Weight

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Weight is a game mechanic based on the concept of weighted probability that is a central part of many other systems found in Path of Exile, including how item drop rate, modifier roll chance, and in Ruthless mode, Extra Content spawn rate.

Overview

Weight systems are used when the chance for an outcome is dependent on the ratio between other outcomes. These systems work by assigning a number (weight) to each rollable outcome, and the weight is compared to the sum of all outcomes' weights to create a ratio. For example, if a modifier with a weight of 1000, and a total weight of 40,000, that modifier has a 2.5% chance to roll (1000/40,000).

The weight system also can apply to systems without data-mineable weights, such as the chance to encounter a master in a map. In these cases, an arbitrary relative weight can be assigned to all outcomes for the purpose of calculating ratios and how modifiers affect them.

Examples of systems that use weights:

  • All global DropPool item drop rates
    • Ancient OrbAncient OrbStack Size: 20Reforges a unique equipment as another of the same item classRight click this item then left click a unique item to apply it. rerolling
    • Chance for a map to be a specific map using the favoured map system
  • All methods of non-deterministically rolling or crafting modifiers
  • VoicesVoices
    Large Cluster Jewel    Adds 3 Jewel Socket Passive Skills
    <Random empty passive skill node mod>    CorruptedOnly a madman would ignore a god's instructions.Place into an allocated Large Jewel Socket on the Passive Skill Tree. Added passives do not interact with jewel radiuses. Right click to remove from the Socket.     # of small passives
  • League mechanic distributions
    • Chance to randomly encounter a specific master in a map
    • Chance to encounter a specific family of Red Beast
    • Chance to encounter a specific faction of Beyond demons
    • Chance to encounter specific faction of Legion armies
    • Chance for a Breach to belong to a specific Breachlord
    • Chance for Harvest crops to be Wild, Primal, or Vivid
    • Chance for a Heist Contract to require a specific job type or job level
  • Core mechanic encounters in Ruthless mode
    • Chance to encounter one of the 11 league mechanics that share a spawn rate

Modifying weights

When multiplying weights, the total weight must always be increased or decreased the same amount as the individual weights. This causes the written multiplier to be different from the actual change.

All similar modifiers with "increased" or "reduced" must be added together before applying the multiplier.

The following modifiers are examples of modifiers that are a more multiplier to weights:

Source Modifier Multiplier
Fossils More X modifiers 10x
Prismatic FossilPrismatic FossilStack Size: 20More Elemental modifiers
No Physical Ailment or Chaos Ailment modifiersPlace in a Resonator to influence item crafting.		 More Elemental modifiers 6x
Divination Scarab #% more Divination Cards found in Area 1.5-3.5x
Reliquary Scarab #% more Unique Items found in Area 1.5-3.5x
Physical Training, Higher Education,
The Fine Arts		 Heist Contracts found in your Maps are 100% more likely to require X 2x
Cartography Scarab #% increased Maps found in your Maps Stackable
Breach passives Breaches in your Maps have #% increased chance to belong to X Stackable
Swarming Hive, Pale Clarion,
Voracious Throng		 Beyond Demons in your Maps have #% increased chance to be followers of X 2x
The Hunt for Saqawal, The Hunt for Craiceann,
The Hunt for Fenumus, The Hunt for Farrul		 Red Beasts in your Maps have #% increased chance to be from X 2x
Hunting Season, Mining Partnership,
Archaeology Tour, Covert Stakeouts		 Master Missions from completing your Maps have #% increased chance to be X
Randomly encountered Masters in your Maps have #% increased chance to be X		 2x
League mechanic increased chance
passives in Ruthless		 Your Maps have #% increased chance to contain X
(Mechanic encounter rates are dependent on each other in Ruthless)		 Stackable

The following modifiers are examples of modifiers that are a less multiplier to weights:

Source Modifier Multiplier
Fossils Fewer X modifiers 0.15x
Harvest passives Harvest Crops in your Maps have #% reduced chance to grow X Plants Stackable

The following modifiers are examples of modifiers that null weights to 0:

Source Modifier Multiplier
Fossils No X modifiers 0x
League mechanic blocking notables in Ruthless Your Maps have no chance to contain X
(Mechanic encounter rates are dependent on each other in Ruthless)		 0x
Example of modifying weights ▾ [Expand] ▾

Example of modifying weights

Using a fictional example:

Assume that Crimson Temple MapCrimson Temple MapMap Level: 79
Map Tier: 12
Guild Character: ©A sanguine supplication to death and depravity.Travel to this Map by using it in a personal Map Device. Maps can only be used once. only contains two cards: The Blazing FireThe Blazing Fire6Chin SolLethal, untouchable, keen, aflame. Just what I was looking for. and The ApothecaryThe Apothecary5Mageblood"You seek the power of my strongest potions, but the price will be far higher than you can imagine.".

  • The total weight of all DropPool items is 8000000.
  • The Blazing Fire has a drop weight of 12586. This means 0.157% (12586 / 8000000) of items dropped will be The Blazing Fire.
  • The Apothecary has a drop weight of 7. This means 0.0000875% (7 / 8000000) of items dropped will be The Apothecary.

