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Combat: Difference between revisions

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Combat (view source)

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→‎Accuracy Rating: Added a note about max going to 120 with TotH
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{{V|0.18.2}}
{{HasGuide}}
{{V|1.1.1}}
[[File:Combat.svg|thumb|right|Combat]]
[[File:Combat.svg|thumb|right|Combat]]
[[File:Combat Page Map.png|thumb|right|Combat page.]]
[[File:Combat Page Map.png|thumb|right|Combat page.]]
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{{PAGENAME}} involves fighting various [[monsters]] throughout the [[combat areas]], [[slayer areas]], and [[dungeons]] of Melvor. [[Food]] and [[Equipment]] cannot be changed while in a [[dungeon]] unless an [[Dungeon Equipment Swapping|upgrade]] has been purchased from the [[shop]].
{{PAGENAME}} involves fighting various [[monsters]] throughout the [[combat areas]], [[slayer areas]], and [[dungeons]] of Melvor. [[Food]] and [[Equipment]] cannot be changed while in a [[dungeon]] unless an [[Dungeon Equipment Swapping|upgrade]] has been purchased from the [[shop]].


Combat stats—viewable from the combat page—are affected by the player's combat skills and any [[Equipment]] worn. The combat skills are {{Skill|Attack}}, {{Skill|Strength}}, {{Skill|Defence}}, {{Skill|Hitpoints}}, {{Skill|Ranged}}, {{Skill|Magic}}, {{Skill|Prayer}}, and {{Skill|Slayer}}. These skills are factored in when calculating the player's combat level, which is an approximation of the player's power. Players start at combat level 3 and can reach a maximum of combat level 126, while [[monsters]] range from combat level [[Chicken|1]] to [[Ragnar|815]]. The player's combat level affects the difficulty of [[monsters]] given in [[Slayer]] Tasks.
Combat stats — viewable from the combat page — are affected by the player's combat skills and any [[Equipment]] worn. The combat skills are {{Skill|Attack}}, {{Skill|Strength}}, {{Skill|Defence}}, {{Skill|Hitpoints}}, {{Skill|Ranged}}, {{Skill|Magic}}, {{Skill|Prayer}}, and {{Skill|Slayer}}. These skills are factored in when calculating the player's combat level, which is an approximation of the player's power. Players start at combat level 3 and can reach a maximum of combat level 126 ({{TotH}} 153), while [[monsters]] range from combat level [[Chicken (monster)|1]] to [[Bane, Instrument of Fear|1300]].


== Combat Info ==
== Combat Info ==
'''Max Hit''' shows the maximum potential damage a successful attack can do. The Max Hit displayed for players and enemies does not factor in damage reduction.<br>
* '''Max Hit''' shows the maximum potential damage a successful attack can do. The Max Hit displayed for players and enemies does not factor in damage reduction.
'''Chance to Hit''' shows the player's percent chance to hit the enemy with their attack.<br>
* '''Chance to Hit''' shows the player's percent chance to hit the enemy with their attack.
'''Accuracy Rating''' affects the likelihood an attack will be successful during combat. The player's Accuracy Rating is compared to the enemy's Evasion Rating when calculating the chance an attack will succeed. <br>
* '''Accuracy Rating''' affects the likelihood an attack will be successful during combat. The player's Accuracy Rating is compared to the enemy's Evasion Rating when calculating the chance an attack will succeed.
'''Dmg Reduction''' reduces any damage received by the percent shown. <br>
* '''Damage Reduction''' (also referred to as '''DR''') reduces any damage received by the percent shown.
'''Evasion Rating''' affects the likelihood an attack will be avoided during combat. There are three types of Evasion Rating; Melee, Ranged, and Magic. The Attack Type being defended against affects which Evasion Rating will be used. The enemy's Accuracy Rating is compared to the player's Evasion Rating when calculating the chance an attack will be avoided.<br>
* '''Evasion Rating''' affects the likelihood an attack will be avoided during combat. There are three types of Evasion Rating; Melee, Ranged, and Magic. The Attack Type being defended against affects which Evasion Rating will be used. The enemy's Accuracy Rating is compared to the player's Evasion Rating when calculating the chance an attack will be avoided.
'''Prayer Points''' are gained by burying [[Prayer#Bones|bones]] and are used to activate [[Prayer#Prayers|prayers]] during combat.<br>
* '''Prayer Points''' are gained by burying [[Prayer#Bones|bones]] and are used to activate [[Prayer#Prayers|prayers]] during combat.
'''Active Prayers''' provide bonuses to the player during combat and use Prayer Points to remain active. Up to two [[Prayer#Prayers|prayers]] can be active simultaneously, so long as the required Prayer Points are available.<br>
* '''Active Prayers''' provide bonuses to the player during combat and use Prayer Points to remain active. Up to two [[Prayer#Prayers|prayers]] can be active simultaneously, so long as the required Prayer Points are available.


== Basic Combat ==
== Basic Combat ==
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All [[monsters]] killed in combat and slayer areas will drop [[Prayer#Bones|bones]] upon death, with a chance for additional [[Monster Loot Tables|loot]] based on the [[Monsters|monster's]] type. The "Drops" option will display the [[Monster Loot Tables|possible loot drops]] a monster can give.
All [[monsters]] killed in combat and slayer areas will drop [[Prayer#Bones|bones]] upon death, with a chance for additional [[Monster Loot Tables|loot]] based on the [[Monsters|monster's]] type. The "Drops" option will display the [[Monster Loot Tables|possible loot drops]] a monster can give.


