--- name: set-calculations description: Reference for the numbers the Set World API calculates about characters and items, with each formula, endpoint and response schema. Use when deriving the 23 attributes from stats, rating a character's power, computing how a trait name changes stats, scoring an item's rarity, or reading an item's power budget and theme channels, either by calling the API or by recomputing locally. license: Free to use when obtained from set.world, commercially too (the API, what it returns, the skills and downloaded models). The source code of Set is © Jimmy Lee under CC BY-NC 4.0 and its commercial use needs a paid waiver. metadata: version: "0.8.9" title: Calculations --- # Calculations Every number Set returns is a pure function of the tables and the inputs. Call the endpoint, or recompute it yourself from the formulas here; both give the same result. This skill owns five calculations. Prices in orbs (crafts, salvage, boosts, drops) are owned by [Crafting an item](https://set.world/skills/crafting-an-item). | Calculation | Endpoint | | --- | --- | | Derived attributes | `/api/attributes?stats=`, `/api/attributes/spec` | | Power rating | `/api/power?stats=&level=&skills=` | | Trait impact | `/api/traits/impact?name=&kind=`, `/api/traits/impacts?kind=` | | Rarity score | `/api/rarity?rolls=` or `indexes=`, `/api/rarity/tiers` | | Item power budget and themes | `/api/modifiers?rolls=` or `indexes=`, `/api/modifiers/spec` | `stats` is nine dash-joined integers from 8 to 24 in the canonical order ([Stats](https://set.world/skills/character-stats)). `rolls` and `indexes` are 19 dash-joined integers ([Item properties](https://set.world/skills/item-properties)). The schemas below reuse `StatName` and `StatBlock` from [Stats](https://set.world/skills/character-stats), and `Grade` and `Material` from [Materials](https://set.world/skills/item-materials). `AttributeName` is one of the 23 names in the table below. ## Derived attributes ```text attribute = base + primaryCoef × (primary − 8) + secondaryCoef × (secondary − 8) ``` Only the five primary stats appear. Each is clamped to 8 to 24 first; results keep four decimals. ```sh curl 'https://set.world/api/attributes?stats=16-15-12-11-15-18-12-13-9' curl 'https://set.world/api/attributes/spec?format=csv' ``` ```ts type AttributesResponse = { stats: StatBlock; attributes: Record }; type AttributeSpec = Record; ``` ```json { "stats": { "strength": 16, "dexterity": 15, "intelligence": 12, "wisdom": 11, "agility": 15, "vitality": 18, "perception": 12, "resolve": 13, "luck": 9 }, "attributes": { "maxHealth": 184, "stamina": 96, "physicalDamage": 25.5, "magicalDamage": 19.5, "actionDamage": 23.2, "physicalDamageReduction": 0.152, "magicalDamageReduction": 0.088, "globalResistance": 0.092, "ailmentResistance": 0.116, "dodgeRate": 0.125, "walkSpeed": 1.155, "attackSpeed": 1.14, "castSpeed": 1.09, "chargeSpeedCast": 1.108, "chargeSpeedAction": 1.126, "carrySpeed": 1.15, "carryCapacity": 110, "jumpHeight": 1.11, "visionRange": 1.095, "criticalHitChance": 0.092, "clarity": 0.083, "initiative": 1.108, "reflexes": 0.119 } } ``` The formula table, as `/api/attributes/spec?format=csv` serves it: ```csv attribute,primary,secondary,base,primaryCoef,secondaryCoef,unit maxHealth,vitality,strength,80,8,3,hp stamina,vitality,strength,40,4,2,sp physicalDamage,strength,dexterity,10,1.5,0.5,dmg per swing magicalDamage,intelligence,dexterity,10,1.5,0.5,dmg per cast actionDamage,dexterity,strength,10,1.2,0.6,dmg per action physicalDamageReduction,vitality,strength,0,0.012,0.004,% mitigated magicalDamageReduction,intelligence,vitality,0,0.012,0.004,% mitigated globalResistance,vitality,intelligence,0,0.008,0.003,% mitigated all ailmentResistance,vitality,intelligence,0,0.01,0.004,% avoid status dodgeRate,agility,dexterity,0.02,0.01,0.005,% avoid hits walkSpeed,agility,vitality,1,0.015,0.005,% of base move attackSpeed,dexterity,agility,1,0.015,0.005,% of base swing castSpeed,intelligence,dexterity,1,0.012,0.006,% of base cast chargeSpeedCast,intelligence,vitality,1,0.012,0.006,% of base wind-up chargeSpeedAction,dexterity,agility,1,0.012,0.006,% of base wind-up carrySpeed,strength,agility,1,0.01,0.01,% of