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Thread: Cast and Recast     submit to reddit submit to twitter

  1. #101
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    99 RDM + Composure + Deodorize => 8s recast

  2. #102
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    That's what I expected after Hasso > Haste. Thanks Yugl :)

    So Composure > Fast Cast... that looks pretty definite.

    I'm predicting all the *1.5, *1.25, *1.2 etc. for Hasso/Seigan, Composure, Arts/Strategem are calculated before Haste.

    It will be a little more tricky testing Composure > Haste, as it's hard to remove Fast Cast from RDM50+

    You can get +12% recast from lv90 magian staves, but at lv87+ you have -15% recast on RDM.
    You can also get +14% from lv99 magian staves.
    I think you'd need to get a COR in your party to purposely bust their Fast Cast roll to give +5% recast.

    So -15% (RDM90) + 12% (magian 90) + 5% (COR FC roll) = +2%, then just find -2% FC recast from gear...

    I guess you can still test Composure > Haste > Fast Cast, but I'd rather stick with 2 terms only, even if it does seems pretty certain recast after Haste is stored with 7 fractional bits.

  3. #103
    Hydra
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    OK, I've found the easiest possible decent test for Composure <> Haste

    RDM96+/BLM48, in a party with a COR79+
    Base recast = 21.75 (Aeroga II -- BLM48)
    Fast Cast recast reduction = 0%
    ... RDM87 FC5 trait (-15%)
    ... Lv90 Ice macc magian staff (+12%)
    ... Caster's Roll, busted (+5%)
    ... Loquacious Earring (-1%)
    ... AF3 Earring (-1%)
    Haste = 120/1024
    ... Walahra Turban (50/1024)
    ... Goliard Saio (40/1024)
    ... Headlong Belt (30/1024)
    Composure = * 1.25 (+25%)

    IF order = Composure > Haste, with n fractional bits after Composure...
    3 fractional bits = 27.125 ... * (1 - 120/1024) = 23.9462890625
    4 fractional bits = 27.1875 ... * (1 - 120/1024) = 24.0014648438

    IF order = Haste > Composure, with n fractional bits after Haste...
    7 fractional bits = 19.1953125 ... * 1.25 = 23.994140625
    8 fractional bits = 19.19921875 ... * 1.25 = 23.9990234375
    9 fractional bits = 19.201171875 ... * 1.25 = 24.0014648438

    So...
    If the recast is "0:24", then the order should be Composure > Haste
    If the recast is "0:23", then the order should be Haste > Composure

    Unless there is reason to believe the amount of fractional bits held by recast after haste is greater than 7, or if after composure the recast is held with less than 4 fractional bits.

    Anyone up for testing that? :P
    Once I can get back on the test server, I just need someone to come along and bust a Caster's Roll on me.

  4. #104
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    My ice staff is the 99Magic Attack one so that will need to wait for test server.

  5. #105
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    Bust status is only applied to the COR who busted the roll.

  6. #106
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    Bah, I had a bad feeling someone was gonna say that... now I'm not really sure how you could completely remove fast cast... :/

  7. #107
    xXNyteFyreXx420Sharingan
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    Addle? I realize I'm adding additional complications here but if you could Molting Burst an addle of the appropriate potency and it is literally just negative fast cast then that should work.

    I don't know if we've established anything regarding Addle potency though, so you'd probably need to investigate that first.

  8. #108
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    I thought Addle only affected cast time? I hope you're right though.

    - Update -
    The calculation order is now more likely the following:

    Hasso > Haste > Fast Cast > Composure


    I haven't tested this for myself yet, but I don't want to leave this thread looking like it's definitely Composure > Fast Cast either.
    If this is correct, the only term missing is Arts/Strategems.
    I also still need to check Seigan is in the same position as Hasso...

    Once the test server is back up, I'll verify the above order myself, then if it's correct I'll start working on the remaining Arts/Strategems term.

    If Fast Cast > Composure is actually correct after all, then it also means it will be possible/necessary to determine how many fractional bits are held for recast after Fast Cast is applied.