Any items enemies drop upon death must be looted manually by selecting "Loot All" or the item itself, unless the {{ItemIcon|Amulet of Looting}} is equipped. If there are more than 16 stacks of loot, the oldest drop disappears. Bones stack and do not time out like other drops. Other drops do not stack even if they are of the same type.
Any items enemies drop upon death must be looted manually by selecting "Loot All" or the item itself, unless the {{ItemIcon|Amulet of Looting}} is equipped. If there are more than 100 stacks of loot, the oldest drop disappears. Bones stack and do not time out like other drops. Other drops do not stack even if they are of the same type.


[[Monsters]] fought in [[dungeons]] will not drop loot when killed (except for God Dungeons, where shards are rewarded after each killed monster) and do not count towards {{Skill|Slayer}} Tasks. When the last [[Monsters|monster]] in a [[dungeon]] is killed the player will be awarded with a [[Dungeons#Dungeon List|reward]], which is sent to the [[Bank]] automatically.  
[[Monsters]] fought in [[dungeons]] will not drop loot when killed and do not count towards {{Skill|Slayer}} Tasks. The God Dungeons are an exception to this rule: the shards are rewarded after each killed monster. When the last [[Monsters|monster]] in a [[dungeon]] is killed, the player will be given a [[Dungeons#Dungeon List|reward]] that is sent to the [[Bank]] automatically.


== Combat Triangle ==
== Combat Triangle ==
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== Gaining Experience ==
== Gaining Experience ==
Players can gain experience in eight different skills while training combat:
Players can gain experience in nine different skills while training combat:


{{Skill|Hitpoints}} experience is gained at a rate of 0.133 experience per damage dealt regardless of the combat style being used.
{{Skill|Hitpoints}} experience is gained at a rate of 0.133 experience per damage dealt regardless of the combat style being used.
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No additional {{Skill|Magic}} experience is directly generated for using [[Magic#Curses|Curses]] or [[Magic#Auroras|Auroras]], although they may indirectly generate additional experience by increasing the amount of damage the player deals.
No additional {{Skill|Magic}} experience is directly generated for using [[Magic#Curses|Curses]] or [[Magic#Auroras|Auroras]], although they may indirectly generate additional experience by increasing the amount of damage the player deals.


Players gain 0.2 {{Skill|Prayer}} experience per damage dealt per prayer point spent on prayers that affected the attack. For example, if {{PrayerIcon|Piety}} (7 prayer point cost) is active, each attack made will generate 1.4 extra experience per damage dealt. Only prayers such as {{PrayerIcon|Thick Skin}} that say 'Provides extra Prayer XP based on damage dealt to the enemy' in their description will generate experience this way - Prayers such as {{PrayerIcon|Protect from Magic}} that say 'Provides no extra Prayer XP' will not contribute towards this experience bonus.
Players gain <math>\frac{1}{30}</math> or <math>0.0\bar{3}</math> {{Skill|Prayer}} experience per damage dealt per prayer point spent on prayers that affected the attack. For example, if {{PrayerIcon|Steel Skin}} (3 prayer point cost) is active, each attack made will generate 0.1 extra experience per damage dealt. Only prayers such as {{PrayerIcon|Thick Skin}} that say 'Provides extra Prayer XP based on damage dealt to the enemy' in their description will generate experience this way - Prayers such as {{PrayerIcon|Protect from Magic}} that say 'Provides no extra Prayer XP' will not contribute towards this experience bonus.


All of the above experience will be multiplied by 1.07 while a {{ItemIcon|Gold Emerald Ring}} is equipped.
All of the above experience will be multiplied by 1.04 while a {{ItemIcon|Gold Emerald Ring}} is equipped.


{{Skill|Slayer}} experience is gained through two sources: Killing monsters on a [[Slayer#Slayer Task|Slayer Task]] and killing monsters in a [[Slayer area]]. Killing the monster that is the player's current Slayer Task will generate experience equal to 10% of the monster's hitpoints. Killing a monster in a Slayer area will generate experience equal to 5% of the monster's hitpoints. If the player's Slayer Task is for a monster in a Slayer area, these bonuses will stack for a total of 15% of the monster's hitpoints in experience per kill.
{{Skill|Slayer}} experience is gained through two sources: Killing monsters on a [[Slayer#Slayer Task|Slayer Task]] and killing monsters in a [[Slayer area]]. Killing the monster that is the player's current Slayer Task will generate experience equal to 10% of the monster's hitpoints. Killing a monster in a Slayer area will generate experience equal to 5% of the monster's hitpoints. If the player's Slayer Task is for a monster in a Slayer area, these bonuses will stack for a total of 15% of the monster's hitpoints in experience per kill.


Slayer Experience cannot be increased by the {{ItemIcon|Gold Emerald Ring}}, however the various pieces of Slayer Equipment that can be purchased from the [[Shop]] using {{Icon|Slayer Coins}} provides an experience bonus when worn.
Slayer Experience cannot be increased by the {{ItemIcon|Gold Emerald Ring}}, however the various pieces of Slayer Equipment that can be purchased from the [[Shop]] using {{Icon|Slayer Coins}} provides an experience bonus when worn.
{{Skill|Summoning}} experience can be gained if the player has equipped [[Summoning#Summoning Tablets|tablets]] for at least one combat familiar. Summoning experience will be granted whenever the familiar attacks the enemy, consuming a tablet in the process. Being a non-combat skill, Summoning experience gained cannot be increased by the {{ItemIcon|Gold Emerald Ring}}.


