Понимание скорости атаки и дпс

Stand and deliver.

A standard attack (also commonly known as an auto attack or a right click) is any unit’s default attack. It is performed by right clicking the target, or attack command & left clicking the target.

An example showing base damage on the left and bonus damage on the right.

47 base damage + 18 bonus damage is shown above

On the HUD, a unit’s base damage value is shown as a white number on the left. Base damage is a unit’s default damage value. For heroes it is their given damage value plus their total primary attribute. Percentage-based attack damage bonuses only affect base damage.

On the HUD, a unit’s bonus damage value is shown as a green number on the right. It is damage given by sources other than the hero, such as damage items. It is not affected by Percentage-based attack damage bonuses.

There are currently 3 different classes of attack damage types (also known as ‘Attack Classes) that manipulate the damage value of a unit’s attack against certain other unit types. Each attack classes deal either reduced, increased, or unchanged damage against heroes, creeps (i.e. non-hero units), and buildings, before all armor reduction values.

The attack classes are represented by 3 abilities visible in the unit’s HUD. If a unit does not have any of these 3 abilities, their attacks deal 100% damage and are only altered by the target’s armor and other damage manipulators.

Units of this attack classification deal reduced attack damage to heroes.

: 0.75

Units of this attack classification deal reduced attack damage to Reinforced units.

: 0.7

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• Specifically affects the total attack damage value.
  • All reduction values are converted to multipliers for wiki calculation convenience.

• Runty units considers as heroes, as creeps.

Units of this attack classification deal reduced attack damage to heroes.

: 0.5

Units of this attack classification deal increased attack damage to creeps.

: 1.5

Units of this attack classification deal reduced attack damage to Reinforced units.

: 0.35

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• Specifically affects the total attack damage value.
  • All reduction values are converted to multipliers for wiki calculation convenience.

• Piercing units considers as heroes, as creeps.

Units of this attack classification take reduced attack damage from heroes and player-controlled units. However, it deals an increased attack damage to its own classification kind.

: 0.5

: 0.9

: 2.5

Units of this attack classification take reduced attack damage from creeps.

: 0.7

Units of this attack classification take reduced attack damage from Piercing units.

: 0.35

Units of this attack classification take reduced attack damage specifically from illusions.

: 0.6

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Attack Class Definition

Attack damage dealt against unit-types can be defined as

Attack Damage Dealt = Total Attack Damage × Attack Class × Damage Manipulation

This table shows how much damage each attack class deals against each defense class, and which units use which attack class:

Each unit in the game has damage spread on their standard attacks. This damage spread is a random variance between a minimum and a maximum value. For example, if your hero is stated to deal 100 damage, but has a damage spread of 10, your hero can deal 105 on the highest roll, and 95 on the lowest roll. The total shown next to the sword icon is the average between the minimum and maximum values. The smaller a hero’s damage spread, the more consistent their damage is.

Hero Damage Spreads

Heroes	Damage Spread
	30
	22
	18
	16
	15
	14
	12
	11
	10
	9
	8
	7
	6
	5
	4
	2

Percentage-based Attack Damage Bonus

These buffs only increase base damage, not bonus damage.

Evasion is mechanic that allows the unit to evade an incoming attack.

All Evasion effects trigger upon landing an attack. This is upon projectile impact and upon attack point for ranged and melee units respectively. Any attack or ability effects that relies on attacks to hit their targets do not trigger, including most attack modifiers and on-hit effects unless explicitly specified.

True Strike and Accuracy are mechanics that nullifies Evasion.

All evasion, blind, and accuracy sources are determined by pseudo-random distribution.

Accuracy and Blind sources do not directly increase the attacked unit’s evasion value, instead, they increase the effective evasion rate of the attacked unit for blind and lower it for accuracy. For effective evasion rate calculation purposes, multiple sources of evasion and accuracy stack diminishingly with each other respectively, while blind sources stack additively with each other and multiplicatively with evasion.

The total evasion displayed on the HUD is defined as: Total Evasion = 1 —
(1 — Evasion _i )

The total blind is defined as: Total Blind =
Blind _i

The total accuracy is defined as: Total Accuracy = 1 —
(1 — Accuracy _i )

• Incoming Attacks
  • Accuracy Sources or True Strike Sources proc
  • Melee Buffer Range check
  • Attack Hits

Effective Evade Chance = (1 — (1 — Total Evasion) × (1 — Total Blind)) × (1 — Melee Buffer Range Miss)

Final Hit Chance = 1 — Effective Evade Chance × (1 — )

The formula written above is color-coded in sections, where indicates the chance that accuracy does not proc, indicates the total blind multiplier, and for the evasion multiplier.

