{hit}}_{\text{max}}$.
• The damage cap, ${\text{dmg}}_{\text{cap}}$, is the maximum damage possible in the non-critical range. This is 10000 damage.
• The critical cap, ${\text{crit}}_{\text{cap}}$, is the maximum damage a critical hit can be. This is 12000 damage unless Erethdor's grimoire is active, in which case it is 15000 damage.
• A forced critical hit are criticals hits that come from the Biting perk, Erethdor's grimoire, Concentrated Blast, Fury, etc.
  • ${\text{crit}}_{\text{min}}^{\text{forced}}$ is the minimum hit of the critical range from forced critical hits.
  • ${\text{crit}}_{\text{min}}^{\text{forced}}={\text{hit}}_{\text{min}}+\lfloor .95\cdot \left({\text{hit}}_{\text{max}}-{\text{hit}}_{\text{min}}\right)\rfloor$
  • ${\text{crit}}_{\text{max}}^{\text{forced}}$ is the maximum hit of the critical range from forced critical hits. It may be slightly off from the maximum hit, ${\text{hit}}_{\text{max}}$.
  • ${\text{crit}}_{\text{max}}^{\text{forced}}={\text{hit}}_{\text{min}}+\left\lfloor {\frac {\lfloor .95\cdot ({\text{hit}}_{\text{max}}-{\text{hit}}_{\text{min}})\rfloor }{.95}}\right\rfloor$
• A natural critical hit are criticals that come from landing a critical hit that does not come from forced criticals.
  • ${\text{crit}}_{\text{min}}^{\text{nat}}$ is the minimum hit of the critical range from natural critical hits.
  • If neither the Equilibrium aura nor perk are used:
    • ${\text{crit}}_{\text{min}}^{\text{nat}}={\text{max}}(\lfloor .95\cdot {\text{hit}}_{\text{max}}\rfloor ,{\text{hit}}_{\text{min}})$
  • If either the Equilibrium aura or perk are used:
    • More information can be found here.
• The purpose of ${\text{z}}_{1}$ is to calculate how much of the forced critical hit range is above the critical cap.
  • ${\text{z}}_{1}={\frac {{\text{crit}}_{\text{cap}}-{\text{crit}}_{\text{min}}^{\text{forced}}}{{\text{crit}}_{\text{max}}^{\text{forced}}-{\text{crit}}_{\text{min}}^{\text{forced}}}}$
• The purpose of ${\text{z}}_{2}$ is to calculate how much of the natural critical hit range is above the critical cap.
  • ${\text{z}}_{2}={\frac {{\text{crit}}_{\text{cap}}-{\text{crit}}_{\text{min}}^{\text{nat}}}{{\text{hit}}_{\text{max}}-{\text{crit}}_{\text{min}}^{\text{nat}}}}$
• The purpose of ${\text{y}}$ is to calculate how much of the non-critical hit range is above the damage cap.
  • ${\text{y}}={\frac {{\text{dmg}}_{\text{cap}}-{\text{hit}}_{\text{min}}}{{\text{crit}}_{\text{min}}^{\text{nat}}-{\text{hit}}_{\text{min}}}}$
• The probability of landing a forced critical hit, ${\text{p}}_{\text{crit}}^{\text{forced}}$, is taken to be the sum of the probabilities from each source. Note: The sum of the probabilities is an assumption. If it is confirmed that the probabilities combine in some other way, this will be changed.
  • ${\text{p}}_{\text{crit}}^{\text{forced}}=\min \left({\text{p}}_{\text{biting}}+{\text{p}}_{\text{grimoire}}+\cdots ,1\right)$
• The probability of landing a natural critical hit depends on whether the Equilibrium aura or perk are used. The effect of the Equilibrium aura overrides the perk.
  • ${\text{p}}_{\text{crit}}^{\text{nat}}={\begin{cases}\min \left({\frac {{\text{hit}}_{\text{max}}}{40\cdot ({\text{hit}}_{\text{max}}-{\text{hit}}_{\text{min}})}}+.0.125,1\right)&{\text{if the Equilibrium aura is active}}\\\min \left({\frac {(25-R)\cdot {\text{hit}}_{\text{max}}}{500\cdot ({\text{hit}}_{\text{max}}-{\text{hit}}_{\text{min}})}}+{\frac {R}{2000}},1\right)&{\text{if the Equilrium perk is used where R is the rank of the perk (Equilibrium aura is not active)}}\\\min \left({\frac {.05\cdot {\text{hit}}_{\text{max}}}{{\text{hit}}_{\text{max}}-{\text{hit}}_{\text{min}}}},1\right)&{\text{if neither the Equilibrium aura nor perk are used}}\end{cases}}$

This article has a calculator here. Calculators determine experience and costs based on real-time prices from the Grand Exchange Market Watch.

The average damage for bleedabilities can be calculated by:

• Finding the minimum and maximum hit (Lunging perk included)

A quick way of finding the minimum and maximum hit of an ability is to use a Training dummy at the Dummy area in War's Retreat under any and all damage modifiers desired, including but not limited to:

• Damage modifying auras which include Berserker aura, Maniacal aura, Reckless aura, Mahjarrat aura
• Use of scrimshaws such as Scrimshaw of the elements, Scrimshaw of cruelty, or their respective superior versions
• Use of Metamorphosis
• Special attacks that modify damage from weapons such as the Dragon battleaxe (stat boost)
• use of potions such as overloads, holy overload potions, supreme overload potions, or elder overload potions
• Use of the vulnerability spell

Once the minimum hit and maximum hit are known, the average damage can be calculated. This calculator only needs the minimum and maximum damage for the first hit of any bleed . This calculator assumes the hit chance is 100%.

• The same calculator along with documentation can be found at the top of this section.

 template  = Calculator:Template/Combat/Average damage (bleeds)
 form      = avgDmgBleedsCalcFormBleeds
 result    = avgDmgBleedsCalcResultBleeds
 param     = bleed|Choose bleed:|Dismember|select|Dismember,Slaughter,Blood Tendrils,Massacre/Deadshot,Fragmentation Shot/Combust,Corruption Shot/Corruption Blast,Incendiary Shot
 param     = minHit|Minimum hit|1000|int|0-10000
 param     = maxHit|Maximum hit|1880|int|0-10000
 param     = mdBleedHit|Massacre/Deadshot bleed hit|1000|int|0-10000
 param     = strcape|Is the Strength cape perk being used?|Yes|select|Yes,No
 param     = lungingPerk|Is the Lunging perk being used?|No|select|Yes (only affects the walk modifier for Fragmentation Shot/Combust),No
 param     = splitSoul|Is Split Soul active?|No|select|Yes (with Amulet of Souls),Yes (without Amulet of Souls),No|Yes (with Amulet of Souls)=splitSoulGroup,vuln;Yes (without Amulet of Souls)=splitSoulGroup,vuln
 param     = splitSoulGroup|Split Soul effects||group|vuln
 param     = vuln|Is Vulnernabilty applied?|Yes|select|No,Yes||Vulnerability affects the Split Soul damage.
 param     = spear|Is the Masterwork Spear of Annihilation being used?|No|select|Yes,No

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