Difference between revisions of "Evasion"

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(Math: The Chance to Miss and the Change to Graze)
(Math: The Chance to Miss, the Chance to Graze, and How They Affect the Chance to Inflict Critical Damage)
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* Attacker's ability to [[Stun]] or [[Grapple]] Target is unaffected.
 
* Attacker's ability to [[Stun]] or [[Grapple]] Target is unaffected.
  
==Math: The Chance to Miss and the Change to Graze==
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==Math: The Chance to Miss, the Chance to Graze, and How They Affect the Chance to Inflict Critical Damage==
 
* In order to Miss, the Target's Roll #1 must be greater than or equal to Attacker's Roll #1.  * Any time the Attacker's Roll is greater than the Evasion Rating of the Target (In the example above, any time the Attacker rolls 41 or greater), the shot will not [[Miss]].
 
* In order to Miss, the Target's Roll #1 must be greater than or equal to Attacker's Roll #1.  * Any time the Attacker's Roll is greater than the Evasion Rating of the Target (In the example above, any time the Attacker rolls 41 or greater), the shot will not [[Miss]].
 
* For all other possibilities, in aggregate, there is approximately 50% chance of a [[Miss]].
 
* For all other possibilities, in aggregate, there is approximately 50% chance of a [[Miss]].
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Write this number down. (120)
 
Write this number down. (120)
 
Take the first number you wrote down (20).
 
Take the first number you wrote down (20).
Divide it by the second number you wrote down (20/120 = 0.16667).
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Divide it by the second number you wrote down (20/120 = 1/6 = 0.16667).
 
Multiply the result by 100% (0.16667 * 100% = 16.667)  
 
Multiply the result by 100% (0.16667 * 100% = 16.667)  
This is the chance to cause a complete [[Miss]]. 16.667%
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This is the chance to cause a complete [[Miss]]. 16.667%, or 1 in 6.
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 +
 
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* In order to [[Graze]], the first Roll cannot result in a [[Miss]]
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* The chance that the first roll does not result in a [[Miss]] will be represented as (1-M)
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* Given that the first result is not a [[Miss]], the chance to [[Graze]] is equal to M.
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Result:
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* G = The chance to [[Graze]]
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G = M * (1-M)
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In the above example, M = 1/6.
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G = 1/6 * (1 - 1/6)
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G = 1/6 * (5/6)
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G = 5/36 = 0.138889
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The chance that any shot will either [[Miss]] or [[Graze]] = M+G = 11/36
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The chance that any shot will Hit (and possible inflict [[Critical]] damage = 25/36 = 69.444%
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 +
How does this affect Critical Hits?  Well, as stated above, an Attacker cannot inflict [[Critical]] damage if he [[Misses]] or [[Grazes]].  So an Attacker's actual chance to inflict [[Critical]] damage is multiplied by the chance to register a Hit.  Let's say, in the above example, the Attacker's [[Critical]] chance was 30%. 
 +
 
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* X = Chance to inflict [[Critical]] Damage
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* C = Attacker's [[Critical]] Chance
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X = 0.30 * (1 - M+G)
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X = 0.30 * (1 - 11/36)
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X = 0.30 * (25/36)
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X = 0.30 * 0.69444
 +
X = 0.208333 = 20.8333%

Revision as of 13:58, 22 October 2013

Evasion

Evasion is a Ship's ability to cause its enemy's attack to either Miss or Graze. Evasion is expressed as a Rating.

A complete miss nullifies the attacker's chance to grapple the target, stun the target, or inflict critical damage. As a side effect, a miss may cause the attacker's weapon cooldown to be reduced. A graze reduces damage against the target by half, nullifies the attacker's ability to inflict critical damage, and does not cause the attacker's weapon cooldown to be reduced. It does not nullify the attacker's ability to stun or grapple the target.

Evasion Mechanic

When a weapon is fired at a target, both the attacker and the target roll the virtual dice. The range of the attacker's dice roll is 1 to (100 + the attacker's Hit Chance Rating). The range of the target's dice roll is 1 to his Evasion Rating. If the target's roll is equal to or greater than the attacker's roll, the shot will result in a Miss.

If the attacker's roll is greater than the target's roll, the dice will be rolled again to determine whether the shot will Graze or hit. Again, the target and the attacker will roll the dice as they did in the first roll. The range of the attacker's dice roll is 1 to (100 + the attacker's Hit Chance Rating). The range of the target's dice roll is 1 to his Evasion Rating. If the target's roll is equal to or greater than the attacker's roll, the shot will result in a Graze.

An Example of the Evasion Mechanic

  • Attacker has +20 Hit Chance
  • Target has +40 Evasion

Roll #1

  • Attacker Roll Range = {1 to 120}
  • Attacker Roll = 70
  • Target Roll Range = {1 to 40}
  • Target Roll = 25

Result: Shot does not Miss; continue to Roll #2

Roll #2

  • Attacker Roll Range = {1 to 120}
  • Attacker Roll = 17
  • Target Roll Range = {1 to 40}
  • Target Roll = 31

Result: Shot Grazes target.

  • Attacker's damage reduced by 50%
  • Attacker cannot cause Critical damage
  • Attacker's ability to Stun or Grapple Target is unaffected.

Math: The Chance to Miss, the Chance to Graze, and How They Affect the Chance to Inflict Critical Damage

  • In order to Miss, the Target's Roll #1 must be greater than or equal to Attacker's Roll #1. * Any time the Attacker's Roll is greater than the Evasion Rating of the Target (In the example above, any time the Attacker rolls 41 or greater), the shot will not Miss.
  • For all other possibilities, in aggregate, there is approximately 50% chance of a Miss.
    • If the Attacker's Roll is close to the Target's Evasion Rating (in the example above, say: 39), then the likelihood of a Miss is very low. If the Attacker's Roll is close to 1, then the chance of a Miss is very high.

The result:

  • H = Attacker's Hit Chance
  • E = Target's Evasion Rating
  • M = Chance to Miss

M = (E/2) / (H+100) * 100%

So, using the above example, take the Target's Evasion Rating (40). Divide by 2 (40/2 = 20). Write the number down. (20) Take the Attacker's Hit Chance (20). Add 100 (20+100 = 120). Write this number down. (120) Take the first number you wrote down (20). Divide it by the second number you wrote down (20/120 = 1/6 = 0.16667). Multiply the result by 100% (0.16667 * 100% = 16.667) This is the chance to cause a complete Miss. 16.667%, or 1 in 6.


  • In order to Graze, the first Roll cannot result in a Miss
  • The chance that the first roll does not result in a Miss will be represented as (1-M)
  • Given that the first result is not a Miss, the chance to Graze is equal to M.

Result:

  • G = The chance to Graze

G = M * (1-M)

In the above example, M = 1/6. G = 1/6 * (1 - 1/6) G = 1/6 * (5/6) G = 5/36 = 0.138889

The chance that any shot will either Miss or Graze = M+G = 11/36 The chance that any shot will Hit (and possible inflict Critical damage = 25/36 = 69.444%

How does this affect Critical Hits? Well, as stated above, an Attacker cannot inflict Critical damage if he Misses or Grazes. So an Attacker's actual chance to inflict Critical damage is multiplied by the chance to register a Hit. Let's say, in the above example, the Attacker's Critical chance was 30%.

X = 0.30 * (1 - M+G) X = 0.30 * (1 - 11/36) X = 0.30 * (25/36) X = 0.30 * 0.69444 X = 0.208333 = 20.8333%