shd.build/docs/STAT_LEVEL_SCALING.md

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:

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:

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:

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

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:

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

Only truncate when producing a game-matching display value.

Gear

The observed stable gear multiplier is:

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:

rawMinimum(level) = hiddenMinimum × gearMultiplier(level)
rawMaximum(level) = hiddenMaximum × gearMultiplier(level)

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 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:

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)

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:

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:

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.