Damage Taken

There are a variety of items and Job Abilities available that permit the reduction of Damage Taken. Sometimes these sources are specific for one type of damage, like Fan Dance or Darksteel Subligar, but occasionally they just reduce damage in general, like Defending Ring.

The three categories of damage that monsters can do to players. Gear with -% Damage Taken can be treated as a member of all categories when doing calculations with it (additive). It does not go past the -50% cap on the various types of damage taken.

• -X% Physical Damage Taken, -50% Cap, (8-bit number /256)*
• -X% Magical Damage Taken, -50% Cap, (8-bit number/256)**
• -X% Breath Damage Taken, -50% Cap, (8-bit number/256)
• There is an overall cap of -87.5% damage taken for players and pets, including sources that bypass the other caps.

There are some pieces of gear and Atma that increase Damage Taken, like the Onyx set and Atma of the Dark Blade. These are simply added instead of subtracted in the equations below.

Physical Damage Taken

Average Physical damage taken (PDT) is dependent upon Monster fSTR, Monster Average pDIF, Monster Base Damage, and the amount of -% Physical Damage Taken stat that the player is using. The calculations are basically analogous to Player -> Monster equations, but applied the other way around.

• Monster fSTR is proportional to (Monster STR - Player VIT). This is the most important way that VIT enters the damage calculations, though recently it was patched to affect Monster -> Player Critical Hit Damage. Generally this term is pretty insignificant, because it is hard to generate negative fSTRs.
• Monster Average pDIF is proportional to upon Monster Attack ÷ Player Defense, and Enemy Critical Hit Rate.

Formula 1: Uncorrected Damage = (Monster Base Damage + Monster fSTR)×(Monster Average pDIF)

Formula 2: Corrected Damage = Uncorrected Damage × (100% -% Physical Damage Taken -% Damage Taken)

The final () term in Formula 2 has a minimum of 50%*, after which adding -% Damage Taken and -% Physical Damage Taken does not affect anything.

Shield blocks offer additional damage reduction when they occur, which is proportional to the size of the shield and its defense.

Formula 3: Shield Blocked Damage = Corrected Damage × (Base + Defense/200)

Fan Dance functions as a further multiplier of "Corrected Damage," lowering it by 90%-20% depending on the current potency.

*Burtgang and Epeolatry are exceptions to this. The Formula for Corrected Damage with Burtgang and Epeolatry is:

Formula 4: Corrected Damage = Uncorrected Damage × (100% -% Physical Damage Taken -% Damage Taken -% Burtgang || Epeolatry)

This allows players with -50% Damage Taken and a Burtgang (Level 99) to take only 32% of the normal physical damage.

This allows players with -50% Damage Taken and a Epeolatry to take only 25% of the normal physical damage.

Magic Damage Taken

Average Magic damage (MDT) taken is generally dependent on "dStat," which is dINT for Black Magic and some TP moves and dMND for White Magic and other TP moves. In fact, as near as we can tell, Monster -> Player Magic Damage is calculated in the same way as Player -> Monster Magic Damage, but with the values from the opposite person.

Formula 5: Magic Damage You Take = Floor( (Magic Damage you would have Taken)×(100% -% Magic Damage Taken -% Damage Taken) )÷( 1 + MDB÷100 )

The damage reduction term, similar to physical damage taken, has a minimum of 50% but can be further reduced through Magic Defense Bonus, which is uncapped.**

**Aegis is an exception to this. The formula for Magic Damage Reduction with Aegis is:

Formula 6: Magic Damage You Take = Floor( (Magic Damage you would have Taken)×(100% (-% Magic Damage Taken -% Damage Taken) -% Aegis Magic Damage Taken )÷( 1 + MDB÷100 ) )

Though the (-% Magic Damage Taken -% Damage Taken) term is still capped at 50%, players can reach 87.5% Magic Damage reduction with Aegis (Level 90) or higher, which is very useful in some situations.

Breath Damage Taken

Breath Damage is somewhat special, and not much testing has been done on it. Unlike other formulas, that are based partially on player stats, Breath Damage is seems to be based only on Monster HP and -Breath Damage Taken gear that the player is wearing. Also, it is generally Conal damage that can be lessened by strafing and can be Resisted like normal magic spells; however, it is not reduced by normal "Magic Damage Taken" gear but is by most if not all augmented "Magic Damage Taken" pieces. Examples: Dark Rings, Skirmish Gear, Sinister Reign, Escha gear etc etc with their augments.

Formula 7:Corrected Damage = (Breath Base Damage)×(1 -% Breath Damage Taken -% Damage Taken -%Augmented Magic Damage Taken)

"Breath Base Damage" above is proportional to monster HP, but capped based (likely) on the level of the monster or the specific TP move. Similar to the other formulas, the final term caps at 50%.

Killer Effects and Circles

Recent testing indicates that Killer effects and circles can affect damage taken. These are applied in two separate steps after all other damage reductions. Unlike the other forms of damage reduction, this one is applied as an actual percentage instead of a fraction out of 256. It is similar to how Fast Cast is applied to Spell Recast.

Formula 8: Final Damage = Corrected Damage × (1 - Circle Bonus) × (1 - Intimidation Rate÷2)***

*** Only when using items comparable to Ferine Gausape +1/+2.

Circle effects from main jobs give -15% damage taken, or -5% when subbed. This includes Killer Instinct.

References

Killer/Circle Testing (Byrth, BG)

MDT Augments counting as BDT Testing (Martel, AH)