Upon missing an attack on an enemy, a red floating text appears, reading MISS, visible to the attacking player only. The enemy, who was just missed by an attack, also sees a floating text, but in white and reading EVADE instead. Furthermore, a missed attack does not play any of the attack impact sounds.

Attack Range Type

For melee units, if the target is farther than 350 range more than the melee unit’s attack range, the attack 100% misses, True Strike does not guarantee hits on units outside of the buffer range.

For most melee heroes, the attack buffer range is defined as:
Total Melee Buffer Range = Unit Total Attack Range + Attacker Bound Radius + Target Bound Radius + 350

Uphill Miss Chance

For ranged units without Flying Movement, the uphill miss chance is conditionally applied upon a ranged attack projectile impact and not on the unit’s attack point — it causes 25% of the ranged attacks to miss if the attacking unit is at a lower terrain level as the target, regardless of the terrain level difference. A unit is considered to be on higher elevated terrain when it is no longer visible to the player due to the terrain. When an enemy stands on a relatively higher ramp, uphill miss chance applies whether if the attacked unit is within vision or not.

This means moving up onto an elevated area after an attack projectile has been launched may cause the projectile to miss on impact to uphill miss chance, even when both units were on the same ground level as the projectile was launched.

Uphill miss chance is considered an evasion source, it does not apply to units and units with flying movement.

Cleave & Splash

Cleave causes the unit’s attack to deal damage in a trapezoid in front of the attacking unit. The damage is based on the unit’s total attack damage values. Cleave can only be used by melee units, ranged units cannot cleave by default.

Cleave does not affect the primary target, and it cannot miss when hitting secondary targets. However, a missed attack does not cleave.
Splash is in some ways the ranged version of cleave. It works similarly as cleave, with the main difference being the damage is typically dealt in a circle around the attacked unit, instead of a trapezoid in front of the attacking unit.

Splash does not affect the primary target, and it cannot miss when hitting secondary targets. However, if an attack misses, no splash damage is applied within the radius. Splash damage works with attack modifiers the same way as cleave does.

Blind is a debuff that makes a unit miss upon attacking other units and sources of blind effects stack additively with each other, rendering an affected unit unable to land any attack. Although a combination of different blind sources can exceed 100%, for effective evasion rate calculation convenience, they can stack up to a maximum value of 100%.

Total Blind is defined as:

Total Blind =
Blind _i

¹ Requires talent.

^2a Requires .

^2b Requires .

The total evasion displayed on the HUD is defined as:

Total Evasion = 1 —
(1 — Evasion _i )

¹ Requires talent.

^2a Requires .

^2b Requires .

¹ Requires talent.

^2a Requires .

^2b Requires .

There is no description for this ability.

• Grants the hero evasion.

• Stacks multiplicatively with other evasion sources.

• Has the following evasion values:
  • 8%/10%/12%/15%/16%/20%/25%/30%/40%/50%/75%

Accuracy is applied as a debuff on the affected target. It does not directly increase the attacked unit’s evasion value. For calculation purposes, the accuracy multiplier can be considered as an evasion source as well.

Total Accuracy = 1 —
(1 — Accuracy _i )

True Strike sources can also be considered as outgoing accuracy.

True Strike prevents the unit’s attacks from missing, negating both evasion and blind sources against any other units, including ward-type units and ally units, except attacks against buildings. However, it does not apply an Accuracy debuff on the attacked unit.

For ranged units, although True Strike prevents the unit’s attack from missing, attack projectiles of ranged units with True Strike can still be disjointed. For melee units, it also prevents the attacking unit’s attack from missing when the attacked target moves more than 350 range away upon its attack point.

All attacks against Runes and against destroyable items have True Strike.

¹ Requires talent.

^2a Requires .

^2b Requires .

Instant Attacks with True Strike

¹ Requires talent.

^2a Requires .

^2b Requires .

True Strike Talents

There is no description for this ability.

• Grants the hero’s attack True Strike, so they cannot miss.

No hero has this talent.

Proc Chance-based Outgoing Accuracy

• Proc Chance: 20%/30%/40% ( 32%/42%/52%)
  Attacks proccing Marksmanship cannot miss.

• Proc Chance: 25%
  Attacks proccing Pierce cannot miss.

• Proc Chance: 25%
  Attacks proccing Chain Lightning cannot miss.

• Proc Chance: 25%
  Attacks proccing Chain Lightning cannot miss.

• Proc Chance: 80%
  Attacks proccing Pierce cannot miss.

Percentage-based outgoing accuracy sources grant attacks a chance to not miss on the target.

