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Bitterkoekje
Feb Member 2015

Bitterkoekje

Posts: 918Gold Posts by user Forum Profile RuneMetrics Profile
Welcome,

this comprehensive thread discusses the mechanics of the Old School Runescape combat system.

The posts below contain an elaborate explanation of how combat skills work in Runescape and how the game uses skill stats with equipment and various bonuses to calculate damage output. I recommend the use of a spreadsheet or some sort of advanced calculator to complete the steps. I've made a google spreadsheet myself, the link is publicly available and can be found on my twitter (see signature below).


Credits:

The maximum hit formula below is largely based on the original maximum hit formula thread by Obliv from back in 2007. I've taken the liberty of updating it for Old School Runescape.

Also thanks to the following players for their contributions, corrections and suggestions to this thread:

Woox
Downlifter
ChocolatOgre
Henke18
Meric


Feel free to leave a comment or question, as I'm always looking for feedback and improvements.
Combat Formulas
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10-Mar-2015 23:25:06 - Last edited on 26-May-2017 19:12:59 by Bitterkoekje

Bitterkoekje
Feb Member 2015

Bitterkoekje

Posts: 918Gold Posts by user Forum Profile RuneMetrics Profile
| 2. |
Table of contents




Post 01.
1.
Introduction
Post 02.
2.
Table of contents
Post 03.
3.
Max hit formula
Post 04.
Post 05.
Post 06.
4.
Magic max hit formula
Post 07.
5.
Accuracy formula
Post 08.
Post 09.
Post 10.
6.
Extra information
Post 11.





Key of colours:
Using
yellow
for chapters:
Melee and ranged maximum hit

Using
orange
for sections:
| 3.4 |
Special attacks
Using
blue
for subsections:
3.4B.

Using
green
for steps:
b.


Other info:
~ indicates an approximation.
? indicates an unknown or uncertain bonus.
• indicates a choice in a list where you can only pick one option.

Visible level means the level with any (potion) boost included.

You can check the defence stats of a monster by using the monster examine spell on it.
For NPC rolls, always use the default stance bonus of +9.
Combat Formulas
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10-Mar-2015 23:25:12 - Last edited on 01-Mar-2017 11:37:59 by Bitterkoekje

Bitterkoekje
Feb Member 2015

Bitterkoekje

Posts: 918Gold Posts by user Forum Profile RuneMetrics Profile
| 3. |
Melee and ranged maximum hit



This formula calculates the maximum melee or ranged hit for a single hitsplat.


| 3.1 |
Maximum base hit


a.
Max hit = 0.5 + A * (B+64) /640
b.
Round down the max hit to the nearest integer. Go to section
3.4
for any special attacks.


To find variables A and B, please look below in section
3.2
and
3.3
.


| 3.2 |
Effective level (A)


a.
Take the visible strength or ranged level from the skills interface.
b.
Multiply the level by the prayer adjustment:




c.
Round down to the nearest integer.
d.
Add the stance bonus from the combat options interface.

Melee:
• Aggressive: +3
• Controlled: +1

Ranged:
* Accurate: +3

e.
Add up +8.
f.
Multiply by the void bonus:
• Void melee: multiply by 1.10. Round down.
• Void ranged: multiply by 1.10. Round down.
• Elite void ranged: multiply by 1.125. Round down.

g.
This is the effective (ranged) strength level. Let this equal 'A' in the formula in
3.1
.


| 3.3 |
Equipment bonus (B)


Take the melee or ranged strength bonus from the equipment stats interface and let this equal 'B' in the formula in
3.1
.
Combat Formulas
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10-Mar-2015 23:25:17 - Last edited on 26-May-2017 19:12:45 by Bitterkoekje

Bitterkoekje
Feb Member 2015

Bitterkoekje

Posts: 918Gold Posts by user Forum Profile RuneMetrics Profile
| 3.4 |
Special attacks


| 3.4a |
Make sure you have rounded down your max hit from
3.1
.

a.
Multiply by the bonus of one of the following items:

Melee:
• Black mask: 7/6
• Salve amulet: 7/6
• Salve amulet (e): 1.20

Ranged:
• Black mask (i): 1.15
• Salve amulet (i): 1.15
• Salve amulet (ei): 1.20

(Note: the black mask bonus is ignored when using a salve amulet)

b.
Round down to the nearest integer.
c.
Multiply by the bonus of one of the following items:

Melee:
• Abyssal dagger: 0.85
• Abyssal bludgeon: between 1 and 1.495 (0.5% for every lost prayer point)
• Arclight: 1.70 (vs. demons)
* Armadyl godsword: 1.10
• Bandos godsword: 1.10
• Barrelchest anchor: 1.10
• Dragon claws: subtract 1 and see
6.4
.
• Dragon dagger: 1.15
• Dragon/crystal halberd: 1.10
• Dragon longsword: 1.25
• Dragon mace: 1.50
• Dragon sword: 1.25
• Dragon warhammer: 1.50
• Leaf-bladed battleaxe: 1.175 (vs. kurask, turoth)
• Obsidian armour: 1.10
• Rune claws: 1.15
• Saradomin godsword: 1.10
• Saradomin sword: 1.10
• Saradomin's blessed sword: 1.25
• Zamorak godsword: 1.10

Ranged:
• Ballista: 1.25
• Dark bow (dragon arrows): 1.50
• Dark bow (other arrows): 1.30
• Diamond bolts: 1.15
• Dragon hunter crossbow: 1.10 (vs. dragons, wyverns, Great Olm)
• Magic longbow, shortbow, composite or seercull: on page 2, see:
6.3
.
• Onyx bolts: 1.20
• Rune thrownaxe: on page 2, see:
6.3
.
• Toxic blowpipe: 1.50
• Twisted bow: (250 + truncate[(3*magic-14) /100] - truncate[(0.3magic-140)² / 100]) /100


d.
Round down to the nearest integer.
e.
If a PvP protection prayer is used, it reduces the max hit by 40% at this point. Multiply by 0.6 and round down to the nearest integer. Go to
3.4b
.
Combat Formulas
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10-Mar-2015 23:25:21 - Last edited on 30-Dec-2017 23:25:00 by Bitterkoekje

Bitterkoekje
Feb Member 2015

Bitterkoekje

Posts: 918Gold Posts by user Forum Profile RuneMetrics Profile
| 3.4b |
Make sure you have rounded down your max hit from
3.1
or
3.4a
.

a.
Apply the bonus of one of the following items:

Melee:
* Armadyl godsword: 1.25
• Bandos godsword: 1.10
• Berserker necklace: 1.20
• Darklight: 1.60 (vs. demons)
• Dharok's set: multiply by: 1+ lost hp/100 * max hp/100
• Gadderhammer: 1.25 or 2.00 (vs. shades), see:
6.2
.
* Keris: 4/3 or 3.00 (vs. kalphites and scarabs), see:
6.2
.
* Verac's set: add up +1.

Ranged:
• Dragonstone bolts: multiply the visible ranged level by 1/5. Round down and add this up to the max hit. (ex: add up +22 with 112 ranged)
• Opal bolts: multiply the visible ranged level by 1/10. Round down and add this up to the max hit.
• Pearl bolts: multiply the visible ranged level by 1/15 (or 1/20). Round down and add this up to the max hit.

b.
Round down to the nearest integer.
c.
In Castle Wars, multiply by:
• Castlewar brace: 1.20 (vs. flagholder)

d.
Round down to the nearest integer.
e.
If the special attack of the Staff of the Dead is used, all melee damage will be reduced by 50% at this point. Multiply by 0.5 and round down to the nearest integer. This is your maximum hit.
Combat Formulas
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10-Mar-2015 23:25:27 - Last edited on 30-Dec-2017 22:58:03 by Bitterkoekje

Bitterkoekje
Feb Member 2015

Bitterkoekje

Posts: 918Gold Posts by user Forum Profile RuneMetrics Profile
| 4. |
Magic maximum hit



This formula calculates the maximum magic hit for a single hitsplat.


a.
Find the base maximum damage a spell can deal.