== Death ==
== Death ==
Receiving damage that would bring the player's total {{Skill|Hitpoints}} to 0 or below will cause the player to die. Upon death a random piece of [[Equipment]] worn will be lost forever (unless the {{PrayerIcon|Protect Item}} prayer is active). If ammo is lost, the entire stack - regardless of size - will be forfeited. Only non-[[food]] items that have been equipped in an active slot can be lost upon death.
Receiving damage that would bring the player's total {{Skill|Hitpoints}} to 0 or below will cause the player to die. Upon death a random equipment slot is selected, any [[Equipment]] within the selected slot will be lost forever (unless the {{PrayerIcon|Protect Item}} prayer is active). If either ammunition or Summoning tablets are lost, the entire stack - regardless of size - will be forfeited. Only non-[[food]] items that have been equipped in an active slot can be lost upon death.


All items equipped have an equal chance of being lost. When the death penalty rolls to determine which item is lost, it starts by rolling a random equipment slot. If the player has nothing equipped in that slot (For example, if they are using Melee and do not have any Ammo equipped) nothing will be lost, and a message saying "Luck was on your side today. You lost nothing." will appear.
All items equipped have an equal chance of being lost. When the death penalty rolls to determine which item is lost, it starts by rolling a random equipment slot. If the player has nothing equipped in that slot (For example, if they are using Melee and do not have any Ammo equipped) nothing will be lost, and a message saying "Luck was on your side today. You lost nothing." will appear.
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The first formula is used to calculate the player's Base Combat Level.
The first formula is used to calculate the player's Base Combat Level.


<math>\small{ \begin{aligned} \text{Base Combat Level} = 0.25 * (\text{Defence Skill Level} + \text{Hitpoints Skill Level} + (\text{Prayer Skill Level} / 2) \end{aligned}}</math>
<!-- JS source: game.js, function playerCombatLevel
--><math>\small{ \begin{aligned} \text{Base Combat Level} = 0.25 \times (\text{Defence Skill Level} + \text{Hitpoints Skill Level} + \lfloor 0.5 \times \text{Prayer Skill Level} \rfloor) \end{aligned}}</math>


The second set of formulas are used to calculate the player's Offensive Combat Levels, only the highest result is used.
The second set of formulas are used to calculate the player's Offensive Combat Levels, only the highest result is used.


<math>\small{\begin{aligned}\text{Melee Combat Level} = 0.325 * (\text{Attack Skill Level} + \text{Strength Skill Level})\end{aligned}}</math>
<math>\small{\begin{aligned}
\text{Melee Combat Level} &= \text{Attack Skill Level} + \text{Strength Skill Level} \\
\text{Ranged Combat Level} &= \lfloor 1.5 \times \text{Ranged Skill Level} \rfloor \\
\text{Magic Combat Level} &= \lfloor 1.5 \times \text{Magic Skill Level} \rfloor
\end{aligned}}</math>


<math>\small{\begin{aligned}\text{Ranged Combat Level} = 0.325 * (3 * \text{Ranged Skill Level} / 2)\end{aligned}}</math>
The third formula is used to calculate the player's Combat Level, rounded down to the nearest whole number.
 
<math>\small{\begin{aligned}\text{Magic Combat Level} = 0.325 * (3 * \text{Magic Skill Level} / 2)\end{aligned}}</math>


The third formula is used to calculate the player's Combat Level, rounded down to the nearest whole number.
<math>\small{\begin{aligned}\text{Combat Level} = \lfloor \text{Base Combat Level} + 0.325 \times \text{Highest Offensive Combat Level} \rfloor\end{aligned}}</math>


<math>\small{\begin{aligned}\text{Combat Level} = \text{Base Combat Level} + \text{Highest Offensive Combat Level}\end{aligned}}</math>
Where: <math> \left \lfloor x \right \rfloor </math> is the [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions floor function].


=== Stun (Freeze) ===
=== Stun (Freeze) ===
{{Main|Reference=Combat Debuff}}
Stun, also known as freeze, is a status effect that can be inflicted by both players and [[monsters]]. Stun can be applied for a number of turns by a [[Special Attacks|special attack]] or a normal attack by the player if the {{ItemIcon|Fighter Amulet}} is equipped. When an attack applies stun the current attack of the target is interrupted, including special attacks that are in progress. If the target is already stunned, it will not be applied again. When stunned, a stun timer counts down with a period equivalent to the target's attack speed. On completion of the timer the number of stun turns is decreased by one, and the status is removed if the resulting amount is zero. In addition to not being able to attack while stunned, a character cannot evade any attacks.
Stun, also known as freeze, is a status effect that can be inflicted by both players and [[monsters]]. Stun can be applied for a number of turns by a [[Special Attacks|special attack]] or a normal attack by the player if the {{ItemIcon|Fighter Amulet}} is equipped. When an attack applies stun the current attack of the target is interrupted, including special attacks that are in progress. If the target is already stunned, it will not be applied again. When stunned, a stun timer counts down with a period equivalent to the target's attack speed. On completion of the timer the number of stun turns is decreased by one, and the status is removed if the resulting amount is zero. In addition to not being able to attack while stunned, a character cannot evade any attacks.
While a player or monster is stunned, they take 30% more damage.
While a player or monster is asleep, they take 20% more damage.


