Attack Speed Breakpoints: When AS Items Beat Damage

How Attack Speed Works in Dota 2

Every attack in Dota 2 is governed by a single formula. Understanding it is the foundation for every item decision you make on an auto-attack-focused hero.

The Formula

Attacks per second (APS) in Dota 2 is calculated as follows:

The attack interval — how long between swings — is simply the inverse: Attack interval = (100 x BAT) / (100 + IAS).

There are two key variables here. Your IAS is something you build toward with items and agility gain. Your BAT is fixed to the hero you pick — it does not change unless a specific ability or mechanic modifies it (which happens with a small number of heroes like Troll Warlord’s Fervor, or when you transform into a different form).

What IAS Counts Toward

IAS (Increased Attack Speed) is the sum of:

• Agility: Each agility point gives 1 IAS. This applies to all heroes, not just agility heroes — but agility heroes gain more agility as their primary attribute grows.
• Item bonuses: Items that grant attack speed contribute directly.
• Ability and buff bonuses: Active steroids, passives, and auras that grant attack speed.

Your base attack speed before any bonuses is 100 by default (which is why the formula uses 100 as the starting point in the numerator). That base 100 represents a neutral, unmodified attack rate scaled to BAT.

Attack Speed Cap

There is a hard upper limit of 700 on total attack speed (base 100 + up to 700 IAS, giving a maximum of 800 effective in the formula). In practice, the combined IAS from items, agility, and abilities will not exceed 700 for normal gameplay on most heroes, but high-agility carries with multiple AS steroids active can approach this ceiling in extended fights.

Notice how a hero with BAT 1.3 attacks 31% faster than a BAT 1.7 hero at the same IAS. That gap is present from level 1 and never closes without changing the item build composition.

Base Attack Time Explained

BAT is the single most important variable in any attack speed calculation. It is the denominator in the formula, which means a lower BAT produces more attacks at the same IAS. Many players treat all carries as equivalent when shopping for attack speed, but two heroes with identical IAS can have APS values that differ by 30% or more purely because of their BAT.

Why BAT Exists

Valve uses BAT as a design lever to control how much a hero’s damage output scales with attack speed. Heroes that are designed to deal most of their damage through physical auto-attacks (carries) tend to have moderate BAT values. Heroes that deal damage primarily through spells are often given high BAT values so that investing in attack speed items feels wasteful for them — the game is nudging you toward spell-amplification items instead.

Hero BAT Groups

The practical takeaway: when you are playing a BAT 1.7 carry like Luna or Drow, each additional point of IAS is worth more in actual APS gain than it would be on a BAT 1.3 hero like Terrorblade. This is why Terrorblade players often pivot toward damage items once they have a moderate AS foundation, while Luna players continue scaling attack speed deeper into the build.

The Breakpoint Crossover: When AS Beats Damage

The “breakpoint” question — does attack speed or damage give more DPS right now — is a marginal analysis problem. You have a fixed amount of gold and two item choices. Each choice multiplies your current DPS by a different factor. The better choice is the one with the larger multiplier.

The Marginal DPS Formula

DPS = average damage per hit x attacks per second.

When you add an attack speed item that gives +dIAS to your current IAS:

• New APS = (100 + IAS + dIAS) / (100 x BAT)
• APS multiplier = (100 + IAS + dIAS) / (100 + IAS)

When you add a damage item that gives +dDmg to your current damage:

• Damage multiplier = (Dmg + dDmg) / Dmg

Attack speed wins when: dIAS / (100 + IAS) > dDmg / Dmg

Rearranged: AS wins when dIAS x Dmg > dDmg x (100 + IAS)

What This Tells You in Practice

This creates a classic S-curve interaction: early in the game, your IAS is low and damage is low, so neither dominates strongly. As you buy your first major carry item, the question becomes whether your IAS or damage is the “lower” of the two multipliers — the lower one gives more return on the next purchase.

A Concrete Example

Suppose your carry has 200 total AS (100 + 100 IAS) and 120 average damage, with BAT 1.7.

• Current APS: 200 / 170 = 1.18 APS. Current DPS: 1.18 x 120 = 141.2.
• Option A: +25 IAS item. New APS = 225/170 = 1.32. DPS = 1.32 x 120 = 158.8. DPS gain: +17.6 (+12.4%).
• Option B: +25 damage item. New DPS = 1.18 x 145 = 171.1. DPS gain: +29.9 (+21.2%).

In this scenario, damage wins. Now advance the same hero to 250 IAS and 220 damage:

• Current APS: 350/170 = 2.06. Current DPS: 2.06 x 220 = 453.2.
• Option A: +25 IAS. New APS = 375/170 = 2.21. DPS = 2.21 x 220 = 486.2. Gain: +33.0 (+7.3%).
• Option B: +25 damage. New DPS = 2.06 x 245 = 504.7. Gain: +51.5 (+11.4%).