    - Update -
    The correct order is: Composure > Fast Cast (see post below for details)

    I also checked whether addle does affect recast timers using Atma of the Foe Flayer, which gives "Addle"+: Superior.
    Klimaform = "3:00", so addle doesn't effect recast time, which is a shame...
    Now testing "Haste <> Composure" may well be impossible without adding Fast Cast to the mix. ; ;

  9. #109
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    OK, now the Test Server is finally back up, I thought it would be easy to completely nail down the recast time calculation order... however...

    Well, I'll start at the beginning again, to show why it's getting so confusing all of a sudden...

    There's five known unique recast time terms, but the order and precision of each are unknown:
    - Fast Cast (& Affinity Recast -%, & Divine Benison)
    - Haste (& Slow, which includes Weakened)
    - RDM Composure
    - SAM Hasso|Seigan
    - SCH Arts|Strategem

    =============
    PREVIOUS TESTS - Skip this part if you've read the last few pages of this thread.
    =============

    (Montenten)
    Base recast = 180 seconds (Klimaform)
    Haste = 30/1024 (Headlong Belt)
    FC recast reduction = 9/100 (/rdm35 FC2, Loquacious Earring, Incantor Stone)

    IF order = Haste > Fast Cast, with n fractional bits after Haste...
    6 fractional bits = 174.71875 ... * (1 - 9/100) = 158.9940625
    7 fractional bits = 159.001171875 ... * (1 - 9/100) = 159.001171875

    IF order = Fast Cast > Haste, with n fractional bits after Fast Cast...
    8 fractional bits = 163.796875 ... * (1 - 30/1024) = 158.9981384277
    9 fractional bits = 163.798828125 ... * (1 - 30/1024) = 159.0000343323

    Tested Recast = 159 seconds

    So, either:
    7+ fractional bits for Haste, if Haste > FC
    9+ fractional bits for Fast Cast, if FC > Haste

    ---
    (Montenten)
    Base recast = 10.75 seconds (Curaga IV)
    Haste = 102/1024 (Blessed Mitts + Goading Belt)
    FC recast reduction = 7/100 (/rdm35 FC2)

    IF order = Haste > Fast Cast, with n fractional bits after Haste...
    7 fractional bits = 9.671875 ... * (1 - 7/100) = 8.99484375
    8 fractional bits = 9.67578125 ... * (1 - 7/100) = 8.9984765625
    9 fractional bits = 9.677734375 ... * (1 - 7/100) = 9.0002929688

    IF order = Fast Cast > Haste, with n fractional bits after Fast Cast...
    7 fractional bits = 9.9921875 ... * (1 - 102/1024) = 8.9968719482
    8 fractional bits = 9.99609375 ... * (1 - 102/1024) = 9.0003890991

    Tested Recast = 8 seconds

    So, for FC > Haste...
    The previous test required at least 9 fractional bits after FC to give the correct answer.
    This test requires fractional bits after FC to be 7, or less, to give the correct anser.
    Therefore, FC > Haste doesn't look possible.

    Correct order = Haste > Fast Cast
    Haste recast precision = 7 or 8 fractional bits

    ---
    RDM99/BLM49
    Base recast = 33.25 seconds (Aero IV)
    Haste = 150/1024 ("Haste" spell)
    FC recast reduction = 26/100 (RDM89 FC5, AF1 head, AF2 body, AF3 earring)

    Haste > Fast Cast, with n fractional bits after Haste...
    7 fractional bits = 28.375 ... * (1 - 26/100) = 20.9975
    8 fractional bits = 28.37890625 ... * (1 - 26/100) = 21.000390625

    In-game menu recast = "0:20" (20 seconds)

    Haste recast precision = 7 fractional bits

    ---
    WHM99/rdm49
    Base recast = 60 seconds (Reraise)
    Haste = 30/1024 (Headlong Belt)
    FC recast reduction = 9/100 (/rdm35 FC2, Loquacious Earring, Incantor Stone)

