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The Loop (Games)

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## Definition

When casting a spell that can resist, there is generally a probability of being not resisted. For elemental magic spells, this is the probability of landing a full damage spell. For most enfeebling spells, this is the probability of having a full duration spell (sleep, poison, burn, elegy). This probability (or rate) is called Magic hit rate.

## Predicting the magic hit rate

- Only 1 parameter governs the magic landing rate : the difference between the Magic Accuracy of the caster (MA) and the Magic Evasion evasion of the target(ME).
- Note that MA is affected by equipment, merits and the stat corresponding to current spell (INT for elemental magic for instance) and that ME is affected by elemental resistance that come from gear, spell (such as Barfire, Barpetrify)
- Keep in mind that all spells don't have the same magic accuracy, or equivalently, monsters/players have different magic evasions to different spells, even without using barspells. For instance, higher tiers of elemental magic resist less than lower tiers (this is unquantified).
- When MA and ME are known, the landing rate (p) is the following

MA range Magic hit rate % MA ≤ ME-90 p = 5 ME-90 ≤ MA ≤ ME p = 50-0.5*(ME-MA) ME ≤ MA ≤ ME+45 p = 50+(MA-ME) ME+45 ≤ MA p = 95

- 5% and 95% are the lower cap and upper cap of the magic hit rate.

- Confirmed. A RDM75 with merit can for instance nuke with stone I a Qiqirn Poulterer with maximum accuracy form gear/skill/INT to see the upper 95% cap. The same rdm can repeatedely cast Poison on a Soulflayer with no accuracy from gear/merit/INT and will see the lower 5% cap for full duration poison spells.
- Note that this does not mean that you have a minimum 5% chance to resist sleep or poison (for instance). It means that you have p=95% chance to land a full duration spell, p*(1-p)=4.75% chance to land a half duration spell, and "only" 0.25% chance to totally resist it.
- Note also that while full duration poison has 5% landing rate as lower cap, half duration poison will happen 4.75% of the time, and therefore ~1/10 of poison spell will land, regardless of your magic accuracy.

- Once p is determined, the partial resists for elemental magic nukes is calculated as follows:

no-resist rate 1/2 resist rate 1/4 resist rate 1/8 resist rate p % p*(1-p/100) % p*(1-p/100)^2 % 100*(1-p/100)^3 %

- For spells that only have 1 form of partial resist (such as sleep), the distribution is

no-resist rate 1/2 resist rate Full resist rate p % p*(1-p/100) % 100*(1-p/100)^2 %

- Complete tests and data for the total Magic Accuracy formula and Magic hit rate can be found here [Openoffice doc](http://rapidshare.com/files/320891736/magic_ac_bis_.ods.html) with the graphical summary here http://wiki.ffxiclopedia.org/wiki/File:Stone-QQP.jpg
- It is unknown if paralyze, bind or gravity can have a level of resistance different than a full resist, as the duration is a random number between 0 and 120 seconds. However, tests for silence on puddings show a 10% landing rate (bottom cap) which suggests that silence has one level of partial resist (probably half duration, which itself would be random).

- If a spell has 5% base landing rate (full duration), the probability for a half resist is 4.75%. For exemple the visual minimal landing rate for poison or sleep is 9.75%.
- Therefore, the landing rate of silence (and paralyze, bind, gravity most likely) is not directly attainable and one has to solve the equation p*(2-p)=x, where x is the visual landing rate, to find p.

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