Info
In general Randomness is rejected from competitive gaming since it can decide over loss and defeat without reflecting the actual skill level. Nonetheless there are a couple of random events within DotA 2, that keep the game less predictable and static. To limit the influence of huge streaks, pseudo-random distribution replaces the true random distribution where it made sense for the developers.
Definition
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
P(T) | P(A) | C | Max N | Most Probable N | Average N | SD | SDt |
---|---|---|---|---|---|---|---|
5% | 5.0% | 0.00380 | 264 | 16 | 20.00 | 10.30 | 19.53 |
10% | 10.0% | 0.01475 | 68 | 8 | 10.00 | 5.06 | 9.50 |
15% | 15.0% | 0.03221 | 32 | 6 | 6.67 | 3.31 | 6.16 |
20% | 20.0% | 0.05570 | 18 | 4 | 5.00 | 2.43 | 4.48 |
25% | 24.9% | 0.08475 | 12 | 3 | 4.02 | 1.90 | 3.49 |
30% | 29.9% | 0.11895 | 9 | 3 | 3.34 | 1.54 | 2.81 |
35% | 33.6% | 0.14628 | 7 | 3 | 2.98 | 1.35 | 2.43 |
40% | 37.7% | 0.18128 | 6 | 2 | 2.65 | 1.17 | 2.10 |
45% | 41.8% | 0.21867 | 5 | 2 | 2.39 | 1.03 | 1.83 |
50% | 45.7% | 0.25701 | 4 | 2 | 2.19 | 0.91 | 1.62 |
55% | 49.3% | 0.29509 | 4 | 2 | 2.03 | 0.83 | 1.45 |
60% | 53.0% | 0.33324 | 4 | 2 | 1.89 | 0.74 | 1.30 |
65% | 56.6% | 0.38109 | 3 | 2 | 1.77 | 0.69 | 1.17 |
70% | 60.1% | 0.42448 | 3 | 2 | 1.66 | 0.63 | 1.05 |
75% | 63.2% | 0.46134 | 3 | 2 | 1.58 | 0.57 | 0.96 |
80% | 66.7% | 0.50276 | 2 | 1 | 1.50 | 0.50 | 0.87 |
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).
- Min Damage: 75/100/125/150
Max Damage: 200/225/250/275
Min Stun Duration: 1/1/1/2
Max Stun Duration: 2/3/4/4
Damage and stun duration are correlated inversely. - Chen Hero Strategy Counters Equipment Gear Responses Sounds Lore Old Abilities Changelogs Chen 23 + 1.8 15 + 2.1 21 + 2.8 Level Base - Test of FaithMin Damage: 50/100/150/200
Max Damage: 100/200/300/400 - Min Damage per Slash: 200
Max Damage per Slash: 225 - Reappear Radius: 325
Random positions within the target area. Calculation might be in polar coordinates with 0-360₰ angle and 0-325 distance units as min/max gradients. - Crystal Maiden Hero Strategy Counters Equipment Gear Responses Sounds Lore Old Abilities Changelogs Crystal Maiden 16 + 2 16 + 1.6 16 + 2.9 Level - Freezing FieldMinimum Explosion Distance: 195
Maximum Explosion Distance: 785
Angle within the four 90₰ sectors (0₰–90₰, 90₰–180₰, 180₰–270₰, 270₰–360₰) may be random.
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.
- Clockwerk Hero Strategy Counters Equipment Gear Responses Sounds Lore Old Abilities Changelogs Clockwerk 26 + 3.2 13 + 2.3 17 + 1.3 Level Base - Battery AssaultNumber of Shrapnels: 16
Search Radius: 275
Interval: 0.7 sec - Ember Spirit Hero Strategy Counters Equipment Gear Responses Sounds Lore Old Abilities Changelogs Known Bugs Ember Spirit 19 + 2.1 22 + 1.8 20 - Searing ChainsMax Targets: 2
Search Radius: 400
Interval: 0 sec - Ember Spirit Hero Strategy Counters Equipment Gear Responses Sounds Lore Old Abilities Changelogs Known Bugs Ember Spirit 19 + 2.1 22 + 1.8 20 - Sleight of FistEffect Radius: 250/350/450/550
Attack Interval: 0.2 sec
Targets are determined upon cast. The order of attacks is random. Hidden units on their turn are skipped. - Enchantress Hero Strategy Counters Equipment Gear Responses Sounds Lore Old Abilities Changelogs Enchantress 16 + 1.3 19 + 1.8 21 + 3.1 Level Base - Nature`s AttendantsNumber of Wisps: 4/6/8/10
Search Radius: 275
Interval: 1.0 sec
Duration: 10 sec
Every second, each wisp chooses a random allied unit to heal. So it is possible to heal up to 4/6/8/10 allies at a time. - Number of Bounces: 4
Bounce Distance: 500
Interval: 0.25 sec - Multicast Amount: 1/2/3
Multicast Range: 1400
Interval: 0.4 sec - Multicast Amount: 1/2/3
Search Radius: 575
