Past while I've been trying to finish up our model of haste. The following is what I found. At the bottom I'll post some of the experimenting and methods I used to obtain these values and findings.
To start, here are the values of Fast Cast as they affect recast timers. (I make zero inferences as to how it affects casting speed.)
Fast Cast I: 50/1024 or 51/1024
Fast Cast II: 72/1024
Fast Cast III: 102/1024
RDM AF1 Hat: 51/1024
RDM AF1+1 Hat: 51/1024
RDM AF2 Body: 51/1024
Loq Earring: 10/1024
Homam Pants: 20/1024
R. Pumps: 9/1024
Marduk Body: 20/1024
When trying to determine the recast when combining fast cast and haste, it's important to know the order in which they are applied. Haste is applied first, and then truncated to the 10ths place. Fast Cast is then applied to the truncated number. The number is then floored(decimal truncated) for the final recast value. The equation would look something like this:
New Recast = floor( [1-Fast Cast] * ( [1-Haste] * Recast ) )
(Round to the 10ths place after each step.)
There are two caps to be aware of when determining a recast. The lower cap is 50% of the original Recast. The upper cap is 255 seconds.
I also tested Hasso/Seigan as they have a dominant effect on recast values. Hasso/Seigan add a 50% multiplier to the original Recast, and is applied before Haste or Fast Cast. With Hasso/Seigan active, the equation would look something like this:
New Recast = floor( [1-Fast Cast] * ( [1-Haste] * ( 1.5 * Recast ) ) )
(Round to the 10ths place after each step.)
The last piece of information I was interested in obtaining was where Slow occurs in the equation. The easiest way to test was by using Slow +% equipment. Unfortunately the math didn't pan out, and I was quick to realize that Slow Equipment appears to work differently than a Slow Effect from Magic/Ability. (Not 100% confirmed). Slow from equipment is subtracted from your total Haste value. It acts as a negative value of Haste. I was also suprised to learn that the values of of Hecatomb were slightly higher than one would assume. I tested three pieces:
Hecatomb Cap: 93/1024
Hecatomb Mittens: 52/1024
Hecatomb Leggings: 41/1024
When I originalli conducted haste testing, I found that you could predict recasts /w slow values from hecatomb by considering them negative haste values. Later when trying to determine the Slow from Demons in Dynamis-Xarc, I found that Haste and Demon Slow appeared to be seperate terms, and concluded a fault in my original tests. I now believe that Magic/Ability slow is a seperate term than slow from equipment. To test this, I ran out to Boyahda tree and started to kraken spiders in order to get slowed. Unfortunately the Spider Slow wasn't lasting long, and the slow inflicted varied. First Slow was between 330/1024-335/1024, and the second Slow was 183/1024-187/1024. If I'm able to find a way to get myself slowed by a consistant source, I'll try to finish the work I started. Otherwise I will wait til I find the time to ballista, and do my testing in one of those reserved pvp things. (Why do they require ballista points to reserve :/)
~~My methods and experiments~~
Honestly, I have about 8 notebook pages worth of stuffs, I'm gonna try to post just the important material, so that others interested in the testing can try this themselves, or continue the testing. I apologize in advance that some of this is hard to read or doesn't make sense. For example, I sometimes refer to 113/1024 and 911/1024 as the same value of haste. (This is because 113/1024 is how we read it, but 1-(113/1024) = 911/1024 and is how I use it when calculating.)
Majorty of the testing was done by using a BRD and varying the amount of the singing skill to raise the haste value in 1/1024 increments. Then casting Reraise or Dread Spikes and recording the recast values.
75 DRK/37 RDM: (Dread Spikes) (Fast Cast II)
/w no haste eq - 2:47 [This puts the value at 69-73/1024]
113/1024 Haste - 2:28
118/1024 Haste - 2:28
119/1024 Haste - 2:27
75 RDM/37 WHM: (Reraise) (Fast Cast III)
/w no haste eq - 54 seconds [86-102/1024]
75 RDM/37 NIN: Utsu: Ni (Fast Cast III)
/w no haste eq- 40 seconds [This narrows the range to 92->102/1024]
75 RDM/37 WHM: (Reraise) (Fast Cast III)
119/1024 Haste - 47 seconds
114/1024 Haste - 47 seconds
113/1024 Haste - 48 seconds
Using the above, the only way the math all works out is by having Haste applied first and rounding the 10ths place. I wish I had a better way to explain it. I proceeded to check and make sure this was correct by determining points at where the recast would change and verifying it. An example of such experiment:
75DRK/37RDM
Speed Belt + Victory March(535 Skill)
61/1024 + 118/1024 + 72/1024(FCII) = 1:18
Speed Belt + Victory March(542 Skill)
61/1024 + 119/1024 + 72/1024(FCII) = 1:17
Having 100% success after performing plenty of these experiments, I went to determine the fast cast on Hat/Body. The following can be used:
75RDM/WHM using Reraise
/w Fastcast Piece - 51 seconds [871-887]
113/1024 Haste - 45 seconds [Narrows Range down to 871-865]
119/1024 Haste - 45 seconds [Narrows Range down to 871-870]
240/1024 Haste* - 39 seconds [Narrows down to 871]
1024-871 = 153/1024 total fast cast... 102 from FC III means 51/1024 from Fastcast Piece.
(*240/1024 Haste = 119/1024 Victory March + 61/1024 Speed Belt + Dusk Feet+1 + Dusk Hands.)
I apologize all of this is messy =x. That experiment works for AF1+1 Head/AF1 Head, and AF2 Body.
Homam Legs can be deduced by the follow. (I had to assume 30/1024 on the haste portion.)
75DRK/--- (Dread Spikes)
/w just pants - :51 [Range of 21-16/1024]
113/1024 - :31 [Narrows to 19-21]
118/1024 - :30 [Narrows to 20-21]
117/1024 - :31 [Narrows to 20/1024]
Most of these are expected values. I don't think it's anything new. I think the last important piece to post is proof that Hasso/Seigan is applied before Haste. I had to find values of haste which would cause a difference if one was applied first as opposed to the other way around. Here are two cases:
@880/1024 Haste
1024-880 = 144/1024 - 114 March + 30/1024(3% Eq Piece)
880/1024 * 180 = 154.6 * 1.5 = 231 seconds
1.5 * 180 = 270 * 880/1024 = 232 seconds
The result came out to be 232 seconds, implying Hasso/Seigan was applied first.
@861/1024 Haste
1024-861 = 163/1024 - 113 March + 30/1024(3% Eq) + 20/1024(2% Eq)
861/1024 * 180 = 151.3 * 1.5 = 226 seconds
1.5 * 180 = 270 * 861/1024 = 227 seconds
The result came out to be 227, giving further proof that Hasso/Seigan was applied first.
To put all of this work together, I mixed and matched equipment and attempted to predict the exact recast value.
113 Victory March + Advancing March + Ace's Helm + Homam Legs + Heca Hands + Heca Feet + Hasso + Loq Earring.
Hasso = Yes~ 1.5
Haste = (113/1024 + 96/1024 + 40/1024 + 30/1024 - 52/1024 - 41/1024) = 186/1024
Fast Cast = (20/1024 + 10/1024) = 30/1024
Recast = floor( 1 - [30/1024] * ( 1-[186/1024] * (1.5 * 180) ) )
(Rounding to the 10ths after each step)
Recast = 3:34
The recast does indeed turn out to be 3:34.
EDIT: Added Fast Cast for R. Pumps and Marduk Body~