Damage still wins here. But now push IAS to 250 and damage to 350:

• Current APS: 350/170 = 2.06. Current DPS: 2.06 x 350 = 721.
• Option A: +25 IAS. New APS = 375/170 = 2.21. DPS = 2.21 x 350 = 773.5. Gain: +52.5 (+7.3%).
• Option B: +25 damage. New DPS = 2.06 x 375 = 772.5. Gain: +51.5 (+7.1%).

Near parity. The crossover has arrived. Push damage further — say to 450 with the same IAS:

• +25 IAS: gain = 0.147 x 450 = +66.2 (+7.3%).
• +25 damage: gain = 2.06 x 25 = +51.5 (+5.7%).

Attack speed has pulled ahead. This is the breakpoint: once your raw damage climbs high enough relative to your accumulated IAS, the next point of attack speed delivers more DPS per gold than the next point of damage.

BAT Groups: Practical Hero Tier Analysis

The crossover point shifts significantly based on your hero’s BAT. A lower BAT means you accumulate APS faster for the same IAS investment — which can push you into “diminishing AS returns” territory earlier in the build.

Low BAT Heroes (0.8 — 1.35): Terrorblade, Weaver

Terrorblade has one of the lowest BATs in the game at approximately 1.3. At his natural agility growth, he reaches comfortable APS totals even with minimal attack speed items. This is why most Terrorblade builds prioritize damage — Demon Marauder (the illusion mechanic) amplifies his raw damage across multiple units. Every point of base damage applies to illusions in specific ways, whereas attack speed on illusions is already higher than the main hero would have without items.

For these heroes, the crossover into “AS beats damage” often happens late — at 4+ items — and typically only makes sense if you are building proc items (like Maelstrom) that scale with attack count.

Standard BAT Heroes (1.7): Luna, Drow Ranger, Gyrocopter

These heroes represent the sweet spot for attack speed items. Their base APS is slow enough that each IAS point produces a larger percentage increase in attacks per second than it would on a lower-BAT hero. Luna, for example, also gains bonus damage on her Lucent Beams crits and her passive Eclipse — but her physical attack chain between spells is the primary source of sustained DPS, making IAS directly valuable.

On a BAT 1.7 hero, the crossover tends to occur around the 3-item mark when one of those items is a significant damage source. You typically want one early damage item (often a Desolator or Daedalus), then attack speed scaling, then alternate based on the crossover math above.

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Moderate BAT Heroes (1.45 — 1.55): Anti-Mage, Phantom Assassin

Anti-Mage benefits heavily from attack speed early because his Mana Break passive procs on each hit. The more he attacks, the more mana he burns per second and the more burst he applies. His BAT is ~1.45, meaning he accumulates APS slightly faster than standard carries. For Anti-Mage, attack speed is valuable not primarily for raw DPS but for proc frequency — this is a different kind of breakpoint analysis covered in the proc section below.

Phantom Assassin operates on a different mechanic: her Coup de Grace crit has a percentage chance per attack. Attack speed directly increases her crit frequency and therefore her effective DPS. Once she reaches high crit damage through Daedalus, adding attack speed becomes a clean multiplication of her burst output.

Key Attack Speed Items in 7.41

Items that provide meaningful attack speed in the current patch span multiple build archetypes. Here is an overview of the most relevant options:

Pure Attack Speed Items

• Yasha: Mid-tier IAS bonus plus move speed. Typically bought as a stepping stone to Sange and Yasha, Manta Style, or Skadi. Its cost efficiency makes it a frequent early-game swing item on agility carries.
• Butterfly: High attack speed combined with 30% evasion and significant agility. The evasion creates pseudo-survivability, making this a dual-purpose item. The attack speed contribution is substantial on BAT 1.7 heroes.
• Mjollnir: Very high attack speed plus Chain Lightning proc and Static Charge active. The attack speed is often the primary reason to buy it on fast-attacking carries because it supercharges the proc rate.

Mixed Damage and AS Items

• Sange and Yasha: Balanced split between attack speed, damage, and status resistance. Strong on melee carries who want a durable mid-game power spike.
• Eye of Skadi: Provides both attribute stats (agility = IAS, intelligence = damage for some heroes) and a powerful slow. The attack speed from agility alone is relevant, and the total package competes well against pure damage options late game.
• Mask of Madness: Cheap and extreme attack speed steroid in berserker mode, but comes with a lifesteal dependency and the armor debuff. Popular on heroes that can time the steroid window in fights. The IAS granted during active is very high, pushing many heroes past their normal breakpoints temporarily.

What These Items Have in Common

Every attack speed item in Dota 2 adds to your IAS total. The formula never changes — you are always asking “does dIAS / (100 + IAS) beat dDmg / Dmg at my current state?” The item labels change but the math does not.