Interval: 0 sec - Witch Doctor Hero Strategy Counters Equipment Gear Responses Sounds Lore Old Abilities Changelogs Witch Doctor 16 + 2.1 13 + 1.4 24 + 2.9 Level - Paralyzing CaskNumber of Bounces: 2/4/6/8
Bounce Distance: 575
Interval: 0.3 sec
Other
- Extra Illusion Chance: 50%
- 2x Multicast Chance: 40%/50%/60%
3x Multicast Chance: 0%/20%/25%
4x Multicast Chance: 0%/0%/12.5%
Hero and unit abilities
- Critical Chance: 20%
- Axe Hero Strategy Counters Equipment Gear Responses Sounds Lore Old Abilities Changelogs Known Bugs Axe 25 + 2.8 20 + 2.2 18 + - Counter HelixHelix Chance: 20%
- Brewmaster Hero Strategy Counters Equipment Gear Responses Sounds Lore Old Abilities Changelogs Known Bugs Brewmaster 23 + 3.2 22 + 1.95 14 + - Drunken BrawlerCritical Chance: 10%/15%/20%/25%
Evasion: 10%/15%/20%/25% - Critical Chance: 10%
- Bash Chance: 10%/15%/20%/25%
- Critical Chance: 20%/25%/30%/35%
- Legion Commander Hero Strategy Counters Equipment Gear Responses Sounds Lore Old Abilities Changelogs Legion Commander 26 + 2.9 18 + 1.7 20 + 2.2 Level - Moment of CourageLifesteal Chance: 25%
- Lycan - ShapeshiftCritical Chance: 40%
- Lycan Wolf - CrippleCripple Chance: 20%
- Outworld Devourer - Essence AuraProc Chance: 40%
- Phantom Assassin - BlurEvasion: 20%/30%/40%/50%
- Phantom Assassin - Coup de GraceCritical Chance: 15%
- Proc Chance (Hero): 40%/45%/50%
Proc Chance (Illusion): 8% - Bash Chance: 15%
- Slardar Hero Strategy Counters Equipment Gear Responses Sounds Lore Old Abilities Changelogs Slardar 21 + 3.1 17 + 2.4 15 + 1.5 Level Base - Bash of the DeepBash Chance: 10%/15%/20%/25%
- Sniper - HeadshotSlow Chance: 40%
- Spirit Bear - Entangling ClawsProc Chance: 20%
- Spirit Breaker - Greater BashProc Chance: 17%
- Tiny - Craggy Exterior
- Troll Warlord - Berserker`s RageBash Chance: 10%
- Wraith King - Mortal StrikeCritical Chance: 15%
Item abilities
- Abyssal Blade - BashBash Chance (Melee/Ranged): 25%/10%
- Abyssal Blade - Damage Block
- Bloodthorn - Critical StrikeCritical Chance: 20%
- Evasion: 35%
- Crimson Guard - Damage Block
- Crystalys - Critical StrikeCritical Chance: 20%
- Daedalus - Critical StrikeCritical Chance: 30%
- Heaven`s Halberd - Lesser MaimMaim Chance: 35%
Evasion: 25% - Javelin - PiercePierce Chance: 25%
- Maelstrom - Chain LightningLightning Chance: 25%
- Mjollnir - Chain LightningLightning Chance: 25%
- Mjollnir - Static ChargeLightning Chance: 20%
- Monkey King Bar - Mini-BashMini-Bash Chance: 35%
- Poor Man`s Shield - Damage Block
- Sange - Lesser MaimMaim Chance: 30%
- Sange and Yasha - Greater MaimMaim Chance: 40%
- Skull Basher - BashBash Chance (Melee/Ranged): 25%/10%
- Evasion: 25%
- Solar Crest - ShineEvasion: 25%
- Stout Shield - Damage Block
- Evasion: 25%
- Vanguard - Damage Block
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.
- Miss Chance: 70%
- Broodmother - Incapacitating BiteMiss Chance: 30%/40%/50%/60%
- Keeper of the Light - Blinding LightMiss Chance: 80%
- Night Stalker - Crippling FearDay Miss Chance: 10%
Night Miss chance: 50% - Radiance - BurnMiss Chance: 17%
- Riki - Smoke ScreenMiss Chance: 40%/50%/60%/70%
- Solar Crest - ShineMiss Chance: 25%
- Troll Warlord - Whirling Axes (Melee)Miss Chance: 60%
Version history
- Juxtapose now uses pseudo-random distribution.
- Craggy Exterior now uses pseudo-random distribution.
- Alpha Wolf Alpha Wolf Jungle Creep Level 4 Health 600 Health regeneration 0.5 Mana regeneration 1 Armor 3 Magic resistance 0% Attack damage 30‒33 Acquisition range 500 Attack range 90 Base attack time 1.35 Attack animation 0.33+0.64 `s Critical Strike now uses pseudo-random distribution.
- Giant Wolf`s Critical Strike now uses pseudo-random distribution.
- Essence Aura now uses pseudo-random distribution.
- Evasion now uses pseudo-random distribution.
- Entangling Claws now uses pseudo-random distribution.
- Greater Bash now uses pseudo-random distribution.