Stats — pathofexile

Stats modify a single statistic of the game. Stats can apply to most aspects of the game, such as the player's character, items, monsters, skills or an area. Common sources of stats include modifiers, passive skills, buffs and skills.

Overview

Each stat has an internal ID (for example maximum_life_+%) and a number of settings associated with it. Stats themselves do not have a value, their values are given by other sources such as modifiers or skills. The values are always integers^[1] and rounds down to the nearest integer if the stat value is modified^[2].

The ID and the values are used for translating the stat into a more human readable format, as such, stats may often appear in descriptions differently then they are used in game. This means they may omit information (i.e. values) or change their text and numbers to be more readable. For example the stat maximum_life_+% will appear as x% increased maximum Life for positive values and x% reduced maximum Life for negative values on things that affect the player's character, but will appear as Extra Life and Reduced Life on monsters respectively.

It is also possible that the description of a stat is omitted entirely and not visible to the player, however stats will still be effective. Very often this is the case for monster modifiers such as hidden item quantity or rarity boosts. This is also the case for stats that have a value of exactly 0.

Sources

An incomplete list of sources:

Modifiers which can be commonly found on items,
Areas
Monsters
Passive Skills from the passive skill tree
Buffs (often granted by auras)
Skills
Base stats, i.e. from the player's character and character class

Interaction

Stats will stack with themselves additively, so two or more stats with the same ID will simply be added up. ^[3]

However, there is a distinction between Global and Local stats:^[4]

Local stats will only be added to the relevant source.

Global stats are applied globally as the name suggests.

Stats with different IDs may also interact with each other, however there is no dead set rule on how different stats interact with each other. Often the interaction can be derived from the description of the stats.

Rule of thumb based on descriptions

The visible description generally hints at a few rules for the interaction. However be wary there may be edge cases where it behaves differently.

Flat, additive and multiplicative stats

Flat stats usually use a form of the word add. They stack additively with other flat stats of the same scope. Resistances are flat stats which use the word increased and are represented as percentages, and so are notable exceptions to the general rules.
Additive stats are usually percentages and use forms of the the words increase or reduce. They are summed with other additive stats of the same scope.
Multiplicative stats are usually percentages and use forms of the words more or less. They stack multiplicatively with other multiplicative stats of the same scope. A multiplicative stat's internal ID can usually be identified by the suffix "_final".

What this means in plain English is that you add the various "increased"/"reduced" effects together into a single multiplier, and multiply the base stat by the result, whereas you multiply the base stat by each "more"/"less" effect in turn.

The total stat value can be calculated as the sum of any added stat, multiplied by the sum of all increases and reductions to stat, multiplied by all more and less stat modifiers.

$\color[RGB]{163,141,109} \begin{align} a & \text{ the total amount of added stats } & a & \in \mathbb{N}_{0} \\ b & \text{ the total amount of increased stats } & b & \in \mathbb{N}_{0} \\ c & \text{ the total amount of reduced stats } & c & \in \mathbb{N}_{0} \\ d & \text{ the total amount of more stats } & d & \in \mathbb{N}_{0} \\ e & \text{ the total amount of less stats } & e & \in \mathbb{N}_{0} \\ \end{align}$

$\color[RGB]{163,141,109} \begin{align} \text{stat}_{total} = & \sum_{i=1}^{a} \text{added stat}_{i} \times \\ & \left( 1 + \sum_{j=1}^{b} \text{increased stat}_{j} - \sum_{k=1}^{c} \text{reduced stat}_{k} \right) \times \\ & \prod_{l=1}^{d} (1 + \text{more stat}_{l}) \times \prod_{m=1}^{e} (1 - \text{less stat}_{m}) \end{align}$

For more information about the symbols, see sum and product notation.

Also see the example section below.

Order of application

Stats are only applied once per calculation. The usual order of application is:

Local flat stats
Local additive and multiplicative stats
Global and skill flat stats
Global and skill additive stats
Global and skill multiplicative stats

Tip: Assuming equal values, "more" is usually far more powerful than increased.

Applicability from other sources

Often a stat has a set of types determining to which statistics it applies. Types can be subtypes or supertypes of other Types. Supertypes affect their subtypes but not vice versa. Many types correspond to Gem Tags; however, this relationship is not strict. For example, Lua error: Error: invalid field alias "items._pageName"; aliases cannot contain dots or quotes.. has the Melee tag, but its projectiles do not do melee damage, and Lua error: Error: invalid field alias "items._pageName"; aliases cannot contain dots or quotes.. has the Attack tag, but the charge detonation does not do Attack damage.