base move carryCapacity,strength,vitality,50,5,2,weight units jumpHeight,agility,strength,1,0.01,0.005,% of base jump visionRange,intelligence,agility,1,0.015,0.005,% of base sight criticalHitChance,dexterity,intelligence,0.02,0.008,0.004,% crit clarity,intelligence,dexterity,0,0.012,0.005,% chance to ignore enemy dodge initiative,agility,intelligence,1,0.012,0.006,% of base cooldown rate reflexes,agility,dexterity,0,0.012,0.005,% chance to counter surprise hits ``` The order of these 23 rows is the order of `AttributeName` and of the first 23 theme channels below. Percent channels are fractions: a `dodgeRate` of 0.125 is 12.5%. Units are advisory: a real-time game reads `attackSpeed` as swings per second, a turn-based game as turn-meter rate. | Stat block | maxHealth | stamina | physicalDamage | attackSpeed | initiative | | --- | ---: | ---: | ---: | ---: | ---: | | All 8 | 80 | 40 | 10 | 1.00 | 1.000 | | All 16 | 168 | 88 | 26 | 1.16 | 1.144 | | All 24 | 256 | 136 | 42 | 1.32 | 1.288 | ## Power rating ```text powerRating = 100 × level + 10 × (strength + intelligence + dexterity + agility + vitality) + 5 × (wisdom + perception + resolve) + 2 × luck + 25 × skills powerRatingMax = 100 × level + 1,708 every stat 24, 4 skills ``` ```sh curl 'https://set.world/api/power?stats=16-15-12-11-15-18-12-13-9&skills=2' ``` ```ts type PowerResponse = { level: number; skills: number; stats: StatBlock; powerRating: number; powerRatingMax: number }; ``` ```json { "level": 1, "skills": 2, "stats": { "strength": 16, "dexterity": 15, "intelligence": 12, "wisdom": 11, "agility": 15, "vitality": 18, "perception": 12, "resolve": 13, "luck": 9 }, "powerRating": 1108, "powerRatingMax": 1808 } ``` `level` defaults to 1 and `skills` to 0 (0 to 4). `level` is your number; Set never interprets it. Equal ratings do not mean equal strength in a fight. ## Trait impacts An advantage or disadvantage is only a name. Its effect is a pinned hash of that name, so every consumer computes the same impact, and any string has one. ```text h = FNV-1a 32-bit (offset 0x811c9dc5, prime 0x01000193) over the UTF-8 bytes of the name in Unicode NFC STATS = [strength, dexterity, intelligence, wisdom, agility, vitality, perception, resolve, luck] primary = STATS[(h & 0xff) % 9] b = ((h >>> 8) & 0xff) % 100; tier = b < 60 → 1, b < 85 → 2, b < 97 → 3, else 4 secondary = STATS[((h >>> 16) & 0xff) % 9], advanced by one on collision with the primary tier 2 and above ``` | Tier | Advantage (primary / secondary) | Disadvantage (primary / secondary) | | --- | --- | --- | | 1 | +5% / none | −8% / none | | 2 | +10% / +5% | −15% / −8% | | 3 | +15% / +10% | −22% / −15% | | 4 | +25% / +15% | −35% / −20% | All of a character's deltas add per stat, then: ```text modifiedStat = clamp(8, 24, round(base × (1 + Σ deltas))) ``` ```sh curl 'https://set.world/api/traits/impact?name=unyielding%20in%20the%20face%20of%20adversity&kind=advantage' curl 'https://set.world/api/traits/impacts?kind=advantage' ``` ```ts type TraitImpact = { name: string; kind: 'advantage' | 'disadvantage'; tier: 1 | 2 | 3 | 4; primary: StatName; primaryDelta: number; // a signed fraction: 0.1 is +10% secondary?: StatName; // tier 2 and above secondaryDelta?: number; }; type TraitImpactsResponse = { kind: 'advantage' | 'disadvantage'; impacts: TraitImpact[] }; ``` ```json { "name": "unyielding in the face of adversity", "kind": "advantage", "tier": 2, "primary": "dexterity", "primaryDelta": 0.1, "secondary": "resolve", "secondaryDelta": 0.05 } ``` The tables of names are in [Advantages](https://set.world/skills/character-advantages) and [Disadvantages](https://set.world/skills/character-disadvantages). ## Rarity score ```text P(item) = P(quality) × P(prefix) × P(slot) × P(material | slot) × P(gear | slot) × P(suffix) score = −log10 P(item) 4 ≈ 1 in 10,000; 7 ≈ 1 in 10,000,000 ``` Each probability is `weight / totalWeight` from the item tables. The grade is separate: it comes from the material alone ([Materials](https://set.world/skills/item-materials)). ```sh curl 'https://set.world/api/rarity?rolls=119899-493-0-430998-9100-0-0-0-52-0-0-0-0-0-0-0-0-0-1108' ``` ```ts type RarityResponse = { indexes: