Equipment tier

Equipment tier is an important value for worn equipment. This is a hidden number which determines the accuracy and damage of weapons, and the armour value, damage bonus, and life point bonus of armour. It is often, but not always, the wield/wear requirement.

Tier is a positive natural number - it is always strictly greater than 0, and is not fractional. Equipment without bonuses is tierless. Currently, the highest tier is.

Other usages of tier
The term tier can be used in many ways, only one of which is equipment tier. Other uses include:


 * Dungeoneering tier - the tier given in the examine text of Dungeoneering items. For most equipment, Dungeoneering tier corresponds to an equipment tier. Some Dungeoneering equipment, and most non-equipable Dungeoneering items, instead use item tier (mentioned below)
 * Citadel tier - the seven-stage upgrade path of the Clan Citadel and its components
 * Divination tier - a number representing the relative levels of the 12 initially released divination wisps and springs
 * God tier - a seven-stage system representing the relative power of Gods
 * Aura tier - the (up to) five-stage upgrade path for auras
 * Item tier - relating to items with multiple versions, such as Duellist's cap (tier 1)

Effects of equipment tier
The following bonuses and effects are influenced by equipment tier:
 * Equipment bonuses:
 * Weapon accuracy
 * Weapon damage
 * Armour value
 * Armour damage bonus
 * Armour life point bonus
 * Damage reduction
 * Ability damage
 * Ability scaling, including:
 * Resonance and Debilitate scale directly with shield tier
 * Bash scales with shield armour value, which depends on tier

The following bonuses/effects are not influenced by equipment tier:
 * Equipment bonuses:
 * Prayer bonus
 * Most set effects and passives

Armour tier penalty
The main types of armour - tank, power, hybrid, PvP - have varying penalties for calculating their equipment stats from their tier.

If a piece of armour has tier $$t$$, its bonuses are with effective tier:

In addition, most standard metal (bronze-dragon, novite-primal) chainbodies and square shields suffer a two tier penalty to their armour and life point values. Here, they are treated as normally tiered items - e.g. the rune chainbody is treated as a normal tier 48 item, not a tier 50 item with a penalty.

Imperfect tiers
Equipment with all their relevant bonuses reflected by a single tier (and correct type and speed) are referred to as perfectly tiered. For example, the drygore mace is a main-hand fastest speed melee weapon; it has tier 90 accuracy, and tier 90 main-hand fastest damage, thus it is perfectly tiered.

Imperfectly tiered equipment is, as the name suggests, not perfectly tiered. This can be due to one or more of the following:
 * Mixed tiers - equipment with bonuses that correspond to different tiers, for example:
 * Enhanced excalibur has tier 70 accuracy, and tier 72 damage
 * The hardened fighter torso has tier 50 armour, and tier 65 damage
 * Incorrect speed - weapons where the damage value is corresponds to the same tier, but a different speed (this often applies to weapons not intended for use in combat). For example:
 * Black canes are tier 5 fastest melee weapons; they have tier 5 accuracy and tier 5 average damage (around 50% more damage than expected)
 * The blessed hatchet is a main-hand fast weapon; it has tier 1 accuracy and tier 1 main-hand fast damage (around 25% less damage than expected)
 * Incorrect hand - weapons where the damage value corresponds to the same tier and speed, but is for a different hand. For example:
 * Exquisite 2h sword is a two-handed average speed melee weapon with a tier 9 and tier 36 variant; these have tier 9/36 accuracy, and tier 9/36 main-hand average damage (so about 2/3 of what they should have)
 * Most pickaxes and hatchets, e.g. the crystal pickaxe, are main-hand weapons with off-hand damage (so half the damage of a normal main-hand weapon of that speed)
 * Custom bonuses - equipment where the bonuses do not line up with a tier at all, for example:
 * Achromatic Balmung and variants have tier 70 accuracy, and damage around halfway between tier 71 and 72; as tier isn't fractional, this is a custom bonus

Formulae

 * For full tabulation of equipment bonuses values, see Calculator:Combat stats

During this section, the following formula is defined:

$$f(t) = 2.5 \left ( \frac{t^3}{1250} + 4t + 40 \right)$$

Where $$t$$ is tier.

Also in use is the floor function $$\lfloor x \rfloor$$, which always rounds down: i.e. $$\lfloor 9.6 \rfloor = 9$$, $$\lfloor 1.1 \rfloor = 1$$

Weapon accuracy
The accuracy of all weapons is dependant solely on tier; class, hand, and speed do not affect it. It is simply $$\lfloor f(t) \rfloor$$.