When Damage Items Win

Attack speed items are not always the answer. There are clear scenarios where raw damage is the better investment:

Early Game (Under 3 Core Items)

Early in the game, your IAS and damage are both low. The returns from both are roughly comparable, but damage items tend to pull ahead because they also make your last-hits more reliable and your right-click harass in lane significantly more threatening. Attack speed without damage just means faster weak hits — opponents can still take them comfortably. A Desolator or Crystalys at this stage does more to establish dominance than equivalent gold in IAS.

Spell-Amp Carries (Storm Spirit, Leshrac, etc.)

If you deal more damage from abilities than from physical attacks, attack speed items are almost always wrong. Your DPS formula is dominated by the spell component, and attack speed does not scale spell damage. Only buy AS on these heroes if a specific proc mechanic or an in-kit mechanic (like Morphling’s attribute shift interaction) changes the calculation.

Burst-Window Heroes

Some heroes win fights in 2-3 seconds — Lina, Invoker, Slardar once BKB is on. For these heroes, the total damage in a short time window matters more than sustained DPS. Damage items frontload your burst. Attack speed items need more time to produce the same total damage. In fights that end before your 3rd or 4th attack lands, IAS is wasted.

Armor Reduction Context

When your team has heavy armor reduction (Desolator, Assault Cuirass, Medallion/Solar Crest on the target), your effective damage per hit rises sharply. This shifts the math in favor of attack speed because your increased hit damage makes each additional attack more valuable. Check the MMR boosting guide for build-order principles that account for team composition, not just individual hero math.

Proc and Orb Effects: How Attack Speed Changes Their Value

This is where attack speed analysis gets interesting for many mid-tier players. Proc-based damage items — Maelstrom, Eye of Skadi’s slow, Diffusal Blade mana burn, Desolator’s armor reduction — trigger on a per-attack basis. More attacks per second means more procs per second.

Proc DPS Formula

Total DPS with a proc item = (Dmg x APS) + (Proc_Dmg x APS x Proc_Chance)

Simplified: Total DPS = APS x (Dmg + Proc_Dmg x Proc_Chance)

Attack speed multiplies your entire DPS package when you have proc items — both the physical component and the proc component grow linearly with APS. This is why Maelstrom is so strong on specific carries: the bonus damage from Chain Lightning is essentially a free rider on every APS improvement you make.

Maelstrom and Mjollnir

Chain Lightning has a proc chance (approximately 25% per attack). Each time you attack, there is a 25% chance to fire a lightning bolt dealing a fixed amount of damage. The expected proc DPS = Proc_Dmg x 0.25 x APS. As APS increases, proc DPS grows at the same rate as physical DPS. This means Mjollnir (which also provides very high IAS) compounds the proc value with the attack speed bonus — a double benefit.

Heroes like Gyrocopter and Phantom Lancer who have multiple proc sources (rocket barrage, illusions) gain disproportionately from APS because every additional attack triggers multiple damage checks simultaneously.

Orb Effects and Attack Modifiers

Orb effects — abilities or items that modify each physical attack — scale directly with APS. Anti-Mage’s Mana Break, Jakiro’s Liquid Frost (not applicable to most carries, but illustrative), Eye of Skadi slow stacking: all of these apply once per attack. The more attacks per second, the faster these effects accumulate on targets.

On Anti-Mage specifically, higher attack speed means mana is burned faster per second, target heroes reach zero mana sooner, and Mana Void deals its damage more quickly when cast. The “breakpoint” for Anti-Mage buying attack speed is therefore lower than a pure damage analysis would suggest — the orb-effect value shifts the math earlier in his favor.

Practical Decision Guide: No Math Required Mid-Match

The theory is useful, but you cannot run the formula in a real game. Here is a simplified heuristic that approximates the math correctly in most situations:

The Two Questions Rule

1. Do I have a proc item (Maelstrom, Diffusal, Desolator, Manta illusions)? If yes, lean toward attack speed — every IAS point multiplies your entire damage package including proc value.
2. Is my raw damage significantly higher than my current APS suggests? High damage (300+) with low attack speed (under 250 IAS) is a strong signal that attack speed buys more DPS per gold than more damage. Conversely, very high APS with low damage means your fast hits are not hitting hard enough — buy damage.

Build Checkpoints by Stage

Hero-Specific Shortcuts

Rather than calculating per game, know your hero’s general tendency:

• Terrorblade: Buy damage. Manta and one moderate IAS item is usually enough AS for your build.
• Phantom Assassin: Buy Daedalus first. Once crit damage is huge, pivot to attack speed to increase crit frequency.
• Gyrocopter: Attack speed and Maelstrom are core synergy. Rocket proc + Chain Lightning proc compound per attack.
• Luna: Standard BAT 1.7 scaling. One damage item, then alternate AS items to scale efficiently.
• Drow Ranger: Her passive gives bonus agility (IAS) from distance. Attack speed items multiply this benefit.

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