# Pseudo Random Distribution

**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.

## Summary[edit]

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.

## Abilities that use PRD[edit]

Hero Abilities | ||
---|---|---|

Hero | Ability | Chance |

Axe | Counter Helix | Counter Helix Chance: 20% |

Brewmaster | Drunken Brawler | Critical Strike Chance: 10% / 15% / 20% / 25% Evasion Chance: 10% / 15% / 20% / 25% |

Chaos Knight | Chaos Strike | Critical Strike Chance: 10% |

Faceless Void | Time Lock | Bash Chance: 10% / 15% / 20% / 25% |

Juggernaut | Blade Dance | Critical Strike Chance: 20% / 25% / 30% / 35% |

Legion Commander | Moment of Courage | Moment of Courage Chance: 25% |

Lycan | Shapeshift | Critical Strike Chance: 40% |

Outworld Devourer | Essence Aura | Mana Restore Chance: 40% |

Phantom Assassin | Blur | Evasion Chance: 20% / 30% / 40% / 50% |

Coup de Grace | Critical Strike Chance: 15% | |

Phantom Lancer | Juxtapose | Hero Chance: 40% / 45% / 50% Illusion Chance: 8% |

Slardar | Bash of the Deep | Bash Chance: 10% / 15% / 20% / 25% |

Sniper | Headshot | Headshot Chance: 40% |

Spirit Breaker | Greater Bash | Bash Chance: 17% |

Tiny | Craggy Exterior | Stun Chance: 25% |

Troll Warlord | Berserker's Rage | Bash Chance: 10% |

Wraith King | Mortal Strike | Critical Strike Chance: 15% |

Unit Abilities | ||

Unit | Ability | Notes |

Lycan Wolf | Cripple | Cripple Chance: 20% |

Giant Wolf | Critical Strike | Critical Chance: 20% |

Alpha Wolf | Critical Strike | Critical Chance: 20% |

Roshan | Bash | Bash Chance: 15% |

Item Abilities | ||

Item | Ability | Notes |

Stout Shield | Damage Block | Damage Block Chance: 50% |

Vanguard | Damage Block | Damage Block Chance: 50% |

Crimson Guard | Damage Block | Damage Block Chance: 50% |

Abyssal Blade | Damage Block | Damage Block Chance: 50% |

Poor Man's Shield | Damage Block | Creep Damage Block Chance: 50% |

Monkey King Bar | Mini-Bash | Mini-Bash Chance: 35% |

Crystalys | Critical Strike | Critical Strike Chance: 20% |

Daedalus | Critical Strike | Critical Strike Chance: 30% |

Skull Basher | Bash | Melee Hero Bash Chance: 25% Ranged Hero Bash Chance: 10% |

Abyssal Blade | Bash | Melee Hero Bash Chance: 25% Ranged Hero Bash Chance: 10% |

Maelstrom | Chain Lightning | Chain Lightning Chance: 25% |

Mjollnir | Static Charge | Static Charge Lightning Chance: 20% |

Chain Lightning | Chain Lightning Chance: 25% | |

Sange | Lesser Maim | Maim Chance: 24% |

Heaven's Halberd | Lesser Maim | Maim Chance: 24% |

Sange and Yasha | Greater Maim | Maim Chance: 30% |

Talisman of Evasion | Evasion | Evasion Chance: 20% |

Heaven's Halberd | Evasion | Evasion Chance: 25% |

Solar Crest | Evasion | Evasion Chance: 25% |

Shine | Evasion Chance: 25% | |

Butterfly | Evasion | Evasion Chance: 35% |