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Introduction

The following are formulas and hidden mechanics for Dota Underlords, whether you're looking to 'theorycraft' or just want to get an edge on your opponent by leveraging some in-game knowledge this page will serve as the foundation. If you're looking for strategy guides to help you put these to use check out our guides.

Special thanks to u/Yusunanyuri who's hard work helped with establishing, verifying, or otherwise testing the information that follows.

Formulas and Calculations

Armor Formula (Damage Multiplier)

The below formula takes your armor value and converts it into a damage modifer that expresses the relationship armor has with damage mitigation:

1-((0.052 x 'armor') / (0.9 + 0.048 x |'armor'| )) 

Effective HP Formula

Effective HP is a way of understanding armor's mitigation contributions by converting it into equivalent amounts of HP, it builds on the 'Damage Multiplier' seen above:

'HP' / 'Damage Multiplier' 

Mana Gain Formula

Mana can be gained through all forms of damage dealt, damage received, and through certain items. The formulas for understanding 'mana gain' through damage dealt and received are below:

Damage Dealt

'Damage Dealt' / 7.5 = 'Mana Gain' 

  • 'Mana Gain' per attack dealt is capped at 10 unless the hero is part of the below alliances.

    • 'Brooch of the Agressor' increases the cap by 50%.

  • Shaman, Warlocks, and Mages gain 50% more mana from 'damage dealt' and have their 'caps' doubled.

  • Mana gains are always rounded up by the game, for example:

    • Tiny deals 80 'actual' damage,  the formula would read 80  / 7.5 = 11 (Rounded up from 10.8) mana gained. 

  • Damage is always factored in 'post' mitigation.

Damage Received

'Damage Received' / 9.5 = 'Mana Gain' 

  • 'Mana Gain' per attack received is capped at 10 for all units. 

    • 'Brooch of the Martyr' increases the cap by 50%.

  • Roughly 20% less efficient than 'Damage Dealt' 

  • Mana gains are rounded up the same way as above. 

  • There are no modifiers that favor specific Alliances for 'Damage Received.'

Attack Speed Calculation

'Attack Speed' is derived by taking the base in-game attack rate of the hero and multiplying it by the following:

(1 + Attack_Speed_Bonus)

Because of this formula, the effect an item has on your DPS will always be equal to the buff it provides to your haste. When stacking haste buffs since they are of the same 'type' they will always interact additively, this means that having the troll buff and 'Gloves of Haste' would require that you simply add the bonuses for a total of 60% for 'Trolls' at the entry-level of the buff and 35 for any allies.

Player Damage Formula

When you lose a round against a player the damage you will take is equal to the 'sum of all remaining enemy heroes star levels plus the 'round' number you were in divided by 10.' Always round up to the nearest whole number. Summoned units that remain on the board do no deal player damage and can be ignored when calculating damage. 

Hidden Mechanics

Splash and Cleave, Bounces etc.

  • Cleave (Battlefury) is pure damage and its damage is calculated before reductions.

  • Splash(Dragon Knight in Elder Form LVL 2+), Luna's Moon Glaives, and Medusa's Split shot all take each hit unit's armor into account separately.

  • Cleave and Splash deal increased damage if the original target was crit upon.

  • All Split Shot attacks can crit separately.

  • Luna's Moon Glaives does not work with any attack modifiers (like life-steal or Skull Basher's stun)

Targeting of Attacks

Melee units target units next to them in this order:

  1. Enemies in horizontal or vertical fields

  2. Enemies in diagonal fields

Ranged units first determine which range they will target, and then a random enemy in that exact range. The ranged targeting is determined in the following way:

  1. Sort the enemy heroes within attack range.

  2. Select the closest range A If there is another range that's available:

    1. 3/4 of the time, choose range A

    2. 1/4 of the time, remove A from the range you are considering and repeat

    3. If there are no other ranges: Choose A

Targeting of Spells

  • For all targeting, summoned units are ignored (except for Lone Druid's Spirit Bear and Arc Warden's duplicates).

  • The following spells have their target selected at random:

    • Doom's Doom

    • Disruptor's Static Storm

    • Enigma's Midnight Pulse

    • Kunkka's boat

    • Gyrocopter's Call Down

  • Pudge hooks an enemy that is the furthest amount of fields away from him.

    • If there are multiple enemies to choose from, the one that is physically the furthest away (the least amount of horizontals/verticals) from Pudge is chosen.

  • Sniper assassinates the enemy who's remaining HP is highest and below Assassinate's damage (magic resist is not accounted for).

Hidden Values

Items

  • Skull basher has a cooldown of 2.3s and deals 100 extra pure damage when it triggers.

  • Maelstrom has a cooldown of 0.2s.

