Pseudo Random Distribution

From Liquipedia Dota 2 Wiki
As chance would have it.

Pseudo Random Distribution (shortened PRD) is a mechanic ported to Dota 2 which originated from the Warcraft 3 engine. Pseudo-random distributions are used to calculate chance based skills including critical strike, bash, and evasion abilities. In more common random distributions, every possible check has the same chance of activation regardless of any prior checks. In pseudo-random distribution streaks of activation or streaks of no activation are less likely, but the overall probability remains the same.


The PRD works by increasing the percentage chance for an activation by a certain amount every time it didnt activate until the chance for activation is over 100%. On the other side right after an activation the chance for another activation is significantly lower than the chance stated in the skill/item description. This means that skills such as critical strike will occur more consistently than they would in more common standard random distributions. Significantly streaks of "good luck" or "bad luck" are less likely to occur, making the game less luck dependent.

The base and incremental chances were precalculated and accessed from table because the calculations needed to produce those chances for each probability under PRD are taking up much more processor runtime than those for the same probability under standard random distribution. The values in Warcraft 3 were in 5% steps and, curiously, incorrect for chances of 15% and higher. These errors increase for each step and become noteworthy from 35% onward. It is assumed that these errors were ported over to Dota 2 for parity reasons.

The chance for an activation on first hit/check is also the amount by which the chance is incremented each time no activation occurs. The chance will not increase by an event in which an activation cannot occur. This makes abusing the PRD difficult, because, for example, hitting a building will not increase the chance of a critical strike, because you critical strike do not work against buildings in the first place.

In the following table, P(E) is the probability that the PRD is trying to mimic. Theoretical C is the value the PRD table should use to result in the correct probability. Actual C is the value used by the Warcraft 3 engine (and presumably Dota 2), resulting in a skewed probability. Max N is the number of attacks after which the chance for an activation(C*N) reaches 100%. P(A) is the actual probability of an activation occurring.

P(E) Theoretical C Actual C Theoretical Max N Actual Max N P(A)
5% 0.00380 0.00380 263 263 5.0%
10% 0.01475 0.01475 67 67 10.0%
15% 0.03222 0.03221 31 31 15.0%
20% 0.05570 0.05570 17 17 20.0%
25% 0.08474 0.08475 11 11 24.9%
30% 0.11895 0.11895 8 8 29.9%
35% 0.15798 0.14628 6 6 33.6%
40% 0.20155 0.18128 4 5 37.7%
45% 0.24931 0.21867 4 4 41.8%
50% 0.30210 0.25701 3 3 45.7%
55% 0.36040 0.29509 2 3 49.3%
60% 0.42265 0.33324 2 3 53.0%
65% 0.48113 0.38109 2 2 56.6%
70% 0.57143 0.42448 1 2 60.1%

The following graphics show how the distribution for a 15% chance differ between PRD and standard random distribution.

Chart 3.png

Chart 2.png

Abilities that use PRD[edit]

Hero Abilities
Hero Ability Chance
Axe Large.png Axe Axe counter helix.png Counter Helix Counter Helix Chance: 20%
Brewmaster Large.png Brewmaster Brewmaster drunken brawler.png Drunken Brawler Critical Strike Chance: 10% / 15% / 20% / 25%
Evasion Chance: 10% / 15% / 20% / 25%
Chaos Knight Large.png Chaos Knight Chaos knight chaos strike.png Chaos Strike Critical Strike Chance: 10%
Faceless Void Large.png Faceless Void Faceless void time lock.png Time Lock Bash Chance: 10% / 15% / 20% / 25%
Juggernaut Large.png Juggernaut Juggernaut blade dance.png Blade Dance Critical Strike Chance: 20% / 25% / 30% / 35%
Legion Commander Large.png Legion Commander Legion commander moment of courage.png Moment of Courage Moment of Courage Chance: 25%
Lycan Large.png Lycan Lycan shapeshift.png Shapeshift Critical Strike Chance: 40%
Outworld Devourer Large.png Outworld Devourer Outworld devourer essence aura.png Essence Aura Mana Restore Chance: 40%
Phantom Assassin Large.png Phantom Assassin Phantom assassin blur.png Blur Evasion Chance: 20% / 30% / 40% / 50%
Phantom assassin coup de grace.png Coup de Grace Critical Strike Chance: 15%
Phantom Lancer Large.png Phantom Lancer Phantom lancer juxtapose.png Juxtapose Hero Chance: 40% / 45% / 50%
Illusion Chance: 8%
Slardar Large.png Slardar Slardar bash of the deep.png Bash of the Deep Bash Chance: 10% / 15% / 20% / 25%
Sniper Large.png Sniper Sniper headshot.png Headshot Headshot Chance: 40%
Spirit Breaker Large.png Spirit Breaker Spirit breaker greater bash.png Greater Bash Bash Chance: 17%
Tiny Large.png Tiny Tiny craggy exterior.png Craggy Exterior Stun Chance: 25%
Troll Warlord Large.png Troll Warlord Troll warlord berserkers rage active.png Berserker's Rage Bash Chance: 10%
Wraith King Large.png Wraith King Wraith king mortal strike.png Mortal Strike Critical Strike Chance: 15%
Unit Abilities
Unit Ability Notes
Lycan Wolf Lycan summon wolves cripple.png Cripple Cripple Chance: 20%
Giant Wolf Giant wolf critical strike.png Critical Strike Critical Chance: 20%
Alpha Wolf Alpha wolf critical strike.png Critical Strike Critical Chance: 20%
Roshan Roshan bash.png Bash Bash Chance: 15%
Item Abilities
Item Ability Notes
Stout Shield.png Stout Shield Damage Block Damage Block Chance: 50%
Vanguard.png Vanguard Damage Block Damage Block Chance: 50%
Crimson Guard.png Crimson Guard Damage Block Damage Block Chance: 50%
Abyssal Blade.png Abyssal Blade Damage Block Damage Block Chance: 50%
Poor Mans Shield.png Poor Man's Shield Damage Block Creep Damage Block Chance: 50%
Monkey King Bar.png Monkey King Bar Mini-Bash Mini-Bash Chance: 35%
Crystalys.png Crystalys Critical Strike Critical Strike Chance: 20%
Daedalus.png Daedalus Critical Strike Critical Strike Chance: 30%
Skull Basher.png Skull Basher Bash Melee Hero Bash Chance: 25%
Ranged Hero Bash Chance: 10%
Abyssal Blade.png Abyssal Blade Bash Melee Hero Bash Chance: 25%
Ranged Hero Bash Chance: 10%
Maelstrom.png Maelstrom Chain Lightning Chain Lightning Chance: 25%
Mjollnir.png Mjollnir Static Charge Static Charge Lightning Chance: 20%
Chain Lightning Chain Lightning Chance: 25%
Sange.png Sange Lesser Maim Maim Chance: 24%
Heavens Halberd.png Heaven's Halberd Lesser Maim Maim Chance: 24%
Sange and Yasha.png Sange and Yasha Greater Maim Maim Chance: 30%
Talisman of Evasion.png Talisman of Evasion Evasion Evasion Chance: 20%
Heavens Halberd.png Heaven's Halberd Evasion Evasion Chance: 25%
Solar Crest.png Solar Crest Evasion Evasion Chance: 25%
Shine Evasion Chance: 25%
Butterfly.png Butterfly Evasion Evasion Chance: 35%

External Links[edit]