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🧮 Combat Formulas & Game Math

The mathematical formulas and details describing how stats scale, damage reduction works, and general multipliers in Task Bar Hero.

System overview

These notes describe the main values used by Probonk calculators. The goal is to make upgrades, farming routes, damage output, and defensive breakpoints easier to compare.

Stats

Flat values, additive percentages, and separate multipliers.

Offense

Attack Speed, Attack Damage, Crit Chance, and Crit Damage.

Defense

Dodge, Block, Armor, Resistance, Damage Reduction, and Absorption.

Stat value scaling

Most stat totals are built in layers. The base value is adjusted first, shared percentage bonuses are added together, and separate multipliers are applied at the end.

final = (base + flatTotal) * (1 + additiveTotal) * multiplierProduct

Base and flat values

Flat bonuses adjust the starting number before percentage scaling is applied.

Shared percent pool

Additive bonuses of the same type are grouped into one combined percentage value.

Separate multipliers

Multiplicative bonuses apply one by one, scaling the current result each time.

Offense estimate

Expected damage output can be estimated with Attack Speed, Attack Damage, Crit Chance, and Crit Damage. Extra damage tags such as melee, projectile, area, or summon can be considered separately when a skill or item supports them.

expectedDps = attackSpeed * attackDamage * (1 + critChance * (critDamage - 1))

Defense flow

Defensive values do not apply as one single bucket. Some checks happen before the hit is reduced, while others apply after the damage type has already been decided.

Avoidance

Dodge is checked first and can stop the hit before damage is calculated.

Block

If the hit is blocked, the incoming value can be reduced before later defenses apply.

Damage type

Physical hits continue through armor, while elemental hits use their matching resistance.

Main defense

Armor or resistance handles the main mitigation depending on the hit type.

General reduction

Damage Reduction scales the remaining value after the type-specific defense step.

Flat absorption

Damage Absorption removes a flat amount near the end of the calculation.

Minimum damage

A successful hit cannot be reduced below 1 final damage.

Physical damage and armor

Armor is used for physical hits. A simple estimate is useful when you only need a quick idea of how much mitigation a stage setup provides.

armorReduction ~= armor / (armor + 14 * stageLevel + 12)The fuller calculation lets larger hits push through more armor by adding part of the incoming hit into the threshold. The practical reduction cap is 75%.

armorReduction ~= armor / (armor + 14 * stageLevel + 12)

armorReduction = armor^2 / (armor^2 + (14 * stageLevel + 12) * (armor + 0.4 * damage))
finalDamage = damage * (1 - armorReduction)

Elemental damage and resistance

Fire, Cold, Lightning, and Chaos hits use resistance instead of armor. The matching resistance value is combined with All Elemental Resistance before the hit is reduced.

effectiveResistance = elementResistance + allElementalResistance
finalDamage = damage * (1 - effectiveResistance / 100)

Farming and reward logic

These rules are used by Probonk farming and progression tools when reading drop chance, offline time, rune bonuses, and player level ranges.

Cube systems

Cube features are handled as separate systems so they can be shown clearly across database pages, calculators, and upgrade tools.

Synthesis

Alchemy

Crafting

Decoration

Engraving

Inscription

Offering

Extraction

Immortal Synthesis unlocks at Cube Lv10. Celestial Synthesis unlocks at Cube Lv50.

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