=== Accuracy Rating ===
=== Accuracy Rating ===
==== Melee Accuracy Rating ====
<!-- JS source: character.js, function computeAccuracy
The first formula is used to calculate the player's Effective Melee Attack Level. The Attack Style Bonus is based on bonuses from other skills, such as from Agility.
-->The calculation used to determine the player's accuracy rating is broadly the same for all combat styles, with some parameters varying depending on the player's current attack type and style:
{| class="wikitable stickyHeader"
|- class="headerRow-0"
! Attack Type !! Attack Style !! Skill Level !! Attack Bonus Stat
|-
| rowspan="3" | {{Icon|Melee}} || {{Skill|Attack|Stab|nolink=true}} || {{Skill|Attack}} || Stab attack bonus
|-
| {{Skill|Strength|Slash|nolink=true}} || {{Skill|Strength}} || Slash attack bonus
|-
| {{Skill|Defence|Block|nolink=true}} || {{Skill|Defence}} || Block attack bonus
|-
| {{Skill|Ranged}} || All || {{Skill|Ranged}} || Ranged attack bonus
|-
| {{Skill|Magic}} || All || {{Skill|Magic}} || Magic attack bonus
|}


<math> \small{\begin{aligned} \text{Effective Melee Attack Level}=\text{Attack Skill Level} + 8 + \text{Attack Style Bonus} \end{aligned}}</math>
The first formula is used to determine the player's effective skill level:


The second formula is used to calculate the player's Melee Accuracy Rating. Melee Attack Bonus can be found in Equipment Stats and changes depending on the Attack Style selected. Simply substitute Stab Bonus, Slash Bonus, or Defend Bonus, from Equipment Stats with Melee Attack Bonus in this formula. The potion and prayer bonuses, will be the relevant numbers written in the potion and prayer descriptions.
<math>\small{\text{Effective Skill Level} = \text{Standard Skill Level} + \text{Hidden Skill Level}}</math>


<math> \small{ \begin{aligned}  
Where 'Standard Skill Level' is the player's skill level as seen in the left-hand navigation bar (up to a maximum of 99, or 120 with {{TotH}}), while 'Hidden Skill Level' is the sum of any hidden skill level bonuses, such as those granted by {{Skill|Astrology}}, some [[Pets]] or items like the {{ItemIcon|Silver Ruby Necklace}}.
\text{Melee Accuracy Rating} = \big\{ &\text{Effective Melee Attack Level} * (\text{Melee Attack Bonus} +64) \\
&{}* (1 + \text{Potion Accuracy Rating Bonus} / 100) * (1 + \text{Prayer Accuracy Rating Bonus} / 100) \big\} \end{aligned} } </math>


==== Ranged Accuracy Rating ====
Next, the base accuracy bonus should be calculated. This is the sum of the relevant attack bonus statistic provided by all currently equipped equipment (as seen in the Equipment Stats interface), plus:
The first formula is used to calculate the player's Effective Ranged Attack Level. The Attack Style Bonus is based on bonuses from other skills, such as from Agility.
* {{Icon|Melee}}
** +15 if fighting a {{Skill|Ranged}} monster while the {{ItemIcon|Minotaur}}/{{ItemIcon|Centaur}} synergy is active
* {{Skill|Ranged}}
** +15 if fighting a {{Skill|Magic}} monster while the {{ItemIcon|Witch}}/{{ItemIcon|Centaur}} synergy is active
** The additional ranged attack bonus provided by {{ItemIcon|Stormsnap}} if equipped, the formula for this is included on the bow's page


<math> \small{\begin{aligned} \text{Effective Ranged Attack Level}=\text{Ranged Skill Level} + 8 + \text{Attack Style Bonus} \end{aligned}}</math>
In addition, the player's accuracy modifier needs to be known. This is the sum of all global accuracy rating and the relevant attack type's accuracy rating increases, provided from places such as [[Herblore#Combat Potions|Potions]], {{Skill|Agility}}, and {{Skill|Astrology}}. If using {{Icon|Magic|Surge spells|nolink=true|img=Wind Surge|type=spell}} from the [[Magic#Standard Magic|standard magic spellbook]], this modifier is increased by a further 6%.


The second formula is used to calculate the player's Ranged Accuracy Rating. Ranged Attack Bonus can be found in Equipment Stats, under Offensive Stats with the bow and arrow icon. The potion and prayer bonuses, will be the relevant numbers written in the potion and prayer descriptions.
Finally, the player's accuracy rating can then be calculated as:


<math>\text{Accuracy Rating} = \left \lfloor \left (\text{Effective Skill Level} + 9 \right ) \times \left (\text{Base Accuracy Bonus} + 64 \right ) \times \left (1 + \frac{\text{Accuracy Modifier}}{100} \right ) \right \rfloor</math>


<math> \small{ \begin{aligned}
Where: <math> \left \lfloor x \right \rfloor </math> is the [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions floor function].
\text{Ranged Accuracy Rating} = \big\{ &\text{Effective Ranged Attack Level} * (\text{Ranged Attack Bonus} +64) \\
&{}* (1 + \text{Potion Accuracy Rating Bonus} / 100) * (1 + \text{Prayer Accuracy Rating Bonus} / 100) \big\} \end{aligned} } </math>


==== Magic Accuracy Rating ====
=== Chance to Hit ===
The first formula is used to calculate the player's Effective Magic Attack Level. The Attack Style Bonus is based on bonuses from other skills, such as from Agility.
<!-- JS source: character.js, function computeHitChance
-->To calculate the chance an attack will hit, the Accuracy Rating of the attacker is compared to the relevant Evasion Rating of the target. If the attacker's Accuracy Rating is lower than the defender's evasion rating the formula is as follows:


<math> \small{ \begin{aligned} \text{Effective Magic Attack Level}=\text{Magic Skill Level} + 8 + \text{Attack Style Bonus} \end{aligned}} </math>
<math> \small{ \begin{aligned} \text{Percentage Hit Chance} = \frac{\text{Attacker Accuracy Rating}}{2 \times \text{Target Evasion Rating}} \times 100 \end{aligned}} </math>


The second formula is used to calculate the player's Magic Accuracy Rating. Magic Attack Bonus can be found in Equipment Stats, under Offensive Stats with the wizard hat icon. The potion and prayer bonuses, will be the relevant numbers written in the potion and prayer descriptions.
Otherwise, the attacker's Accuracy Rating is higher than or equal to the target's Evasion Rating, and the formula is instead:


<math> \small{ \begin{aligned}  
<math> \small{ \begin{aligned} \text{Percentage Hit Chance} = 1 - \frac{\text{Target Evasion Rating}}{2 \times\text{Attacker Accuracy Rating}} \times 100 \end{aligned}}</math>
\text{Magic Accuracy Rating} = \big\{ &\text{Effective Magic Attack Level} * (\text{Magic Attack Bonus} +64) \\
&* (1 + \text{Potion Accuracy Rating Bonus} / 100) * (1 + \text{Prayer Accuracy Rating Bonus} / 100) \big\} \end{aligned} } </math>


=== Chance to Hit ===
When the attacker's Accuracy Rating and the target's Evasion Rating are the same, the chance to hit is 50%. The higher the attacker's Accuracy Rating is above the targets Evasion Rating, the less valuable each point will be. At double the target's Evasion Rating, the attacker will hit 75% of the time, at triple, the attacker will hit 83.3% of the time.
To calculate the chance an attack will hit, the Accuracy Rating of the attacker is compared to the relevant Evasion Rating of the defender. If the attacker's Accuracy Rating is lower than the defender's evasion rating the formula looks like this.


<math> \small{ \begin{aligned} \text{Hit Percent Chance}=\ (0.5 * \text{Accuracy Rating} / \text{Evasion Rating}) * 100 \end{aligned}} </math>
=== Max Hit ===
<!-- JS source: character.js, function computeMaxHit -->
==== Melee and Ranged Max Hit ====
<!-- JS source: character.js, functions computeMeleeMaxHit, computeRangedMaxHit
-->First, calculate the player's effective {{Skill|Strength}} level for the melee max hit, or the effective {{Skill|Ranged}} level for the ranged max hit:


If the attacker's Accuracy Rating is higher than the defender's Evasion Rating the formula looks like this.
<math>\small{\text{Effective Skill Level} = \text{Standard Skill Level} + \text{Hidden Skill Level}}</math>


<math> \small{ \begin{aligned} \text{Hit Percent Chance}=\ (1 - 0.5 * \text{Evasion Rating} / \text{Accuracy Rating}) * 100 \end{aligned}}</math>
Where 'Standard Skill Level' is the player's skill level as seen in the left-hand navigation bar (up to a maximum of 99), while 'Hidden Skill Level' is the sum of any hidden skill level bonuses, such as those granted by {{Skill|Astrology}}.


When the attacker's Accuracy Rating and the target's Evasion Rating are the same, the chance to hit is 50%. The higher the attacker's Accuracy Rating is above the targets Evasion Rating, the less valuable each point will be. At double the targets Evasion Rating, the attacker will hit 75% of the time, at triple, the attacker will hit 83.3% of the time.
Next, the strength bonus should be calculated. This is the sum of the relevant statistic provided by all currently equipped equipment (as seen in the Equipment Stats interface), where the relevant statistic is:
* '''Melee strength bonus''' for {{Icon|Melee}}
* '''Ranged strength bonus''' for {{Skill|Ranged}}


=== Max Hit ===
Given these figures, the base max hit (i.e. max hit before modifiers) is then calculated as:
==== Melee Max Hit ====
The first formula is used to calculate the player's Effective Strength Level.


<math> \small{ \begin{aligned} \text{Effective Melee Strength Level} = \text{Strength Skill Level} + 8 + \text{petBonus} \end{aligned}} </math>
<math>\text{Base Max Hit} = \left \lfloor M \times \left ( 2.2 + \frac{\text{Effective Skill Level}}{10} + \frac{\text{Effective Skill Level} + 17}{640} \times \text{Strength Bonus} \right ) \right \rfloor</math>


petBonus is 4 if {{PetIcon|Lil Ron}} is unlocked, or 1 if not.
Where <math>M</math> varies based on the [[Game Mode]] being played, and is equal to:
* 10 if playing [[Game_Mode#Standard|Standard]] or {{Icon|Hardcore}} mode
* 100 if playing {{Icon|Adventure}} mode


The second formula is used to calculate the player's Max Hit. Strength Bonus can be found in Equipment Stats next to the flexed arm icon. The potion and prayer bonuses will be the relevant numbers written in the potion and prayer descriptions.
This base max hit is then adjusted by the percentage and flat max hit modifiers to arrive at the final max hit figure, where the modifiers include both global max hit increases as well as increases specific to the relevant attack type:


<math> \small{ \begin{aligned} \text{Max Hit} = 10 * \big\{ &(1.3 + \text{Effective Melee Strength Level} / 10 + \text{Strength Bonus} / 80 + \text{Effective Melee Strength Level} * \text{Strength Bonus} / 640)\\
<math>\text{Max Hit} = \left \lfloor \text{Base Max Hit} \times \left ( 1 + \frac{\text{Percentage Max Hit Modifier}}{100} \right ) \right \rfloor + \text{Flat Max Hit Modifier}</math>
&* (1 + \text{Potion Strength Bonus} / 100) * (1 + \text{Prayer Strength Bonus} / 100) \big\} \end{aligned}}</math>


