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P = 1 - (1 - E) * (1 - M) * (1 - T1) * (1 - T2)
Where P is your Probability to Dodge damage, E is your chance for Evasion, M is your opponent's chance to Miss, T1 is your opponent's chance to "miss" due to Terrain disadvantage, and T2 is your chance to avoid damage due to Triggered Evasion. Each of the four factors (Evasion, Miss, Terrain, and Triggered) work independently of each other. As such, a source of Evasion will always stack diminishingly with a source of Miss or Triggered.
To give precise definitions, "Dodge" refers to your total ability to avoid taking damage. "Evasion" refers to skills or items which gives a percent chance for Evasion. "Miss" refers to skills which cause an opponent to Miss on a certain percentage of attacks. "Terrain Advantage" refers to a ranged attacker being below the attacked unit. "Triggered" refers to a JASS triggered ability to avoid damage. "Normal attack" refers to a hero's attack command, i.e. pressing A and then clicking on a unit, auto-acquiring a target, or manually casting an Orb effect (which is technically considered a spell).
The first type of chance to Dodge is Evasion. Evasion comes from items like The Butterfly and Radiance, and skills like Jinada (Bounty Hunter), Drunken Brawler (Panda), Blur (Phantom Assassin), and Phantom Edge (Phantom Lancer). Evasion does not stack with other sources of Evasion. The highest source of Evasion overrides all other sources of Evasion. So if Phantom Assassin with 4 levels of Blur (28% Evasion) obtains a Radiance (8% Evasion), she will have 28% chance for Evasion. If she obtains a Radiance (8% Evasion) and The Butterfly (30% Evasion), she will have 30% chance for Evasion. Evasion only works against normal attacks.
The second type of Dodge is Miss. Miss is typically a debuff on the opponent which causes them to miss. This comes from spells like Smoke Screen (Stealth Assassin), Laser (Tinker), Blind (Troll), Drunken Haze (Panda), Incapacitating Bite (Spider), and Crippling Fear (Night Stalker). Laser, Drunken Haze, Incapacitating Bite, and Crippling Fear do not stack with each other, but they will stack with Smoke Screen and Blind. To calculate a total chance to Miss, use the same 1 - (1 - A)*(1 - B)*(1 - C) formula. Miss only works against normal attacks.
The 3rd type Dodge chance to miss is Terrain Advantage. Terrain Advantage occurs when a ranged attacker attacks uphill. Currently, this is a 25% chance to miss. Terrain Advantage only works for normal, ranged attacks.
The 4th and final chance to miss is Triggered, a.k.a. Pseudo-Evasion, a.k.a. Heal. Triggered evasion works different depending on the skill. Currently there are 6 skills on 5 heroes that have a triggered chance to miss damage.
Craggy Exterior on Tiny, the Stone Giant--Tiny has a skill known as Craggy Exterior, which gives a 6%/12%/16%/24% chance to stun a melee attacker when attacked. In the case of Craggy Exterior and another Dodge proccing on the same attack, Craggy Exterior will take precedence. Craggy Exterior only works against normal, melee attacks.
Backtrack on Darkterror, the Faceless Void--Darkterror has a skill known as Backtrack, which gives him a 10%/15%/20%/25% chance to heal him for the amount of damage that he would normally take. In the case of another non-Triggered source of Dodge proccing on the same attack, Backtrack will lose precedence. Backtrack works against all sources of damage, including spells and triggered damage.
Dispersion on Mercurial, the Spectre--Mercurial has a skill known as Dispersion, which has a 4%/8%/12%/16% chance to heal Mercurial for the amount of damage taken and also deal this damage back in a 400 AoE around her, as well as give a small stun. In the case of Dispersion and another non-Triggered source of Dodge occurring on the same attack, Dispersion loses precedence. Dispersion works against all sources of damage, including spells and triggered damage.
Aphotic Shield on Abbadon, Lord of Avernus--Aphotic Shield gives a 100% chance to heal over damage dealt to a unit. In the case of Borrowed Time and another non-Triggered source of Dodge occurring on the same attack, Aphotic Shield will lose precedence. Aphotic Shield works for all sources of damage, including spells and triggered damage.
Borrowed Time on Abbadon, Lord of Avernus-- Borrowed Time gives a 100% chance to heal over damage dealt to a Abaddon. In the case of Borrowed Time and another non-Triggered source of Dodge occurring on the same attack, Borrowed Time will lose precedence. Borrowed Time works for all sources of damage, including spells and triggered damage.
Refraction on Lanaya, the Templar Assassin--Refraction gives a 100% chance to heal over damage dealt to Lanaya for 3/4/5/6 sources of damage. In the case of Refraction and another non-Triggered source of Dodge occurring on the same attack, Refraction will lose precedence. Refraction works for all sources of damage, including spells and triggered damage.
- Attacks which break wind walk (including from Lothar's Edge) can never Miss or be Evaded. They can still be affected by Triggered chances to Dodge, or by actively dodging the projectile (if applicable) with a Blink. The only exception to this rule is Meld. Attacks that break Meld can sometimes Miss/be Evaded.
- There is a "range buffer" on all attacks and spells. Your target must be within your range (plus footstep? I'm not sure). By the attack point, your target must be within your range plus attack buffer. I believe all heroes in DotA have an attack buffer of 250. I'll verify this later. If you dodge an attack with this method, then it will be the equivalent of a Miss.
- A hexed unit has 0% Evasion (but all other Misses/Triggered/etc. remain).
