shd.build/docs/STAT_LEVEL_SCALING.md

Weapon and gear stat level scaling

Use these observed rules to adjust weapon and gear stat ranges by item level. Apply each rule to both endpoints of a configured range.

In-game observations, rather than published game mechanics, support these formulas. Preserve source observations with new samples and revise constants when a larger data set disproves them.

Numeric representation and display

Store stat ranges as unrounded decimals. The game display truncates them:

displayedValue = floor(rawValue)

Avoid ceil and repeated leveling of displayed integers. Both accumulate errors. A level-1 display of 0 can hide a positive fractional raw value that appears 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:

floor(0.7)        = 0
floor(0.7 × 3.01) = 2

Predictions from displayed integers can miss by one because truncation loses information. That error does not indicate rounding upward.

Shared progression model

The stable portion of both progressions is linear:

rawStat(level) = hiddenBase × multiplier(level)

The multiplier increases by 0.05 per level. Equivalently, each level adds a fixed 5% of the hidden base:

rawStat(level + 1) - rawStat(level) = hiddenBase × 0.05

Do not calculate a new level as previousDisplayedValue × 1.05. That compound growth model conflicts with the observations.

For a range [minimum, maximum], calculate each endpoint separately:

scaledMinimum = hiddenMinimum × multiplier(level)
scaledMaximum = hiddenMaximum × multiplier(level)

Truncate at the game-display boundary.

Gear

The observed stable gear multiplier is:

gearMultiplier(level) = 0.91 + 0.05 × level

Samples across Standard, Specialized, and High-end qualities validate this rule for levels 10 through 50. Quality changes hidden stat ranges; the observed late-level multiplier remains the same.

Given hidden level-independent endpoints:

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:

targetRaw =
  referenceRaw
  × gearMultiplier(targetLevel)
  / gearMultiplier(referenceLevel)

Gear example

At level 42:

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:

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 outside the stable multiplier. Do not extrapolate it from one level-1-to-level-2 change. Until more samples define the early curves, store authoritative ranges or label 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:

weaponMultiplier(level) ≈ 1.14 + 0.05 × level

This gives approximately:

weaponMultiplier(40) = 3.14
weaponMultiplier(50) = 3.64

and predicts a level-40-to-level-50 ratio of:

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:

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:

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 remains provisional; observations only validate it from level 40 to 50. Retain 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:

753 × (3.64 / 3.14) ≈ 872.95
floor(872.95) = 872

The calculation misses by one because 753 is truncated. The ratio applied to the unrounded source value produces 873, so calculations require stored decimal endpoints.

The observed changes over those ten levels were linear:

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 at level 1. An Exotic sample's level-1 and level-50 displays fit a 2.91 endpoint ratio for most stats, which conflicts with extending the level-40-to-level-50 offset backward. Weapons appear to have an early transition or 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.