This, simplified, is equivalent to
==== Magic Max Hit ====
 
<!-- JS source: character.js, function computeMagicMaxHit
<math> \text{Max Hit} = \left( 22 + \text{Strength Skill Level} + \dfrac{17 + \text{Strength Skill Level}}{64}\cdot \text{Strength bonus} \right) \cdot \left( 1 + \frac{\text{Potion Strength Bonus}}{100} \right) \cdot \left( 1 + \frac{\text{Prayer Strength Bonus}}{100} \right) </math>
-->The player's Max Hit with [[Magic#Spells|spells]] changes depending on the spell being used. A spell's max hit is listed in the spell's description and is different for every spell. Magic Damage Bonus can be found in the Equipment Stats interface.


If the pet is unlocked, the 17 will instead be a 20.
For [[Magic#Ancient Magicks|Ancient Magick spells]] the max hit is simply as stated in the spell's description, and cannot be increased by the Magic Damage Bonus stat or any max hit modifiers - only the [[Combat Triangle]] damage bonus/penalty applies.


==== Ranged Max Hit ====
For [[Magic#Standard Magic|standard spells]], first determine the max hit stated in the spell's description along with the player's effective {{Skill|Magic}} level by using the same effective level formula as [[#Melee and Ranged Max Hit|Melee and Ranged max hit]] does. The base max hit is then:
The first formula is used to calculate the player's Effective Ranged Strength Level. The Attack Style Bonus when using the Accurate Attack Style is 4, otherwise it's 1.


<math> \small{\begin{aligned} \text{Effective Ranged Strength Level} = \text{Ranged Skill Level} + \text{Attack Style Bonus} \end{aligned}}</math>
<math>\text{Base Max Hit} = \left \lfloor \text{Spell Max Hit} \times \left ( 1 + \frac{\text{Magic Damage Bonus}}{100} \right ) \times \left ( 1 + \frac{\text{Effective Magic Level} + 1}{200} \right ) \right \rfloor</math>


The second formula is used to calculate the player's Max Hit. Strength Bonus can be found in Equipment Stats next to the bow and arrow icon. The potion and prayer bonuses will be the relevant numbers written in the potion and prayer descriptions.
This base max hit is then adjusted by the percentage and flat max hit modifiers to arrive at the final max hit figure, where the modifiers include both global and magic max hit increases. Any damage increases with the same element as the spell being used (such as that provided by the {{ItemIcon|Cloudburst Staff}}) are also added to the flat max hit modifier:


<math> \small{ \begin{aligned} \text{Max Hit} = 10 * \big\{ &(1.3 + \text{Effective Ranged Strength Level} / 10 + \text{Strength Bonus} / 80 + \text{Effective Ranged Strength Level} * \text{Strength Bonus} / 640)\\
<math>\text{Max Hit} = \left \lfloor \text{Base Max Hit} \times \left ( 1 + \frac{\text{Percentage Max Hit Modifier}}{100} \right ) \right \rfloor + \text{Flat Max Hit Modifier}</math>
&* (1 + \text{Potion Strength Bonus} / 100) * (1 + \text{Prayer Strength Bonus} / 100) \big\} \end{aligned}}</math>


==== Magic Max Hit ====
=== Minimum Hit ===
The player's Max Hit with [[Magic#Spells|spells]] changes depending on the spell being used. Spell Max Hit is listed in the spells description and is different for every spell. Magic Damage Bonus can be found in Equipment Stats under % Damage Bonus. The potion and prayer bonuses will be the relevant numbers written in the potion and prayer descriptions.
<!-- JS source: character.js, function computeMinHit
-->For [[Special Attacks]] the minimum hit varies depending on the attack. Otherwise, for normal attacks the base minimum hit starts at 1. To this base value, both modifiers for "+X% of Maximum Hit added to Minimum Hit" as well as increased flat minimum hit damage are applied. In addition, if a spell from the [[Standard Magic|standard]] or [[Archaic Magicks|Archaic spellbook]] is being used then element specific modifiers granting flat minimum hit damage for the same element as the spell being used are also included. The minimum hit is at least 1, and no more than the max hit.


<math> \small{\begin{aligned} \text{Magic Max Hit} = \big\{ &\text{Spell Max Hit} * (1 + (\text{Magic Skill Level} + 1) / 200) * (1 + \text{Magic Damage Bonus} / 100)\\
The minimum hit calculation for normal attacks is therefore:
&* (1 + \text{Prayer Magic Damage Bonus} / 100) * (1 + \text{Potion Magic Damage Bonus}) \big\} \end{aligned}}</math>


[[Magic#Ancient Magicks|Ancient Magick spells]] do not use this formula. Instead, they have deal exactly the listed damage. The only modifier that affects the damage dealt by Ancient Magick spells is the [[Combat Triangle]] bonus or penalty.
<math>\begin{aligned}\text{Min Hit} = \min(\max(&\left \lfloor 1 + \text{Max Hit} \times \text{Percentage Max Hit added to Min Hit Modifier} \right \rfloor \\
&+ \text{Flat Min Hit Modifier}, 1), \text{Max Hit})\end{aligned}</math>


===Calculating Damage Dealt===
===Calculating Damage Dealt===
Line 177: Line 205:


====Post-Roll Modifiers====
====Post-Roll Modifiers====
Some effects are applied after the damage roll is done. The main two are enemy Damage Reduction and [[Player Modifiers]] that affect damage to all monsters or to a subset of monsters such as Slayer Monsters or Boss Monsters. These modifiers can increase the player's damage beyond their listed maximum hit.
Some effects are applied after the damage roll is done. The main two are enemy Damage Reduction and [[Player Modifiers]] that affect damage to all monsters or to a subset of monsters such as Slayer Monsters or Boss Monsters. These modifiers can increase the player's damage beyond their listed maximum hit.


