Random distribution

Info

Definition

The effects of PRD on the number of attacks until the next proc.

The uniform or true random distribution describes the probability of random event that underlies no manipulation of the chance depending on earlier outcomes. This means that every "roll" operates independently.

The pseudo-random distribution (often shortened to PRD) in DotA refers to a statistical mechanic of how certain probability-based items and abilities work. In this implementation the event`s chance increases every time it does not occur, but is lower in the first place as compensation. This results in the effects occurring more consistently.

The probability of an effect to occur (or proc) on the Nth test since the last successful proc is given by P(N) = C ℂₗ N. For each instance which could trigger the effect but does not, the PRD augments the probability of the effect happening for the next instance by a constant C. This constant, which is also the initial probability, is lower than the listed probability of the effect it is shadowing. Once the effect occurs, the counter is reset.

Videos

Example

Slardar   Hero   Strategy   Counters   Equipment   Gear   Responses   Sounds   Lore   Old Abilities   Changelogs     Slardar 21 + 3.1 17 + 2.4 15 + 1.5 Level Base `s Bash of the Deep has a 25% chance to stun Stun is a status effect that prevents active actions like moving, turning, using spells or items, but does not prevent passive abilities, such as evasion and Damage Block. Stuns also interrupt spell casts, channeling spells the target. On the first attack, be that as it may, it only has an ~8.5% probability to bash. Each subsequent attack without a bash increases the probability by ~8.5%. So on the second attack, the chance is ~17%, on the third it is ~25.5%, etc. After a bash occurs, the probability resets to ~8.5% for the next attack. These probabilities average out so that, over a moderate period of time, Bash of the Deep procs nearly 25% of the time.

Effects based on PRD rarely proc many times in a row, or go a long time without happening. This makes the game less luck based and adds a great deal of consistency to many probability-based abilities in Dota 2. Gameplay wise, PRD is difficult to exploit. It is theoretically possible to increase your chance to bash or critical strike on the next attack by attacking creeps several times without the effect happening, but in practice this is nearly impossible to do. Note that for instances that would not trigger the effect, the probability counter does not increase. So a hero with critical strike Critical strike is a passive ability that gives a chance to deal bonus damage on a successful attack. Contents 1 Mechanics 2 Stacking 3 Interaction with other passive abilities 4 Sources of chance-based critical strike attacking buildings Buildings are special units that are immune to most spells, use structure armor, and are immobile. Destroying a building rewards you with a bounty, similar to most creeps or heroes. Destroying towers rewards the entire does not increase its chance to critical strike on its next attack, since critical strike does not work against buildings. The chance is not reset/increased as long as the ability is on cooldown as well (e.g. Bash).

The probabilities listed in the game are theoretical percentages, which are slightly higher than the actual probabilities. In the following table, P(T) is the theoretical probability while P(A) is the actual average. C is the PRD constant. Max N is the minimum number of attacks that would result in C ℂₗ N becoming greater than 1 (i.e. guaranteed proc). Average N is the expected value of N: the sum of the products of N and probabilities. SDSD cards use flash memory to provide nonvolatile storage is the standard deviation of N, a measure of how spread the data is, using the population formula. The lower the deviation, the more consistent the procs are. For comparison, SDt is the standard deviation of N in true random distribution, using the sample formula from N = 1 to N = 264. These are higher than those of PRD, hence not as consistent.

Percentages

Flat distribution

Some mechanics roll a random value between 0 and 1 and scale it along the minimum / maximum gradient. This includes

• Physical right click damage
  • Including heroes   Main   Mechanics   Attributes Table   Release Dates   Grid Layout     Heroes are the essential element of Dota 2, as the course of the match is dependent on their intervention. During , summons This page is about in-game units. For cosmetic pets, see Summoned Unit. Summons are a type of units that are created with spells. Players do not encounter them, unless they play as, with or against , creep Creeps are basic units in Dota 2. Every unit which is not a hero, building, ward or courier is considered a creep. Creeps can belong to either faction, be neutral, or be player-controlled units. Unlike and tower Buildings are special units that are immune to most spells, use structure armor, and are immobile. Destroying a building rewards you with a bounty, similar to most creeps or heroes. Destroying towers rewards the entire damage.
  • Excluding some wards This page is about in-game units. For cosmetic pets, see Summoned Unit. Summons are a type of units that are created with spells. Players do not encounter them, unless they play as, with or against .
• Last hit gold “ Play Now that s how you make gold. Click to listen— Alchemist ” Gold is the currency used to buy items or instantly revive your hero. Gold can be earned from killing heroes, creeps, or buildings. Contents bounty.
  • Including enemy and neutral creeps Creeps are basic units in Dota 2. Every unit which is not a hero, building, ward or courier is considered a creep. Creeps can belong to either faction, be neutral, or be player-controlled units. Unlike , most summons This page is about in-game units. For cosmetic pets, see Summoned Unit. Summons are a type of units that are created with spells. Players do not encounter them, unless they play as, with or against , towers, barracks Buildings are special units that are immune to most spells, use structure armor, and are immobile. Destroying a building rewards you with a bounty, similar to most creeps or heroes. Destroying towers rewards the entire and filler buildings Buildings are special units that are immune to most spells, use structure armor, and are immobile. Destroying a building rewards you with a bounty, similar to most creeps or heroes. Destroying towers rewards the entire .
  • Excluding heroes   Main   Mechanics   Attributes Table   Release Dates   Grid Layout     Heroes are the essential element of Dota 2, as the course of the match is dependent on their intervention. During , creep-heroes and denies “ Play Denied! Click to listen— Juggernaut ” Denying is the act of preventing enemy heroes from getting the last hit on a friendly unit by last hitting the unit oneself. Enemies earn reduced experience if the .
• Roshan For Roshan as he appears in holiday events, see Roshan (Diretide 2012) and Roshan (Diretide 2013) Roshan Ancient Jungle Creep Level 30 Health 5500 Health regeneration 20 Armor 15 Magic resistance 55% Attack damage 65 respawn timer (8 to 11 minutes).

Discrete distribution

A couple of random events have discrete states that have similar probability.

• Powerup Runes For the runes that come with cosmetic items, see Inscribed Gem.   Main   Changelogs     Runes are special boosters that spawn on the game map. They come in two categories. Bounty Runes can with a discrete clamping over the 6 types and 2 locations.
• Neutral camps Neutral creeps are a type of creep not controlled by any player. They are aligned to neither of the teams, and offer an alternative source of gold and experience. Neutral creeps appear in small camps can spawn different creeps for each of the small, medium, hard and ancient camps.

Other

Hero and unit abilities

Item abilities

Blind

Since 6.87, Evasion uses pseudo random distribution. It was not mentioned whether Blind and the 25% uphill miss chance are affected by this change. So far no testing has been done.

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