- It is possible to actively use Blink to Dodge projectile spells. This only works for "true Blinks:" Anti-mage and Akasha's Blinks, as well as Furion's Teleport and Kelen's Dagger of Escape. Spells such as Blink Strike or Nether Strike are pseudo-blinks and are incapable of dodging projectiles. If you blink while a projectile is en route to its target (you), it will miss.
- The 4 heal type Triggered Evasions will only heal over the damage dealt in that attack. If the attack were say, a bash, or had a slow orb on it, they would still be bashed or slowed respectively. This is not the case with Craggy Exterior, as no attack actually lands on the hero.
- Craggy Exterior deals a stun (or has a chance to, rather) at the beginning of the attack animation. Other sources of Dodge are calculated at the attack point, which occurs after the start of the attack animation. This effectively means that Craggy Exterior takes precedence over all other sources of Dodge.
- For Dispersion, Aphotic Shield, Borrowed Time, and Refraction, a rather lengthy series of triggers determines the correct amount to heal. This is not the case with Backtrack, where the heal is simply dealt before the damage is taken.
- For any of the Heal type Triggered Dodges, if an incoming attack deals more damage than the receiving hero's maximum HP, the hero will die.
- If two Heal type Triggers proc on the same attack (i.e. Abbadon has Borrowed Time and Aphotic Shield on, or if Mercurial Disperses while having an Aphotic Shield on), the hero's HP will rise (assuming the heals are enough, which they always will be as the game is currently coded). What happens is that the hero is healed twice for only one damage.
- In the case of Mercurial obtaining The Butterfly, Dispersion loses precedence to Evasion. What this means is that she has a 30% chance to Evade and an 11.2% chance to Disperse. This means that if her HP is 1000, and a series of 10-dmg attacks are dealt to her, without The Butterfly it would require approximately on average 119.05 attacks to kill her, and that 19.05 would be Dispersed. With The Butterfly, it would require 170.07 attacks to kill her, with 51.02 being Evaded and 19.05 being Dispersed. Note that she will disperse the same amount of attacks regardless of if she has The Butterfly or not. The loss of dps from Dispersion is perfectly balanced with her added survivability from The Butterfly.
- Triggered skills which deal damage "when attacked" (such as Axe's Counter-Helix or Centaur's Return) will still trigger on attacks which are evaded. To be more specific, the check for these spells is triggered when the attack begins (just like Craggy Exterior, which is triggered the same way).
List of triggered "on damage taken" heals
This is a list of a class of spells which are very closely related. All of these spells have an X% chance to heal over Y% of the damage taken on an incoming attack. "Tightly coded" refers to how the spell is coded. For some spells, the heal is simply dealt before the damage is taken. This causes issues if your hero's HP is near its maximum. If a spell is "tightly coded," then an extensive series of triggers will make sure that the hero is healed for the correct amount, regardless of how much HP he currently has. Note that even if a spell is "tightly coded," the hero will still die if the incoming damage is greater than his maximum HP. The incoming damage must be greater than (i.e. not equal to) the "Minimum damage."
Skill name - Hero name, hero title - Percent chance to proc - Percent of incoming damage to heal - Minimum damage - Tightly coded? (Y/N) - Alias
Aphotic Shield - Abaddon, the Lord of Avernus - 100% - 100% - 0 - Y - A0MF
Actively cast. Lasts for 20 seconds or until 125/175/225/275 damage is taken. If the shield is removed due to receiving damage, then that much damage will be reflected back into a 600 AoE as Attack Type Spells, Damage Type Magic. On the attack which "breaks" the shield, only a portion of the incoming damage will be healed over (enough so that the total amount of healing for that shield is equal to 125/175/225/275 HP.)
Backtrack - Dark Terror, the Faceless Void - 10%/15%/20%/25% - 100% - 0 - N - A0CZ
Borrowed Time - Abaddon, the Lord of Avernus - 100% - 100% - 1 - Y - A0NS
Actively cast. Lasts for 3/4/5 seconds. Is automatically cast if Abaddon takes damage and his HP is below 400 after the damage.
Bristleback (damage taken from behind)- Rigwarl, the Bristleback - 100% - 10%/20%/30%/40% from the back, 5%/10%/15%/20% from the sides - 10 - N - A0M3
"Back" is defined as 110 to 180 degrees away from the direction Rigwarl is facing. "Side" is defined as 60 to 110 degrees. Once 200 damage is taken, a quill spray is released. Does not work against towers or other structures.
Dispersion - Mercurial, the Spectre - 4%/8%/12%/16% - 100% - 5 - Y - A0NA
If Dispersion procs, then the amount of the heal is dealt back as damage (capped at current HP) into a 400 AoE as Attack Type Hero, Damage Type Magic, and also a mini-stun is applied. The fountain's attack cannot be Dispersed.
Gravekeeper's Cloak - Visage, the Necro'lic - 100% - 5%/10%/15%/20% - n/a - N - A0MD
The amount of the heal is dealt back into a 600 AoE as Attack Type Hero, Damage Type Magic. Only works if the incoming damage is less than 1400 (should only be possible from Mana Void, Maledict, Reaper's Scythe, and Culling Blade). Damage will only be reflected back if the incoming damage is greater than 10.
Refraction - Lanaya, the Templar Assassin - 100% - 100% - 5 - Y - A0RE
Actively cast. Lasts for 2/3/4/5 sources of incoming damage. Also gives her +20/+40/+60/+80 damage, which works independently of the heal.
Special thanks to TrabajarTrabajar for his in depth explanation of triggered heal spells.
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