Hugglebeary
Tank Theorycrafting
Defence scaling, EHP analysis, time-to-kill curves, and DEF vs HP perk breakpoints.

+8% HP vs +12% DEF Calculator

Enter your unit's stats to see which perk gives more EHP.

Steady III vs Cautious III
Steady III
Increases Max Health by 8%. When Health drops below 50% for the first time, increase it by an additional 8%.
Cautious III
Gain 12% Armor. This effect doubles for 10s after the start of battle.

Assuming the base +8% HP and +12% DEF are roughly equal for your build (use the calculator above to check), the choice comes down to the conditional bonus:

  • Short fights / burst-heavy content → Cautious III (front-loaded value — 24% Armor for the first 10 seconds)
  • Long fights / sustained damage → Steady III (insurance when HP drops below 50%, effectively 16% HP when you need it most)

Summary

DEF vs damage reduction

DMG_REDUCTION = DEF / (DEF + 100)

Defence converts to damage reduction on a diminishing-returns curve. The first 100 DEF buys 50% reduction; doubling to 200 only reaches 66.7%. Reaching 90% costs 900 DEF, and 99% costs 9,900. The formula ensures every point of DEF always helps, but each one helps a little less than the last.

+12% DEF perk: damage reduction gained

Gain = f(1.12 × DEF) − f(DEF)
where f(x) = x / (x + 100)

A percentage-based DEF perk doesn't give flat returns. At low DEF, 12% of a small number is still small. At high DEF, diminishing returns eat into the gain. The perk peaks around 100 DEF at roughly +2.8% damage reduction, then tapers. This hump shape — unlike a pure derivative — is what makes the perk's value position-dependent.

Time to kill vs DEF

TTK multiplier = 1 / (1 − DR) = (DEF + 100) / 100

Substituting the DR formula back into effective HP reveals a perfectly straight line. Every point of DEF gives the same survivability gain as the last — 100 DEF = 2× TTK, 500 DEF = 6×, 900 DEF = 10×. This linearity is the entire purpose of the DEF/(DEF+100) formula: it makes DEF stacking feel consistently rewarding without ever becoming broken.

Time to kill vs HP% bonuses

Total HP = Base HP × (1 + Σ HP% Bonuses)
TTK multiplier from HP% = (1 + HP%)

HP% bonuses are additive with each other, so the TTK multiplier from HP stacking is also a straight line — 50% HP bonus = 1.5× TTK, 100% = 2×. However, because each additional +8% HP is added to an ever-growing sum, the marginal EHP gain per perk diminishes: the first +8% gives 8% more TTK, but at 100% existing HP% it only gives 4%.

+12% DEF vs +8% HP

Total DEF = Base DEF × (1 + Σ DEF%)
Effective perk = 0.12 / (1 + existing DEF%)
+12% DEF EHP gain = effective perk × DEF / (DEF + 100)
+8% HP EHP gain  = 0.08 / (1 + HP%)
0%
+12% DEF wins +8% HP wins Breakeven
Lv.50 Hugglebeary — STR(5) Dominator, UGL(2) Mr Avocado Buff
222 DEF | 68% HP%

With the game's actual perk ratio of 12% DEF to 8% HP, the DEF perk dominates for most mid-to-late game builds. At Hugglebeary's 222 DEF and 68% HP%, the +12% DEF perk gives +8.30% EHP versus +4.76% from +8% HP — DEF wins by 3.54%. The breakeven line shows that above 200 DEF, even 0% existing HP% favours DEF.

+1% DEF vs +1% HP

Total DEF = Base DEF × (1 + Σ DEF%)
Effective perk = 0.01 / (1 + existing DEF%)
+1% DEF EHP gain = effective perk × DEF / (DEF + 100)
+1% HP EHP gain  = 0.01 / (1 + HP%)
0%
+1% DEF wins +1% HP wins Breakeven
Lv.50 Hugglebeary — STR(5) Dominator, UGL(2) Mr Avocado Buff
222 DEF | 68% HP%

At equal 1:1 ratios, HP is far stronger — you need 100 DEF just to break even with 0% existing HP%. At Hugglebeary's stats, the two perks are much closer than in the 12-vs-8 comparison. The devs intentionally gave DEF a 1.5× multiplier (12% vs 8%) to compensate for the +100 constant in the formula always diluting DEF's value.