Spells with fixed max hit:



The maximum hit of these spells depends on your visible magic level:



b.
Increase the base damage:
• God spells (level 60) in combination with Charge (level 80): the base max hit is 30.
* Bolt spells in combination with Chaos gauntlets: add up +3.

c.
The following bonuses stack by adding up.
Multiply by: (1+...)
• Ancestral equipment: +0.02 per piece
• God cape (imbued): +0.02
• Kodai wand: +0.15
• Occult necklace: +0.10
• Salve amulet (i): 0.15
• Salve amulet (ei): 0.20
• Smoke staff: +0.10 (normal spellbook only)
• Staff of the dead: +0.15
• Tormented bracelet: +0.05
• Elite void magic: +0.025
(ex: Occult + SotD + Torm. bracelet: multiply by 1.30.)

d.
Round down to the nearest integer.
e.
On a slayer task, multiply by:
• Black mask (i): 1.15

f.
Round down to the nearest integer.
g.
If a fire spell is used, multiply by:
• Tome of fire: 1.5

h.
Round down to the nearest integer.
i.
In Castle Wars, multiply by:
• Castlewar brace: 1.20 (vs. flagholder)

j.
Round down to the nearest integer. This is your maximum hit.
Combat Formulas
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10-Mar-2015 23:25:31 - Last edited on 15-Feb-2019 15:22:12 by Bitterkoekje

Bitterkoekje
Feb Member 2015

Bitterkoekje

Posts: 918Gold Posts by user Forum Profile RuneMetrics Profile
| 5. |
Accuracy formula



| 5.1 |
Attack and defence roll

The maximum roll is calculated as follows:

a.
Max roll = A * (B+64)
b.
If you're using special attacks: go to
5.4
. To calculate the chance to hit: go to
5.6


To find the variables A and B, please look below in section
5.2
and
5.3
.


| 5.2 |
Effective level (A)


a.
Take the visible attack, ranged, magic or defence level from the skills interface.
b.
Multiply the level by the prayer adjustment:




c.
Round down to the nearest integer.
d.
Add the stance bonus from the combat options interface.

Melee attack:
• Accurate: +3
• Controlled: +1

Ranged attack:
• Accurate: +3

Magic attack:
• Accurate +3 (trident only)
• Long range +1 (trident only)

Defence:
• Defensive: +3
• Controlled: +1
• Long range: +3

e.
Add up +8.
f.
Multiply by the void bonus:
• Void melee: multiply melee attack by 1.10.
• Void ranged: multiply ranged attack by 1.10.
• Void magic: multiply magic attack by 1.45.

g.
Round down to the nearest integer. This is the effective level. Let this equal 'A' in
5.1



| 5.3 |
Equipment bonus (B)


Take the corresponding stab, slash, crush, ranged or magic attack bonus from the equipment stats interface and let this equal 'B' in
5.1
Combat Formulas
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10-Mar-2015 23:25:35 - Last edited on 16-Jun-2017 09:24:32 by Bitterkoekje

Bitterkoekje
Feb Member 2015

Bitterkoekje

Posts: 918Gold Posts by user Forum Profile RuneMetrics Profile
| 5.4 |
Special attacks


a.
Multiply by the bonus of one of the following items:

Melee:
• Black mask: 7/6
• Salve amulet: 7/6
• Salve amulet (e): 1.20

Ranged or magic:
• Black mask (i): 1.15
• Salve amulet (i): 1.15
• Salve amulet (ei): 1.20

(Note: the black mask bonus is ignored when using a salve amulet)

b.
Round down to the nearest integer.
c.
Multiply by the bonus of one of the following items:

Melee:
• Arclight: 1.70 (vs. demons)
• Abyssal dagger: 1.25
• Abyssal whip: 1.25
• Barrelschest anchor: 2.00
• Dinh's Bulwark: 1.20
• Dragon dagger: 1.15
• Dragon mace: 1.25
• Dragon scimitar: 1.25
• Dragon sword: 1.25
• Godsword, any: 2.00
* Rune claws: 1.15
• Saradomin sword: 2.00
• Saradomin's blessed sword: 2.00