[[Magic#Ancient Magicks|Ancient Magick spells]] are not affected by post-roll modifiers aside from enemy Damage Reduction, although weapon special attacks that do a fixed amount of damage are.
[[Magic#Ancient Magicks|Ancient Magick spells]] are not affected by post-roll modifiers aside from enemy Damage Reduction, although weapon special attacks that do a fixed amount of damage are.


=== Damage Reduction ===
==== Damage Reduction ====
<!-- JS source: character.js, function computeDamageReduction
-->{{Main|Reference=Damage Reduction}}
Damage Reduction (often abbreviated as 'DR') is a stat that does exactly what it suggests: It reduces the amount of damage taken by a player or monster. Unlike other combat numbers that are complex calculations, a player's damage reduction is determined by simply adding together all damage reduction bonuses the player has, whether from equipment or something else like a {{ItemIcon|Damage Reduction Potion}} or {{PetIcon|Defence}}.


Damage Reduction is a stat that does exactly what it suggests: It reduces the amount of damage taken by a player or monster. Unlike other combat numbers that are complex calculations, a player's Damage Reduction is determined by simply adding together all Damage Reduction bonuses the player has, whether from equipment or something else like a [[Damage Reduction Potion]] or {{PetIcon|Defence}}.
Many of the [[monsters]] in the game have natural damage reduction, with boss monsters typically having higher damage reduction than other monsters around the same combat level. Some monsters also have [[Special Attack#Monster Special Attacks|special attacks]] or passive effect which temporarily grant additional damage reduction, such as Stone Wall used by {{MonsterIcon|Terran}}.


As of v0.17.0, there are no monsters in the game with natural Damage Reduction. However, {{MonsterIcon|Earth Guard}}s and {{MonsterIcon|Terran}} in the {{ZoneIcon|type=Dungeon|Earth God Dungeon}} have special attacks that grant them temporary Damage Reduction.
The player's damage reduction while engaged in combat can be calculated as their damage reduction % outside of combat ('Base Damage Reduction'), less any penalties that apply when in combat (such as the Intimidation passive effect present on many {{TotH}} [[monsters]]), all multiplied by the [[Combat Triangle]] damage reduction modifier. Damage reduction has a maximum value of 95% and a minimum of 0%, where the in-combat damage reduction can be calculated as:


Whenever a player or monster with Damage Reduction greater than 0% would receive damage, instead the damage the damage they take is equal to:
<math>\text{Damage Reduction %} = \min \Big( \max \Big( \Big\lfloor \left ( \text{Base Damage Reduction %} - \text{In-Combat Penalties} \right ) \times \text{Combat Triangle Modifier} \Big\rfloor , 0 \Big), 95 \Big)</math>


<math>\text{Damage Taken} = \text{Base Damage} * (1 - \text{Damage Reduction})</math>
Where: <math> \left \lfloor x \right \rfloor </math> is the [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions floor function].


Note that the [[Combat Triangle]] will affect how much damage reduction the player has if they are using a different style from the monster.
Whenever a player or monster with Damage Reduction greater than 0% would receive damage, the damage taken is reduced. This reduced damage can be calculated as follows:


=== Evasion Rating ===
<math>\text{Damage Taken} = \left \lfloor \text{Base Damage} \times \left ( 1 - \frac{\text{Damage Reduction %}}{100} \right ) \right \rfloor</math>
==== Melee Evasion Rating ====
The first formula is used to calculate the player's Effective Defence Level.


<math> \small{\begin{aligned} \text{Effective Defence Level} = \text{Defence Skill Level} + 8 \end{aligned}}</math>
==== Critical Hit ====
With specific pieces of equipment, there is a chance that hits dealt by the player may become critical. When a critical hit occurs, any damage dealt by that hit will be increased by 50% - this increase is multiplicative with any other damage increasing bonuses currently in effect.


The second formula is used to calculate the player's Melee Evasion Rating. Melee Defence Bonus can be found in Equipment Stats under Defensive Stats with a shield icon. The potion and prayer bonuses will be the relevant numbers written in the potion and prayer descriptions.
The player's critical chance starts at 0% (at which point critical hits do not occur), and can be increased by the following:
{{ModifierTable|MeleeCritChance,RangedCritChance,MagicCritChance|Critical Chance|true|}}


<math> \small{\begin{aligned} \text{Evasion Rating} = \big\{ &\text{Effective Defence Level} * (\text{Melee Defence Bonus} + 64)\\
==== Damage Per Hit, Average Hit, and Damage Per Second ====
&* (1 + \text{Potion Evasion Rating Bonus} / 100) * (1 + \text{Prayer Evasion Rating Bonus} / 100) \big\} \end{aligned}}</math>
If a player or monster successfully connects with an attack, the damage dealt will be a random integer value between their minimum and maximum hit. This random value is uniformly distributed, or in other words any value between and including the minimum and maximum hit is equally likely to be rolled.