Percentage-based Outgoing Accuracy

• Accuracy: 25%
  Attacks have a chance to not miss.

• Neutral Radius: 800
  Player Controlled Radius: 1200
  Accuracy: 40%/43%/46%/51%
  The effects are provided by an aura, which grants allies a chance to not miss on attacks.

• Accuracy: 50%
  Attacks have a chance to not miss.

• Same values and notes from applies.

¹ Requires talent.

^2a Requires .

^2b Requires .

Multiple sources of evasion stack diminishingly with each other, while sources of blind effects stack additively with each other and multiplicatively with evasion.

All evasion and accuracy sources are determined by pseudo-random distribution.

Example 1

Interactions between incoming attacks and Evasion.

Incoming attacks to hit ‘s wielder is 65%, because the item grants 35% evasion.

within the radius has 100% evasion. Without any other evasion negating sources, all incoming attacks to hit are missed if the Self is within the radius.

Example 2a

Evasion sources stacks diminishingly.

An enemy is attacking who has a and . What are the chances of incoming attacks hitting ?

Evasion sources:

: 0.5

: 0.35

Effective Evade Chance

= 1 — (1 — Total Evasion) × (1 — Total Blind)

= 1 — × (1 — 0)

= 0.675

Final Hit Chance

= 1 — Effective Evade Chance

= 1 — 0.675

= 0.325

Alternatively, Blur and Butterfly have the corresponding 0.5 and 0.65 chance to hit. Then the combined chance to hit is their product, showing a multiplicative stacking:

Final Hit Chance

= 0.5 × 0.65

= 0.325

in this example has 32.5% chance of getting hit by incoming attacks, because she has 67.5% evasion.

Example 2b

Blind sources stack additively of itself, then stacks diminishingly with evasion sources.

An enemy attacking from the previous example is now affected by and . What are the chances of incoming attacks hitting ?

‘s Total Evasion: 0.675

Blind sources:

: 0.15

: 0.75

Effective Evade Chance

= [1 — (1 — Total Evasion) × (1 — Total Blind)]

= [1 — (1 — 0.675) × (1 — (0.15 + 0.75))]

= [1 — × ]

= 0.9675

Final Hit Chance

= 1 — Effective Evade Chance

= 1 — 0.9675

= 0.0325

Although ‘s total evasion did not change, the blind applied to the enemy increases ‘s effective evade chance to 96.75%. Therefore, has 3.25% chance of getting hit by incoming attacks.

Final Hit Chance

Stacking Evasion, Blind and Accuracy

Given a unit with an Effective Evade Chance and subjected to Total Accuracy as defined in the above sections, the final chance to hit in the previous example can be derived to be:

Final Hit Chance = + (1 — ) × (1 — Effective Evade Chance)

An intuitive way to view this calculation — The attacking unit’s attacks have a guaranteed chance to trigger True Strike based on the value, whereas (1 - ) of the attacks that do not trigger True Strike will be subjected to the Effective Evade Chance.

Or alternatively, it can be simplified as:

Final Hit Chance = 1 — Effective Evade Chance × (1 — )

This can also be interpreted as — Normally, Effective Evade Chance of the attacks will miss. But due to accuracy, only (1 - ) of these would-be-missed attacks actually miss since attacks based on the value will hit the target due to True Strike.

Example 3

The same enemy from the previous example is still affected by and .

The enemy’s just delivered Monkey King Bar and continues to attack . What are the chances of incoming attacks hitting ?

‘s Total Evasion: 0.675

Total Blind applied on the enemy: 0.9

Accuracy sources:

: 0.8

Effective Evade Chance

= [1 — (1 — Total Evasion) × (1 — Total Blind)]

= [1 — (1 — 0.675) × (1 — (0.15 + 0.75))]

= [1 — × ]

= 0.9675

Final Hit Chance

= + (1 — ) × (1 — Effective Evade Chance)

= + (1 — ) × [1 — (1 — 0.675) × (1 — (0.15 + 0.75))]

= + × 0.0325

= 0.8065

The enemy’s attacks have 80.65% chance to hit .

In this example with Monkey King Bar equipped, 80% of those attacks is guaranteed to hit due to True Strike. The remaining 20% of the attacks that do not have True Strike, have a 3.25% chance to hit Phantom Assassin.

Or alternatively,

Final Hit Chance

= 1 — Effective Evade Chance × (1 — )

= 1 — 0.9675 × (1 — )

= 1 — 0.9675 ×

= 1 — 0.1935

= 0.8065

The enemy’s attacks against normally have 96.75% chance to miss.