Ranged:
• Armadyl crossbow: 2.00
• Ballista: 1.25
• Dragon hunter crossbow: 1.10 (vs. dragons, wyverns, Great Olm)
• Dragon thrownaxe: 1.25
• Twisted bow: (140 + truncate[(3*magic-10) /100] - truncate[(0.3magic-100)² / 100]) /100

Magic attack:
• Smoke staff: 1.10 (normal spellbook only)

Defence:
• Torag's set (with Amulet of the Damned): 1+ lost hp/100 * max hp/100

d.
Round down to the nearest integer. This is the max roll after special attacks. Go to
5.6
Combat Formulas
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10-Mar-2015 23:25:43 - Last edited on 30-Dec-2017 23:26:04 by Bitterkoekje

Bitterkoekje
Feb Member 2015

Bitterkoekje

Posts: 918Gold Posts by user Forum Profile RuneMetrics Profile
| 5.5 |
Magic defence roll


(This only applies to players; NPC magic defence is 100% based on the magic level and bonus)

a.
Calculate your effective defence level as described in
5.2
, steps
a-g
.
b.
Multiply your effective defence level by 0.30 and round down to the nearest integer.
c.
Take your visible magic level from the skills interface.
d.
Multiply the magic level by the prayer adjustment.

Magic defence:
• Mystic will: 1.05
• Mystic lore: 1.10
• Mystic might: 1.15
• Augury: 1.25

e.
Round down to the nearest integer.
f.
Multiply this by 0.70 and round down to the nearest integer.
g.
Add up the defence value from step
b
and let this equal 'A' in the formula in
5.1
.
h.
Take your magic defence bonus from the equipment stats interface and let this equal 'B' in
5.1



| 5.6 |
Hit chance


With the max attack roll and the max defence roll, you can calculate the chance to hit with the next formula:

• If the max attack roll is higher:
Accuracy = 1 - (def+2) / (2*(atk+1))

• Or else:
Accuracy = atk / (2*(def+1))

Note: 'atk ' and 'def ' refer to the max roll value as calculated in
5.1
,
5.4
or
5.5
).
Combat Formulas
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10-Mar-2015 23:25:47 - Last edited on 10-Jan-2017 22:28:04 by Bitterkoekje

Bitterkoekje
Feb Member 2015

Bitterkoekje

Posts: 918Gold Posts by user Forum Profile RuneMetrics Profile
| 6. |
Extra info



| 6.1 |
Combat experience


Some monsters in Runescape give increased experience (more than 4 exp/damage) in the combat related skills. The normal amount of experience is multiplied by a percentage and the percentage is based on the stats of the NPC, as described below. If a monster has a multiplier, you'll be able to receive bonus exp in the following skills: attack, strength, defence, ranged, magic, hitpoints and slayer.

Multiplier = 1 + floor(average level * (average def bonus + str bonus + atk bonus) /5120) /40

Where:
average level = floor((Attack + Strength + Defence + Hitpoints) /4)
average def bonus = floor((stab def + slash def + crush def) /3)


| 6.2 |
Probabilities of special effects


• Bone dagger special: guaranteed hit if you weren't the last to attack the target.
• Diamond bolt (e): guaranteed hit if the special triggers, see below.
• Dorgeshuun crossbow special: guaranteed hit if you weren't the last to attack the target.
• Gadderhammer: 1/20 chance to deal double damage, 19/20 chance to hit 25% higher.
• Keris: 1/51 chance to deal triple damage, 50/51 chance to hit 33.3% higher.
• Magic longbow, comp bow, seercull special: guaranteed hit.
• Poisoning your target: 1/4 for melee, 1/8 for ranged. Damage must be 1 or higher.
• Ruby bolt (e): fixed damage (20% of HP) if the special triggers, see below.
• Verac's set: 1/4 chance on a guaranteed hit with +1 additional damage.
• Bolt activation probability (image by Mod Ash):

Combat Formulas
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10-Mar-2015 23:25:51 - Last edited on 26-May-2017 19:50:28 by Bitterkoekje

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