Adding Damage reduction as another variable

Final Damage = ATK × 100 / (DEF + 100) × (1 − DR₁) × (1 − DR₂) × … + k

Simple Defense in HNA passes through three multiplicative layers. First, the attacker's ATK is reduced by the target's DEF via the familiar DEF/(DEF+100) formula. Then each source of damage reduction multiplies independently — a 5% and a 20% DR source give 1−(0.95×0.80) = 24% total, not 25%. k represents other variables, which we will explore in a seperate subsection

Damage reduction test data
Attacker Target DR% Formula Expected Actual
Muscimmon (119 ATK)Apollinis (161 DEF)0%119×100/2614646
Muscimmon (119 ATK)Apollinis (161 DEF)3%×0.974444
Muscimmon (119 ATK)Apollinis (161 DEF)5%×0.954343
Muscimmon (119 ATK)Apollinis (161 DEF)20%×0.803636
Bladehound (204 ATK)Apollinis (161 DEF)0%204×100/2617878
Bladehound (204 ATK)Apollinis (161 DEF)20%×0.806363
Bladehound (204 ATK)Apollinis (161 DEF)3%+20%×0.97×0.806161
Bladehound (204 ATK)Nomnom (55 DEF)0%204×100/155131131
Bladehound (204 ATK)Nomnom (55 DEF)5%×0.95125125
Bladehound (204 ATK)Nomnom (55 DEF)30%×0.709292
Bladehound (204 ATK)Nomnom (55 DEF)5%+30%×0.95×0.708787

Damage Reduction sources are 3%/5% Aspect Synegies for Pride(2)/Pride(3) and Apollinis 20% Damage Reduction while skill is active, Nomnom 30% Damage Reduction while skill is active.

Stacking DR: multiple sources vs one

Two sources of X%: multiplier = (1−X%)²
One source of 2X%: multiplier = (1−2X%)

One larger source always wins — splitting loses to multiplicative stacking penalty

Because DR stacks multiplicatively, two 10% sources give 19% total DR (0.9×0.9 = 0.81), not 20%. A single 20% source is strictly better — it gives the full 20% reduction. The gap widens with larger values: two 15% sources give 27.75% total, while one 30% source gives the full 30%. Always prefer one large DR source over two smaller ones that add up to the same value.

DR vs DEF% vs HP%: Time To Kill (TTK) scaling

HP%: TTK increase = HP% (linear)
DEF%: TTK increase = Base DEF × DEF% / (Base DEF + 100) (linear, slope < 1)
DR: TTK increase = 1 / (1 − DR) − 1 (accelerating)

HP% gives a 1:1 linear TTK increase — +50% HP means +50% TTK. DEF% is also linear but with a weaker slope that depends on base DEF (at 222 base: slope ≈ 0.69). DR is the outlier — it accelerates. Each additional % of DR gives more TTK than the last, making it the only survivability stat with increasing returns.

Equal TTK: stat equivalence

For the same +8% TTK increase:

HP% = 8%
DR = 1 − 1/1.08 = 7.41%
DEF% = 8% × (Base DEF + 100) / Base DEF

To get the same survivability as +8% HP, you need only 7.41% DR — DR is more efficient point-for-point because of its accelerating curve. DEF% requires more than 8% because its slope is always less than 1 (it depends on base DEF).

HP%
12%
DR
10.71%
DEF%
17.41%
222
0%
0%
0%

DR is always 7.41% regardless of existing bonuses — it scales independently. HP% and DEF% both need more the higher your existing bonuses are. This demonstrates why DR is the most efficient survivability stat to stack.

Annex: test data
My unit Opponent
Unit Lv ATK DEF MDEF DEF% MDEF% Unit Lv ATK DEF MR DEF% MDEF%
DEF% formula verification — Puddlipup (Base DEF: 63)
Buffs active Σ DEF% Expected Actual
12% disposition12%70.5670
24% disposition24%78.1278
12% disposition + 40% skill52%95.7695
24% disposition + 40% skill64%103.32103

Formula: Total DEF = Base DEF × (1 + Σ DEF%). Values truncated to integer in-game.

HP% formula verification — Hugglebeary (Base HP: 1,914)
Build Σ HP% Expected Actual
Aspect STR(1)15%2,2012,201
DOM(1)23%2,3542,345
STR(3)24%2,3732,374
DOM(3)36%2,6032,603
STR(5)38%2,6392,632
DOM(5)56%2,9862,991
DOM(5) + UGL(2) Mr Avocado Buff68%3,2163,221

Formula: Total HP = Base HP × (1 + Σ HP%). Minor variance (≤5) likely from hidden decimal precision on base stats or buff values.

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