number[]; score: number; probability: number; // 10^(−score) materialRank: number; tier: number; tierGrade: Grade; tierName: string; orbValue: number; material: Material; breakdown: Array<{ slot: 'quality' | 'prefix' | 'material' | 'slot' | 'gear' | 'suffix'; name: string; p: number; contribution: number }>; // largest first }; ``` ```json { "indexes": [5, 5, 0, 10, 3, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10], "score": 10.7359, "probability": 1.8368537066135063e-11, "materialRank": 9, "tier": 4, "tierGrade": "C", "tierName": "Grade C", "orbValue": 125, "material": { "name": "steel", "materialRank": 9, "tier": 4, "tierGrade": "C", "tierName": "Grade C" }, "breakdown": [ { "slot": "suffix", "name": "dawn", "p": 0.0007733952049497294, "contribution": 3.111598524880394 }, { "slot": "prefix", "name": "burning", "p": 0.0015337423312883436, "contribution": 2.81424759573192 }, { "slot": "gear", "name": "sword", "p": 0.006896551724137931, "contribution": 2.161368002234975 }, { "slot": "material", "name": "steel", "p": 0.06333189828470179, "contribution": 1.1983774944104577 }, { "slot": "slot", "name": "tool", "p": 0.17926565874730022, "contribution": 0.7465028986418792 }, { "slot": "quality", "name": "fine", "p": 0.19777394880915988, "contribution": 0.7038309151328761 } ] } ``` `/api/rarity/tiers` returns the seven grade definitions: `{ tiers: [{ tier, grade, name, share }], note, rules, gradeRanges: { tools: 23, wearables: 31 } }`. ## Item power budget and themes Items never ship resolved modifiers. Set grades a budget and names a theme; what a point buys is your game's tuning. ```text budget(tier) = 0 for F, else 2^(tier − 2) F 0, E 1, D 2, C 4, B 8, A 16, S 32 channel(word) = CHANNELS[fnv1a32(word) % 31] one per name factor; "-" is skipped CHANNELS = the 23 attributes in the order above, then fire, frost, lightning, poison, shadow, holy, arcane, nature ``` ```sh curl 'https://set.world/api/modifiers?rolls=119899-493-0-430998-9100-0-0-0-52-0-0-0-0-0-0-0-0-0-1108' ``` ```ts type ModifiersResponse = { indexes: number[]; score: number; materialRank: number; tier: number; tierGrade: Grade; tierName: string; orbValue: number; material: Material; budget: number; themes: Array<{ factor: 'quality' | 'prefix' | 'material' | 'gear' | 'suffix'; name: string; channel: string }>; }; ``` ```json { "indexes": [5, 5, 0, 10, 3, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10], "score": 10.7359, "materialRank": 9, "tier": 4, "tierGrade": "C", "tierName": "Grade C", "orbValue": 125, "material": { "name": "steel", "materialRank": 9, "tier": 4, "tierGrade": "C", "tierName": "Grade C" }, "budget": 4, "themes": [ { "factor": "quality", "name": "fine", "channel": "frost" }, { "factor": "prefix", "name": "burning", "channel": "magicalDamageReduction" }, { "factor": "material", "name": "steel", "channel": "carrySpeed" }, { "factor": "gear", "name": "sword", "channel": "carrySpeed" }, { "factor": "suffix", "name": "dawn", "channel": "jumpHeight" } ] } ``` A theme comes from the hash, not the word's meaning: `burning` gets the `magicalDamageReduction` channel, whatever the word suggests. `/api/modifiers/spec` returns the budget per grade, the 31 channels and the hash rule: `{ contract, budgets: [{ tier, tierGrade, tierName, budget, craftCost }], budgetRule, channels, elementalChannels, themeDerivation }`. A hypothetical way to spend a budget in your game: ```ts type ItemModifier = { channel: string; operation: 'add' | 'multiply'; value: number }; // One point per theme channel, in turn, until the budget is spent. The values are your tuning: // { channel: 'carrySpeed', operation: 'multiply', value: 1.02 }, { channel: 'frost', operation: 'add', value: 3 }, … ``` ## Beyond these Prices in orbs: [Crafting an item](https://set.world/skills/crafting-an-item). One attack or one window of turn order: [Combat](https://set.world/skills/basic-lightweight-combat), optional and experimental. Weight, protection and real-time combat in Set's own game: [Derived stats](https://set.world/skills/anima-derived-stats) and [Derived combat](https://set.world/skills/anima-derived-combat). Full derivations: [Algorithms](https://set.world/skills/algorithms).