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Evasion
Evasion is a rating that measures a character's ability to avoid being struck by enemy attacks. Evasion is opposed by the attacker's Accuracy.
All classes start with 53 base evasion rating and gain 3 additional evasion per level. The first level is included in this, so a level 1 character will have 56 base evasion. This gives a base of 353 evasion at level 100.
Dexterity also grants bonuses to evasion. Every 5 points of dexterity provides 1% increased evasion rating. Nonmultiples of 5 will be rounded up to the nearest multiple of 5. (142 dexterity will be rounded to 145)
Movement speed is beneficial for characters that employ evasion as the primary form of damage reduction, since it requires a play style where physically avoiding enemy spells and attacks is often necessary.
Contents 
Mechanics
Evading an attack prevents all damage and other harmful effects including status ailments and stun. Only melee and ranged attacks can be evaded; spells will automatically hit. The chance to evade an attack is based on the defenders evasion rating verses the attacker's accuracy.
Chance to Evade = 1  Attacker's Accuracy / ( Attacker's Accuracy + (Defender's Evasion / 4) ^ 0.8 ) ^{[1]}
Chance to evade can never be lower than 5%, nor higher than 95%. The exception to this is when Cannot Evade enemy Attacks applies from the Unwavering Stance keystone or Ezomyte PeakEzomyte Peak
Iron HatArmour: (23 to 33)
20% increased Physical Damage
+(15 to 25) to Armour
+(25 to 50) to maximum Life
Cannot Evade enemy AttacksCenturies of servitude, a day
of glory, an eternity of death.; this completely removes the character's chance to evade.
Evasion also gives an implicit chance to avoid taking critical strikes from attacks.^{[2]} Critical strikes from spells can't be evaded. If an incoming critical strike succeeds its hit roll, a second independent hit roll is performed to determine if the critical is evaded or not. If this roll succeeds, a critical strike is scored. If it fails, the attack still hits, but only for regular damage.
Evasion is not purely based on chance in the sense that each hit is independent. Instead, it uses a system of "entropy" to ensure that enemies won't get long strings of hits or misses by chance.^{[2]} To summarize, these are the calculation steps in each attack:
 If it is first time an entity is attacked or if the time between the last attack and this one is larger than 6 seconds, randomise the entropy from 099.
 Calculate chance to hit of the attacker using the above formula, and add this integer to the entropy counter.
 If this is 100 or greater, the check counts as a hit. Subtract 100 from the entropy counter. Otherwise it is a miss and the entropy counter doesn't change.
 A critical hit is evaded on a separate random roll and will not affect this entropy value.
This system is designed to evenly spread out hits and misses such that players always evade an average number of times according to their ‘chance’ to evade. It is still based on chance because of the entropy counter's randomization in the first step. Note that if multiple mobs are attacking one character, all of the mobs' attacks share the same entropy counter.^{[3]} Also note that the chance to evade calculation on the character page is based on the average accuracy of a monster at the player's level.
Example
A player is fighting three monsters, one(A) with a 70% chance to hit and two(B,C) with a 45% chance to hit.
 A attacks. The player's entropy is a random number between 099, in this case 37.
 A adds 70 to the counter, raising it to 100 or greater, and hits. 100 is subtracted and the counter is now 7.
 B attacks, adding 45. 52
 C attacks, adding 45. 97
 A attacks, adding 70. This hits and the counter becomes 67. It happens to be a critical strike, which means it has a 70% chance to do bonus damage. This roll is independent and doesn't affect entropy.
 The player runs away for >6 seconds, so a new entropy value will be rolled on the next attack.
Interaction with Dodge
Chance to Dodge bonuses granted by sources like Acrobatics function similar to evasion, but are rolled separately and are pseudorandom rather than entropybased. Phase Acrobatics grants a chance to dodge spells.
Assuming a character has a 40% chance to evade and a 20% chance to dodge, a character has a 52% chance to avoid taking damage.
Chance to Avoid Attack = 1  ( (1  Chance to Evade) * (1  Chance to Dodge) )
Passives
There are passive skill nodes that grant additional evasion or a combination of bonuses including evasion.
Evasion
These passives increase evasion rating by a percentage.
In the case of Ondar's Guile, the chance to evade projectile attacks is doubled.
Name  Bonuses 

Evasion 

Armour and Evasion 

Cloth and Chain 

Evasion and Energy Shield 

Evasion Per Frenzy Charge 

Evasion and Life 

Leather and Steel 

Nullification 

Ondar's Guile 

Reflexes 

Revenge of the Hunted 

Void Barrier 

Miscellany
These passives are related to evasion, but don't fit into any other category.
Name  Bonuses 

Iron Reflexes 

Unwavering Stance 

References
 ↑ Malice (November 14, 2011). "Mechanics thread". Path of Exile Forum. Retrieved October 20, 2013.
 ↑ ^{2.0} ^{2.1} Mark_GGG (December 10, 2012). "Mechanics thread". Path of Exile Forum. Retrieved February 7, 2013.
 ↑ Mark_GGG (September 14, 2012). "Mechanics thread". Path of Exile Forum. Retrieved October 20, 2013.