  • The following items cannot be offered again once you've obtained them:

    • Embarrassment of Riches

    • Radiance

    • Smuggler

  • Eye of Skadi slows attack speed by 45 and movement speed by 35%. The slow duration is 5s for melee users and 2.5s for ranged users.

  • Shiva's Guard slows attack speed by 45 and movement speed by 50%.

  • Maelstrom, Unstable Reactor and Radiance deal magic damage.

Heroes

  • Batrider's Sticky Napalm also slows turn rates by 70% (regardless of stacks).

  • Batrider's Sticky Napalm has a max stack amount of [4/7/10] and a duration of 20s.

  • Clockwerk's Battery Assault goes off every 0.7s. It goes off [8/8/15] times total.

  • Dragon Knight's Elder Dragon Form's damage over time is magic damage.

  • Dragon Knight's Breath Fire has a range of 3.

  • Tusk's Walrus Punch deals [300/400/500]% damage.

  • Luna's Moon Glaives bounce 3/5/7 times. The bounces do not include the primary target.

  • Lone Druid's Spirit Bear has a 25% chance to stun for 3 seconds. This does not have a cooldown.

  • Axe's Berserker's Call has a duration of [2/3/4]s.

  • Shadow Fiend's Requiem of Souls' line count is [6/8/10].

  • Chaos Knight's Chaos Bolt deals [50/100/150] to [200/300/400] damage and stuns for 1 to [2/3/4]s.

  • Doom's Doom also disables passives and global item effects.

  • Viper's Viper Strike lasts for 5s. The given damage is the damage per second.

  • Abilities that summon units have different cast ranges:

    • Venomancer's and Arc Warden's have a cast range of 1 and will not trigger when there is no adjacent empty field.

    • Lone Druid's, Nature's Prophet's and Lycan's have a cast range of 2.

Common Misconceptions

General Mechanics

  • Any aura also applies to its source (like Assault Cuirass).

  • Summoned Units also have tags; these are the following:

    • Savage: Venomancer's wards, Lycan's wolves, Lone Druid's Spirit Bear

    • Druid: Nature's Prophet's Trees, Lone Druid's Spirit Bear

    • Primordial: Eidolon Spawns

Heroes

  • Arc Warden's duplicate is considered a summoned unit.

  • Beastmaster's Wild Axes also amplify his item damage (Radiance, Maelstrom, etc.).

  • Multiple instances of Drow Ranger's aura do not stack.

  • Medusa's Split Shot can apply Skull Basher, Maelstrom, Eye of Skadi, Blight Stone and Crits.

    • The former two cannot be applied multiple times though (due to their cooldown).

  • Medusa chooses her primary target like any other unit does, so her passive's effect can be reduced by positioning to abuse that.

  • Medusa's Split Shot can hit a maximum of [3/4/5] targets in total. The primary target does not take reduced damage. It will not target enemies outside of Medusa's attack range.

  • Multiple Batriders amplify each other's damage, though the damage of all of their Sticky Napalms is determined by which one applied the first stack to that unit. This not appearing to be the case is a visual bug.

    Lone Druid's Spirit Bear and Arc Warden's duplicates deal damage to other players, other summoned units don't.
  • Treant Protector's Leech Seed goes off 4 times in total (once immediately when he applies it and then every 1.5s).

  • Techies' bomb deals half damage to enemies that are not right next to it (unless Techies is LVL 3).

Items

  • Skull Basher does not have separate chances for ranged and melee units.

  • Blade Mail does not decrease damage taken in any way.

  • Kills caused by Blade Mail damage are attributed to its carrier.

  • Eye of Skadi's and Shiva's Guard's slow effects stack.

    • This results in a DPS decrease of 90%, as the target will only attack at 10% of their original attack speed.

  • Blood Bound and Demon bonus stack multiplicatively.

  • Force Staff always pushes a unit towards the edge that is furthest away from the carrier.

  • Force Staff results in at least 1s of disabling (the time the unit is in the push-back animation).

Synergies

  • Demon bonus' pure damage is calculated before damage reduction.

  • The Demon Hunter bonus pure damage and that of Demon work independently.

    • As a result, a Terror Blade can have up to +150% pure damage (with an allied Anti Mage and no other Demons).

  • Knight's damage reduction does not affect pure damage.

  • The Warlock synergy's bond will target whichever allied unit has the lowest health percentage-wise.

  • A unit hexed by the Shaman synergy has a fixed movement speed.

    • As a result, slow will not increase the duration of the disable.

  • The Shaman synergy can hex a specific unit only once per fight.

    • This restriction is per-source -> a Shaman can still hex a unit that was hexed by another.

  • Savage's bleed acts like 'pure damage' and bypasses armor calculations.

  • Elusive's evasion is bypassed when the attacker rolls a 'critical strike.'

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