However, 80% of those 96.75% attacks is guaranteed to hit due to True Strike. Therefore, only 19.35% of the attacks will miss, resulting in a 80.65% chance for attacks to hit Phantom Assassin.

• The following sources now grant attacks True Strike upon proc:
• Increased outgoing accuracy from 35% to 40%.

There are a lot of misconceptions when it comes to Attack Speed and DPS. For some reason most players heavily lean towards larger damage numbers when it comes to DPS optimisation and while there are reasons for it, it is not always optimal. Today we would like to spend some time diving into Dota 2 AS and DPS mechanics and clear some misunderstandings related to them.

Attack Speed (AS) = Attack Damage (AD)

A single point of AS is equal to a single point of Damage. Kind of, as it all depends on relative amounts of AS and Damage. To maximise DPS, a hero should have equal AS and Damage, so when a hero is lacking Damage, buying damage is preferable and vice versa.

Most heroes start the game with 100+ AS and ~55 Damage, hence why early on we see a high return on damage item purchases. As the game progresses, however, many right-clicking cores start scaling damage at a faster pace, compared to their AS scaling.

It could be a result of them having damage-increasing abilities, or it could be a result of itemisation, but we quite frequently see heavily skewed Damage and AS numbers even in higher level pubs.

This is a test we did to check our point. A level 30 Alchemist with Reaver and Blades of Attack has an exactly equal amount of AS and Damage. One of them was later given a Divine Rapier, while the other was given three Moon Shards, one consumed, as well as Blade of Alacrity.

Essentially, starting from equal AS and Damage, one was given +350 Attack Damage and the other was given +350 Attack Speed. As can be seen from the screenshot, after some time, their DPS values on their respective dummy targets were nearly identical, with minimal discrepancy due to Attack Damage having some variance.

This is why we claim that every point of AS = every point of AD when it comes to DPS. But what are the practical applications of it?

Useful adaptations

The idea for this type of post started from a trend from several years ago, where most professional players playing core Tiny would rush a Moon Shard as their first item. Intuitively it felt like it didn’t make sense, but it was, indeed, the most efficient way to spend gold on a farming hero that has a very strong damage steroid, but has an AS malus built-in.

Right-clicking Tiny is well and truly a thing of the past, but the realisation stayed and in many cases it can now be applied to other heroes as well. For example, Sniper currently has a guaranteed +110 (or +140 with level 10 talent) AD boost from Headshot when using Take Aim. With the latter effect activated, his DPS becomes skewed towards AD, so it’s only natural that he starts needing extra AS to maximise efficiency.

The idea is similar to many heroes with built-in critical hits or proc effects. It is worth noting, though, that while long-term efficiency is great for farming, the burst DPS for the first several seconds of the fight favours AD over AS:

But what about BAT?

More knowledgeable readers are probably aware of BAT (Base Attack Time) that is the basis of most Attacks/Second calculations in Dota. Most heroes have 1.7 BAT, meaning that with 100 AS they will attack once every 1.7 seconds, but there are exceptions to the rule, like Juggernaut, Anti-Mage and about ~20 other heroes.

Alchemist has a decreased BAT when using Chemical Rage and when using the same two Alchemists from the previous test we get:

Once again, a roughly identical DPS, with either +350 AD or +350 AS. So BAT doesn’t really have an impact on this discussion, with a small caveat of a very weird interface design decision made by Valve. For some reason when calculating AS on a non-1.7 BAT hero Dota adjusts AS values in the interface. Get a Gloves of Haste on Juggernaut? Your AS will rise by ~24 rather than 20, because of this interfacing decision. The effect is the same, it is just expressing the 1.4 BAT hero attack speed as if they were on a 1.7 hero, and as such the values can even rise higher than 700.

Efficiency isn’t everything

Finally, there is a third Alchemist:

He got +175 AD (Blue Rapier + Nullifier) and +175 AS ( Moon Shard + Blitz Knuckles). It is clear how much higher his DPS is, compared to his unbalanced brothers and it is why we feel understanding this rather trivial concept is important.

That said, efficiency isn’t everything in Dota. In fact, most of the time efficiency isn’t even a priority, since the enemy is posing particular threats and the hero needs to respond with particular tools to deal with them. It might be very efficient to buy a Moon Shard on Sniper, but most of the time you will need a Hurricane Pike to stay safe. Or a Black King Bar.

There are times where the problem to solve is the lack of DPS and this information might come in very handy in such scenarios. It can also be relevant when the patch is finally released, as there could be new items or reworked heroes, who will need their builds reevaluated.

Thank you for reading and let us know whether you found this blog post useful in the comment section below! Your feedback will allow me to make better content plans in the future.