Some words have special meanings:

If a stat specifies only one Type, or if the word and is used to combine multiple Types, then the stat applies to any combination of the Types. For example, armour and energy shield affects armour, or energy shield, or both armour and energy shield.
If a stat specifies multiple Types not combined using the word and, then it only applies to all of the Types together. For example, elemental damage with maces would not affect non-elemental damage with maces, nor non-damage elemental effects with maces, nor elemental damage not dealt with maces.
If the word while is used in conjunction with an item Type, the stat is effective globally whether the statistic applies directly to the item or not. For example, while wielding a staff would apply to spells cast while wielding a staff, even though the staff is not involved in the casting of spells.
If the word with is used in conjunction with an item Type, the stat is effective only when that item is being directly used. For example, with claws would only affect attacks made with the claws themselves.

Converted statistics count as both the Type converted from and converted to, but can only be affected by a particular stat at most once.

Effectiveness of stacking stat values

The following applies to most statistics that can be stacked, as it's a side effect of the linearity of the stats.

From the general interactions it is possible to derive some basic rules for the effectiveness of stacking stats:

Stats that will stack towards infinity will become less effective per point as you increase them (diminishing return)
Stats that will stack towards zero will become more effective per point as you decrease them (slippery slope)

Remember that some stats have altered descriptions and in reality often values behave differently from what is shown. A good example are resistances - it is better to think of them as damage reduction in this case (75% being 75% less damage, aka a 0.25 multiplier).

Rule of thumb

For increased and more modifiers, they generally scale as:

$\color[RGB]{163,141,109} 1+{x \over 100}$

Compared to base		Compared to last 100
Points	Multiplier	Effectiveness
100	2	2
200	3	1.5
300	4	1.333
400	5	1.25

Similarly, for the reduction:

Compared to base		Compared to last result
Points	Multiplier	Effectiveness
20	0.8	1.25
40	0.6	1.33
60	0.4	1.5
80	0.2	2
100	0	infinity

Examples

more vs increased

You have 1000 base damage and "100% increased damage" from gear and "100% increased damage" from passives. You can then choose between slotting either of two support gems:

Gem A gives "100% increased damage".

Gem B gives "100% more damage".

Calculation:

Gem A: gear+passive+gem = 300% increased, so 1000*(1+3.0) = 4000 damage.

Gem B: (gear+passive)*gem = 200% increased and 100% more, so 1000*(1+2.0)*(1+1.0) = 6000 dmg

"Reduced" is equivalent to "increased" (but getting smaller instead of larger); likewise "less" works in the equivalent way as "more".

Global stats

If you have

3x +1 Maximum Frenzy Charges from the Passive Skill Tree
+1 Maximum Frenzy Charges from Equipment
+3 Maximum Frenzy Charges your Character starts with

You will get:

+7 Maximum Frenzy Charges total

Local stats

Assume you are dual wielding two one-handed melee weapons.

On each of the weapons, you have rolled the modifiers Lua error: Error: invalid field alias "mods.name"; aliases cannot contain dots or quotes.. and Lua error: Error: invalid field alias "mods.name"; aliases cannot contain dots or quotes.. at their maximum value, which grant the following respectively:

Lua error: Error: invalid field alias "mods.name"; aliases cannot contain dots or quotes..% increased Physical Damage
Lua error: Error: invalid field alias "mods.name"; aliases cannot contain dots or quotes..% increased Physical Damage and Lua error: Error: invalid field alias "mods.name"; aliases cannot contain dots or quotes.. to Accuracy Rating

On each weapon, you will get a total of:

Expression error: Unexpected < operator.% increased Physical Damage
Lua error: Error: invalid field alias "mods.name"; aliases cannot contain dots or quotes.. to Accuracy Rating

However, as you can see the stats from each weapon will not add up, because they're local to each weapon.

Interaction of flat, additive, multiplicative stats and conversion

For this example, we assume the following:

75-75 Physical Damage from our weapon
Local stats on the weapon: Adds 25-25 Physical Damage
Local stat on the weapon: 100% increased Physical Damage
Global stat: 100% increased Physical Damage
Global stat: 100% increased Lightning Damage
Skill stat: 50% of Physical Damage converted to Lightning Damage (i.e. from Lua error: Error: invalid field alias "items._pageName"; aliases cannot contain dots or quotes.. or Lua error: Error: invalid field alias "items._pageName"; aliases cannot contain dots or quotes..)

First the local stats are applied:

75-75 Physical Damage +25 min, +25 max
100-100 Physical Damage *2 (i.e. +100%))
200-200 Physical Damage

Method A: Stats first

Adding the global physical damage increase:

200-200 Physical *2 (i.e. +100%)
400-400 Physical

In the next step, damage conversion. Broken down into two individual branches

Branch 1 (Physical)

400-400 Physical Damage *0.5 (i.e. 50% non-converted damage)
200-200 Physical Damage

Branch 2 (Lightning)

400-400 Physical Damage *0.5 (i.e. 50% converted damage)
200-200 Lightning Damage * 3/2 (i.e. in a prior step, we already applied a increased stat of 100% (/2). We apply another 100% on top of the other 100%, for a total of 200% (*3))
300-300 Lightning Damage

Total

200-200 Physical 300-300 Lightning Damage

Method B: Conversion first

We break it down into two branches right away: