# Weapon and gear stat level scaling This document records the empirically observed rules for adjusting weapon and gear stat ranges by item level. The rules apply independently to both endpoints of a configured range. These formulas are based on in-game observations rather than published game mechanics. Preserve source observations when adding new samples and revise the constants if a larger data set disproves them. ## Numeric representation and display Stat ranges must retain their unrounded decimal values. The integer shown by the game is consistent with truncation: ```text displayedValue = floor(rawValue) ``` Do not use `ceil`, and do not repeatedly level an already displayed integer. Both approaches accumulate errors. A level-1 value displayed as `0` can still have a positive fractional raw value that becomes visible at a higher level. For example, a standard gear item displayed `0 ENG` at level 1 and `2 ENG` at level 42. With a level-42 multiplier of `3.01`, a raw base near `0.7` explains both values: ```text floor(0.7) = 0 floor(0.7 × 3.01) = 2 ``` When only displayed integers are available, a prediction can be off by one. That is expected information loss, not evidence for rounding upward. ## Shared progression model The stable portion of both progressions is linear, not compounded: ```text rawStat(level) = hiddenBase × multiplier(level) ``` The multiplier increases by `0.05` per level. Equivalently, each level adds a fixed `5%` of the hidden base: ```text rawStat(level + 1) - rawStat(level) = hiddenBase × 0.05 ``` Never calculate a new level as `previousDisplayedValue × 1.05`; that describes compound growth and does not match the observations. For a range `[minimum, maximum]`, calculate each endpoint separately: ```text scaledMinimum = hiddenMinimum × multiplier(level) scaledMaximum = hiddenMaximum × multiplier(level) ``` Only truncate when producing a game-matching display value. ## Gear The observed stable gear multiplier is: ```text gearMultiplier(level) = 0.91 + 0.05 × level ``` This rule is validated for levels 10 through 50 across Standard, Specialized, and High-end samples. Quality changes the hidden stat ranges; the observed late-level multiplier does not change with quality. Given hidden level-independent endpoints: ```text rawMinimum(level) = hiddenMinimum × gearMultiplier(level) rawMaximum(level) = hiddenMaximum × gearMultiplier(level) ``` ISAC gear `base_health` and `base_armor` endpoints are these hidden, level-independent bases. Builder base survivability therefore uses the direct multiplier form above rather than treating those endpoints as observations at the row's legacy reference level. Rolled Attributes and shared core profiles retain their separately defined reference semantics. Given an unrounded range recorded at a known reference level: ```text targetRaw = referenceRaw × gearMultiplier(targetLevel) / gearMultiplier(referenceLevel) ``` ### Gear example At level 42: ```text gearMultiplier(42) = 0.91 + 0.05 × 42 = 3.01 ``` A Standard item with approximate hidden bases of `615.0 HP`, `107.4 AR`, `10.0 FP`, `11.4 TGH`, and `0.7 ENG` produces: ```text HP = floor(615.0 × 3.01) = 1851 AR = floor(107.4 × 3.01) = 323 FP = floor(10.0 × 3.01) = 30 TGH = floor(11.4 × 3.01) = 34 ENG = floor(0.7 × 3.01) = 2 ``` ### Early gear levels Levels 1 through 9 show a quality-dependent transition and do not follow the stable multiplier directly. Do not extrapolate that transition from a single level-1-to-level-2 change. Until the early curves are sampled more completely, store authoritative ranges for those levels or mark calculated results as estimates. ## Weapons Weapon observations from levels 40 through 50 show the same fixed `0.05` multiplier increase per level, but a different offset: ```text weaponMultiplier(level) ≈ 1.14 + 0.05 × level ``` This gives approximately: ```text weaponMultiplier(40) = 3.14 weaponMultiplier(50) = 3.64 ``` and predicts a level-40-to-level-50 ratio of: ```text 3.64 / 3.14 ≈ 1.15924 ``` Two observed weapons produced ratios of approximately `1.15960` and `1.15936`. The small difference is consistent with hidden fractional bases and truncated display values. Given an unrounded weapon range at a known reference level: ```text targetRaw = referenceRaw × weaponMultiplier(targetLevel) / weaponMultiplier(referenceLevel) ``` Per-weapon damage endpoints in ISAC are hidden base ranges, not observations at the shared core profile's reference level. Calculate weapon damage directly: ```text damageRaw(level) = storedDamageBase × weaponMultiplier(level) ``` Firepower, Toughness, and Engineering remain shared reference-level observations and continue to use the ratio form. SHD.build stores the reference level associated with each weapon-tier range. Builder calculations use that recorded observation level in the ratio above. The curve's level-1 origin does not imply that every stored range was observed at level 1. T2 availability limits likewise do not change a range's recorded reference level. Firepower, Toughness, and Engineering nominal tier ranges are stored once in the shared core-allocation configuration at reference level 50. Scale those nominal endpoints to the target level using the appropriate equipment-family multiplier, then derive the combined pool bounds by multiplying each endpoint by three. Redistribution changes the split between the three cores without changing the selected item's total allocation. The `1.14` offset is provisional and is currently validated only for the level-40-to-level-50 interval. Preserve enough decimal precision to revise it without migrating rounded data. ### Weapon example A weapon changed from `753 DMG` at level 40 to `873 DMG` at level 50: ```text 753 × (3.64 / 3.14) ≈ 872.95 floor(872.95) = 872 ``` The displayed-source calculation misses by one because `753` is already truncated. Applying the ratio to the unrounded source value produces the observed `873`. This is why calculations must use stored decimal endpoints. The observed changes over those ten levels were linear: ```text DMG: 753 → 873 (12.0 raw points per level) FP: 44 → 51 (about 0.7 per level) TGH: 15 → 18 (about 0.3 per level) ENG: 45 → 52 (about 0.7 per level) ``` ### Early weapon levels Do not apply the provisional late-level weapon offset to level 1. An Exotic sample's displayed level-1 values and level-50 values fit a `2.91` endpoint ratio for most stats, which is incompatible with simply extending the level-40-to-level-50 offset backward. Weapons therefore also appear to have an early transition or another quality-dependent input. Until more intermediate samples are available: - use the weapon formula only within the validated level 40–50 interval; - do not derive a hidden base directly from a displayed level-1 value; - prefer authoritative low-level ranges where exact results are required. ## Implementation requirements 1. Store range endpoints as decimals and retain their reference level. 2. Scale minimum and maximum independently using raw values. 3. Calculate directly from the reference value; never chain per-level rounded results. 4. Truncate only at the presentation boundary when matching the game display. 5. Clamp supported levels to `1–50`. 6. Treat gear levels below 10 and weapon levels below 40 as provisional until their curves are verified. 7. Add observed intermediate values as regression fixtures before changing a multiplier or rounding rule. ## Current regression observations Useful known outputs include: - Specialized gear at level 27: `1610 HP`, `280 AR`, `29 FP`, `23 TGH`, `10 ENG`. - Standard gear at level 42: `1851 HP`, `323 AR`, `30 FP`, `34 TGH`, `2 ENG`. - High-end gear: level 40 `2682 HP`, `464 AR`, `47 FP`, `16 TGH`, `36 ENG`; level 41 `2728 HP`, `472 AR`, `48 FP`, `16 TGH`, `37 ENG`; level 50 `3143 HP`, `544 AR`, `55 FP`, `19 TGH`, `43 ENG`. - Weapon sample: level 40 `1886 DMG`, `120 FP`, `123 TGH`, `31 ENG`; level 50 `2187 DMG`, `139 FP`, `142 TGH`, `36 ENG`. - Weapon sample: level 40 `753 DMG`, `44 FP`, `15 TGH`, `45 ENG`; level 50 `873 DMG`, `51 FP`, `18 TGH`, `52 ENG`.