==== Ranged Evasion Rating ====
Damage Reduction is applied after this initial damage per hit is calculated, which means it is possible for a player to deal less than their minimum hit against a monster that has Damage Reduction.
The first formula is used to calculate the player's Effective Defence Level.


<math> \small{\begin{aligned} \text{Effective Defence Level} = \text{Defence Skill Level} + 9 \end{aligned}}</math>
The player's average hit is thus:


The second formula is used to calculate the player's Ranged Evasion Rating. Ranged Defence Bonus can be found in Equipment Stats under Defensive Stats with a bow and arrow icon. The potion and prayer bonuses will be the relevant numbers written in the potion and prayer descriptions.
<math>\text{Average Hit} = \frac{\text{Max Hit} + \text{Min Hit}}{2} \times (1 - \text{Enemy DR})</math>


<math> \small{\begin{aligned} \text{Ranged Evasion Rating} = \big\{ &\text{Effective Defence Level} * (\text{Ranged Defence Bonus} + 64)\\
And their damage per second can be calculated as:
&* (1 + \text{Potion Evasion Rating Bonus} / 100) * (1 + \text{Prayer Evasion Rating Bonus} / 100) \big\} \end{aligned}}</math>


==== Magic Evasion Rating ====
<math>\text{DPS} = \frac{\text{Average Hit}}{\text{Attack Speed (Seconds)}} \times \text{Hit Chance}</math>
The first formula is used to calculate the player's Effective Magic Defence Level. The result here is always rounded down to the nearest whole number.


<math> \small{\begin{aligned} \text{Effective Magic Defence Level} = \text{Magic Skill Level} * 0.7 + \text{Defence Skill Level} * 0.3 + 9 \end{aligned}}</math>
=== Evasion Rating ===
<!-- JS source: character.js, function computeEvasion
-->The calculation used to determine the player's evasion rating varies depending on the attack type the player is defending against. Each requires the calculation of effective skill levels, the formula for which is as follows:


The second formula is used to calculate the player's Magic Evasion Rating. Magic Defence Bonus can be found in Equipment Stats under Defensive Stats with a wizard hat icon. The potion and prayer bonuses will be the relevant numbers written in the potion and prayer descriptions.
<math>\small{\text{Effective Skill Level} = \text{Standard Skill Level} + \text{Hidden Skill Level}}</math>


<math> \small{\begin{aligned} \text{Magic Evasion Rating} = \big\{ &\text{Effective Magic Defence Level} * (\text{Magic Defence Bonus} + 64)\\
In addition, the player's evasion modifier need to be known. This is the sum of all global evasion rating and the relevant attack type's evasion rating increases, provided from places such as [[Herblore#Combat Potions|Potions]], {{Skill|Agility}}, and {{Skill|Astrology}}.
&* (1 + \text{Potion Evasion Rating Bonus} / 100) * (1 + \text{Prayer Evasion Rating Bonus} / 100) \big\} \end{aligned}}</math>


=== Damage Per Hit, Average Hit, and Damage Per Second ===
==== Melee and Ranged Evasion Rating ====
First determine the relevant defence bonus, this will be the melee defence bonus for the {{Icon|Melee}} evasion rating, or the ranged defence bonus for the {{Skill|Ranged}} evasion rating. These stats can be found in the Equipment Stats interface.


If a player or monster successfully connects with an attack, the damage dealt will be a random value between their minimum and maximum hit. If no relevant equipment or [[Magic#Auroras|Auroras]] are active, the player's minimum hit is 1. The minimum hit is applied after all strength and damage bonuses are calculated, which means that only bonuses that directly impact minimum hit will affect minimum hit. (in other words, if a player's minimum hit is 40 and they have +10% damage, they still have a minimum hit of 40 rather than 44)
Given this, the evasion rating is then:


Damage Reduction is applied after this initial damage per hit is calculated, which means it is possible for a player to deal less than their minimum hit against a monster that has Damage Reduction.
<math>\text{Evasion Rating} = \left \lfloor \left ( \text{Effective Defence Level} + 9 \right ) \times \left ( \text{Defence Bonus} + 64 \right ) \times \left ( 1 + \frac{\text{Evasion Modifier}}{100} \right ) \right \rfloor</math><!--
Note: Strictly the evasion rating calculation also includes an element of scaling when the 'globalEvasionHPScaling' applies, however this is only available through the 'Fleeting Defence' enemy passive, so currently does not apply to the player -->


The player's average hit is thus:
==== Magic Evasion Rating ====
The calculation for Magic evasion is slightly different from that for Melee and Ranged. The defence bonus used should naturally be the magic defence bonus. In addition, the effective defence level becomes a calculation that factors in both the player's effective Defence and Magic levels:


<math>\small{\begin{aligned} \text{Average Hit} = ((\text{Max Hit} + \text{Min Hit}) / 2) * (1 - \text{Enemy DR}) \end{aligned}}</math>
<math>\small{\text{Effective Level} = \left \lfloor 0.3 \times \text{Effective Defence Level} + 0.7 \times \text{Effective Magic Level} \right \rfloor}</math>


And their damage per second can be calculated as:
Then the magic evasion rating becomes:


<math>\small{\begin{aligned} \text{DPS} = (\text{Average Hit} / \text{Attack Speed}) * \text{Hit Chance} \end{aligned}}</math>
<math>\text{Evasion Rating} = \left \lfloor \left ( \text{Effective Level} + 9 \right ) \times \left ( \text{Magic Defence Bonus} + 64 \right ) \times \left ( 1 + \frac{\text{Evasion Modifier}}{100} \right ) \right \rfloor</math>


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