Damage Reduction Stacking Sheet
Multiply what gets THROUGH, then subtract from one. Reductions never add.
BFCBrilliance · bfcbrilliance.com/tools/damage-reduction-stacking-calculator
The arithmetic
- Combined reduction
- 1 - (1-a)(1-b)(1-c)(1-d)
- Easier in your head
- multiply what gets THROUGH
- 30% + 20%
- 0.7 x 0.8 = 0.56 through = 44%
- NOT
- 50%
- 30 + 20 + 15
- 52.4% real, 65% naive
- A 10% source adds
- 10 points of what is LEFT
- But always multiplies EHP by
- 1 / 0.9 = 1.111
- A zero source
- changes nothing - leave it
- Then take the combined figure
- to an effective health calculator
This build
- Game and character
- Date
- Source 1
- Source 2
- Source 3
- Source 4
- GETS THROUGH
- COMBINED REDUCTION
- Naive sum
- Overstatement
- Considering
- It would add
Compare items honestly
| Item | Reduction | Points added | EHP multiplier | Take it? |
|---|---|---|---|---|
Before trusting a defensive number
- Sources multiplied, not added
- Checked whether YOUR game stacks multiplicatively
- Checked for a cap on total reduction
- Armour and elemental resistance checked separately - often different curves
- A duplicate source entered separately to see the second copy's real worth
- Item compared on EFFECTIVE HEALTH, not on percentage points
- Health considered too - it multiplies with reduction
- Combined figure carried to an effective health calculation
Points shrink, value does not
A 10% source added to nothing gives 10 points; added on top of 52% it gives under 5. Yet in both cases it multiplies your effective health by 1.111. It looks weaker and is worth the same - which is why percentage points are the wrong unit for judging a defensive item and effective health is the right one.
Work in what gets through
Stopping 30% is awkward to combine. Letting 70% through is not: multiply the fractions that get past each source, and subtract from one at the very end. 0.7 x 0.8 x 0.85 = 0.476, so 52.4% reduction. Doing it this way makes the multiplicative behaviour obvious instead of surprising.