Using a Module Error: No results found for item using search term "item_name = Winged Divination Scarab" causes the weights of Divination cards to be multiplied by 3.5 (250% more).

  • The Blazing Fire now has a drop weight of 44051. (12586 * 3.5) This adds 31465 to the DropPool. (44051 - 12586 = 31465)
  • The Apothecary now has a drop weight of 24. (7 * 3.5) This adds 17 to the DropPool. (24 - 7 = 17)
  • The total weight of all DropPool items is now 8031472.
  • This means 0.548% (44051 / 8031472) of items dropped will be The Blazing Fire. The actual chance to drop was multiplied by 3.49, not 3.50. (0.548 / 0.157)
  • This means 0.000299% (24 / 8031472) of items dropped will be The Apothecary. The actual chance to drop was multiplied by 3.42, not 3.50. (0.000299 / 0.0000875)


Complex example of dynamic weights using the All Hands keystone ▾ [Expand] ▾
Main page: All Hands

All Hands adds a 40% chance to encounter a random master when a master mission is not selected on the map device, increasing it to 50% chance to encounter a random master. This 50% value is split evenly between the four masters by default using a weighting system of 1:1:1:1 for Einhar/Niko/Alva/Jun respectively, and can be modified by the notables that affect randomly encountered Masters in your Maps have #% increased chance to be a specific Master (Hunting Season, Mining Partnership, Archaeology Tour, and Covert Stakeouts), skewing a 12.5% chance to encounter a specific master to 20%.

It also disables the ability to gain a master mission on completing a map. Note that while this disables the gaining of Kirac missions, it does not enable Kirac to be encountered in a map.

Modifiers to chance to grant an additional Master Mission on Map Completion instead apply to chance for that Master to be randomly encountered in your Maps at 150% of their value causes passives that read Your Maps have #% chance to grant an additional (Einhar/Niko/Alva/Jun) Mission on Completion to apply a flat chance instead to encounter that master. This means that 10% to gain a specific master's mission is translated into 15% chance for that specific master to be randomly encountered, stacking additively with the 50% above. Each master can gain up to 10% mission chance on the tree (12% with Wandering Path), or 15% (18%) chance to encounter a master in a map. By investing into multiple masters to get a total of ≥34% mission chance across the four masters, it is possible to encounter random masters in every map.

Examples (with Jun as the desired master):

  1. All Hands, no additional mission chance:
    1. Chance to encounter a random master: 10% + 40% = 50%
    2. Chance for randomly encountered Masters in your Maps to be Jun: 1:1:1:1 = 1/4 * 50% = 12.5%
      1. Chance for randomly encountered Masters in your Maps to be another master: 1:1:1:1 = 1/4 * 50% = 12.5% each
    3. Chance for Jun to be randomly encountered: 0% * 1.5 = 0%
    4. Chance to encounter Jun in a map: 12.5% + 0% = 12.5%
  2. All Hands, no additional mission chance, Covert Stakeouts:
      1. Chance to encounter a random master: 10% + 40% = 50%
    2. Chance for randomly encountered Masters in your Maps to be Jun: 1:1:1:2 = 2/5 * 50% = 20%
      1. Chance for randomly encountered Masters in your Maps to be another master: 1:1:1:2 = 1/5 * 50% = 10% each
    3. Chance for Jun to be randomly encountered: 0% * 1.5 = 0%
    4. Chance to encounter Jun in a map: 20% + 0% = 20%
  3. All Hands, 10% mission chance:
    1. Chance to encounter a random master: 10% + 40% = 50%
    2. Chance for randomly encountered Masters in your Maps to be Jun: 1:1:1:1 = 1/4 * 50% = 12.5%
      1. Chance for randomly encountered Masters in your Maps to be another master: 1:1:1:1 = 1/4 * 50% = 12.5% each
    3. Chance for Jun to be randomly encountered: 10% * 1.5 = 15%
    4. Chance to encounter Jun in a map: 12.5% + 15% = 27.5%
  4. All Hands, 12% mission chance (Wandering Path):
    1. Chance to encounter a random master: 10% + 40% = 50%
    2. Chance for randomly encountered Masters in your Maps to be Jun: 1:1:1:1 = 1/4 * 50% = 12.5%
      1. Chance for randomly encountered Masters in your Maps to be another master: 1:1:1:1 = 1/4 * 50% = 12.5% each
    3. Chance for Jun to be randomly encountered: 12% * 1.5 = 18%
    4. Chance to encounter Jun in a map: 12.5% + 18% = 30.5%
  5. All Hands, 10% mission chance, Covert Stakeouts:
    1. Chance to encounter a random master: 10% + 40% = 50%
    2. Chance for randomly encountered Masters in your Maps to be Jun: 1:1:1:2 = 2/5 * 50% = 20%
      1. Chance for randomly encountered Masters in your Maps to be another master: 1:1:1:2 = 1/5 * 50% = 10% each
    3. Chance for Jun to be randomly encountered: 10% * 1.5 = 15%
    4. Chance to encounter Jun in a map: 20% + 15% = 35%

References

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