Weapon damage
The displayed weapon damage is a simply a multiple of the weapon's tier. The multiplier varies with hand, speed, and weapon type.

The following table applies to the shown bonuses of all melee weapons, all thrown weapons, and all Ranged weapons which generate their own ammunition (e.g. the crystal bow). For magic and other ranged weapons, the hover-overs won't directly show these numbers, but the combined effect of ammunition/spell should give damage in this table too.
 * General

Most ranged weapons get some or all of their damage from the ammunition in use. Those that generate their own ammunition, or thrown weapons, have a damage value using the above table.
 * Other ranged weapons
 * Main- and off-hand weapons that do not provide their own ammunition do not have a damage bonus (generally dual-wielded crossbows)
 * Ammunition provides the same bonus as a main-hand fastest weapon: $$\lfloor 9.6t \rfloor$$
 * Two-handed fast weapons (most shortbows) have a damage bonus of $$\lfloor 8.775t \rfloor$$
 * Two-handed average weapons (most two-handed crossbows and longbows, but not shieldbows) have a damage bonus of $$\lfloor 12.75t \rfloor$$
 * Shieldbows (which are two-handed average) have a damage bonus of $$\lfloor 5.3t \rfloor$$

The damage for ammunition and weapon are added together with speed/hand weightings, with the overall result giving the above table. The damage is capped at the lowest of the tiers of the ammunition and the weapon.

Magic weapons do not have a damage bonus, as it is entirely provided by the spell selected and scaled to speed. The overall damage will correspond to the above table. Damage is capped at the lowest of the tiers of the spell and the weapon.
 * Magic


 * Ability damage

When using abilities, the damage of the weapon is scaled to its speed. Thus, it doesn't matter exactly what your exact damage bonus is, your ability damage is:
 * Main-hand: $$\lfloor 9.6t \rfloor$$
 * Off-hand: $$\lfloor 4.8t \rfloor$$
 * Two-handed or dual-wielding (when using the same tier in both hands): $$\lfloor 14.4t \rfloor$$

For ranged and magic, the tier used to calculate damage is the lower of the tier of the weapon wielded and the ammunition/spell used.

Armour value
Armour value is calculated similar to accuracy, with a multiplier for the slot. Remember to apply effective tier penalties for hybrid and power armour.
 * Head: $$0.2f(t)$$
 * Body: $$0.23f(t)$$
 * Legs: $$0.22f(t)$$
 * Hands: $$0.05f(t)$$
 * Feet: $$0.05f(t)$$
 * Cape: $$0.03f(t)$$
 * Ring: $$0.02f(t)$$
 * Shield: $$0.2f(t)$$
 * Set (of all the same tier):
 * Head, body, legs, gloves, boots: $$0.95f(t)$$
 * Head, body, legs, gloves, boots, shield: $$1.15f(t)$$
 * Head, body, legs, gloves, boots, cape, ring: $$f(t)$$
 * Head, body, legs, gloves, boots, cape, ring, shield: $$1.2f(t)$$

Armour damage bonus
Damage bonus, much like weapon damage, is a simple multiplier of the tier. This is scaled with speed and hand to add to weapon damage/ability damage. Damage bonus only depends on tier for the following slots (the damage bonus of capes, rings, necklaces, etc does not depend on tier):
 * Head: $$0.25t$$
 * Body: $$0.375t$$
 * Legs: $$0.3125t$$
 * Gloves: $$0.15625t$$
 * Boots: $$0.15625t$$
 * Set (all parts, same tier): $$1.25t$$

Armour life points bonus
Life point bonuses only apply to shields tier 70 and greater, and head, body, and leg armour tier 80 and greater.


 * Head: $$20(t-69)$$
 * Body: $$40(t-69)$$
 * Legs: $$30(t-69)$$
 * Shield: $$35(t-69)$$

Damage reduction
The damage reduction of armour depends on the slot, type, and tier. PvM damage reduction is exclusive to tank armour and shields, while PvP damage reduction is available to all armour types.

The 2-tier penalty for chainbodies and square shields does not apply here.


 * PvM damage reduction (tank armour only)


 * PvP damage reduction

Dungeoneering tier
For most equipment, Dungeoneering tier $$d$$ corresponds to equipment tier $$t$$ using the following formula: $$t = \begin{cases} 5, & \mbox{if }d = 1 \\ 99, & \mbox{if }d = 11 \\ 10 \times (d-1), & \mbox{otherwise} \\ \end{cases}$$