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The Calculation (Simplified)
- Note: This process is technically a slight simplification due to how FFXI stores numbers. Its fractions can come out a tiny bit lower than the numbers we'd see here. This way of doing it is accurate in most cases and easier to follow. For full details see The Calculation (Full).
Spell recast is calculated by taking a spell's Recast Time and multiplying it by three different terms in any order. The three terms are:
- 1 - (Equipment Haste + Magic Haste - Magic Slow) ÷ 100
- 1 - (Combined total Fast Cast ÷ 2, result rounded down) ÷ 100
- 1 - Job Abilities spell recast reduction ÷ 100
- Math reminder: division is done before subtraction.
The result after these three multiplications is then rounded down to the nearest whole number (AKA floored). In other words a result of 10.998 would be rounded down to 10.
Stun has a Recast Time of 45 seconds. A player with 25% Gear Haste, 30% Magic Haste, 55% Fast Cast and 10% JA recast reduction would progress through the equation as follows:
- 45 seconds * (1 - (25 Gear Haste + 30 Magic Haste - 0 Magic Slow) ÷ 100) * (1 - (55 Fast Cast ÷ 2, result rounded down) ÷ 100) * (1 - (10 Job Ability) ÷ 100)
- 45 * (1 - 55 ÷ 100) * (1 - 27 ÷ 100) * (1 - 10 ÷ 100)
- 45 * (1 - 0.55) * (1 - 0.27) * (1 - 0.1)
- 45 * 0.45 * 0.73 * 0.9 = 13.30425
After rounding down you are left with a 13 second recast time.
- Fast Cast has an effective cap of 80%, meaning that 40% reduction (or ×0.6) is the best that it can do for recast.
- Recast reduction caps at 80% of the original casting time.
The Calculation (Full)
The following four terms are multiplied to give the experienced recast:
- Initial Recast - 10 bit number, raging from .25 seconds to 256 seconds.
- This is listed on the page of most spells.
- Magical and Equipment forms of Haste and Magic Slow - two 8 bit numbers (0:255) that multiply Recast.
- Fast Cast - Stored as a whole number, potentially as low as 7 bits but likely 8.
- Job Abilities that specifically affect recast, like Composure, Hasso, and the Scholar abilities - It is unclear how they are stored, but they form unique terms that are just 1 if you don't have them up.
Equation 1: Post-Haste Recast = (Initial Recast: 10 bits)×(1 - (Haste÷255) + (Slow÷255))
In the first equation, Haste from gear and magic is factored in.
Equation 2: Post-FC Recast = (Post-Haste Recast)×(Shifted Fast Cast÷100)
Fast Cast is applied. Fast Cast undergoes some modification before being used. Mechanistically, the computer shifts Fast Cast right one bit and drops the remainder, which is the same as dividing by 2 and flooring in base 10. This number is then applied to the Post-Haste Recast.
Equation 3: Final Recast (10 bits) = (Post-FC Recast)×(Job Ability Modifier 1)×(Job Ability Modifier 2)×...
Finally, several generic and job ability specific terms are applied. This section is still heavily under development, as there are many different job abilities that affect recast.
Keep in mind that the final and starting recasts are made to be 10 bits (similar to Flooring). Though SquareEnix goes to great lengths to keep their variable sizes small, they seem to take no issue with floating point operations. And it seems that nothing about these questions are optimized for processing speed. Apart from that, this also means that the order of operations essentially cannot be determined and that the above "1->2->3" is arbitrary.
Known Job Ability Terms
- Samurai Job Ability Term
- Scholar Job Ability Term is a sum of:
- Red Mage Job Ability Term
- Composure (+25%)
These are all separate, and simply sum within the term.