    Haste > Fast Cast, with n fractional bits after Haste...
    6 fractional bits = 58.234375 ... * (1 - 9/100) = 52.99328125
    7 fractional bits = 58.2421875 ... * (1 - 9/100) = 53.000390625

    In-game menu recast = "0:53" (53 seconds)

    Haste recast precision = 7 fractional bits

    ---
    SCH99/sam49
    Base recast = 30 seconds (Stoneskin)
    Haste = 91/1024 (Goliard body, Goading Belt)
    SAM Hasso|Seigan = * 1.5 (or +50%, both Hasso and Seigan tested)

    IF order = Hasso|Seigan > Haste, with n fractional bits after Hasso|Seigan...
    0 fractional bits = 45 ... * (1 - 30/1024) = 41.0009765625

    IF order = Haste > Hasso|Seigan, with n fractional bits after Haste...
    7 fractional bits = 27.328125 ... * 1.5 = 40.9921875
    8 fractional bits = 27.33203125 ... * 1.5 = 40.998046875
    9 fractional bits = 27.333984375 ... * 1.5 = 41.0009765625

    In-game menu recast = "0:41" (41 seconds)

    Haste has been determined to be 7 fractional bits, so...

    Correct order = Hasso|Seigan > Haste


    =========
    NEW TESTS - This is where everything starts going pear-shaped. :/
    =========

    BLM99/sam49
    Base recast = 21.75 seconds (Aeroga II)
    Haste = 51/1024 (Goading Belt)
    SAM Hasso|Seigan = * 1.5 (or +50%, both Hasso and Seigan tested)

    IF order = Hasso|Seigan > Haste, with n fractional bits after Hasso|Seigan...
    0 fractional bits = 32 ... * (1 - 51/1024) = 30.40625
    2 fractional bits = 32.5 ... * (1 - 51/1024) = 30.8813476563
    3 fractional bits = 32.625 * (1 - 51/1024) = 31.0001220703

    IF order = Haste > Hasso|Seigan, with n fractional bits after Haste...
    7 fractional bits = 20.6640625 ... * 1.5 = 30.99609375
    11 fractional bits = 20.6665039063 ... * 1.5 = 30.9997558594
    12 fractional bits = 20.6667480469 ... * 1.5 = 31.0001220703

    In-game menu recast = "0:30" (30 seconds)

    So, with Hasso|Seigan > Haste, apparently the recast after Hasso|Seigan can't be stored with more than 2 fractional bits...
    I guess that could be possible, but I just thought it seemed unlikely...

    Hasso|Seigan recast precision = 0 to 2 fractional bits

    ---
    BLM99/sch49
    Base recast = 45.5 seconds (Thunder V)
    Haste = 30/1024 (Headlong Belt)
    SCH Arts|Stratagem = * 1.2 (Light Arts)

    IF order = Light Arts > Haste, with n fractional bits after Light Arts...
    8 fractional bits = 54.59765625 ... * (1 - 30/1024) = 52.9981155396
    9 fractional bits = 54.599609375 ... * (1 - 30/1024) = 53.0000114441

    IF order = Haste > Light Arts, with n fractional bits after Haste...
    7 fractional bits = 44.1640625 ... * 1.2 = 52.996875
    9 fractional bits = 44.166015625 ... * 1.2 = 52.99921875
    10 fractional bits = 44.1669921875 ... * 1.2 = 53.000390625

    In-game menu recast = "0:53" (53 seconds)

    Now this one is where it starts getting hard to accept the results, as Haste is supposed to be 7 fractional bits (or at least 7 fractional bits by the time Fast Cast is applied...)
    The results from this test seem to show that Light Arts is applied before Haste, and the result held with 9 fractional bits, minimum...
    To store 54.599609375 bit-shifted as an integer would require a total of 15 bits (6 integer bits + 9 fraction bits)
    This seems unlikely, especially if it's actually held as a floating point value, which would require at least a couple more bits on top of this...
    However, this seems to be the only possibility at current, so...

    Correct order = Light Arts > Haste
    Light Arts recast precision = 9 fractional bits (or more...)

    ---
    RDM99/blm49
    Base recast = 8 seconds (Deodorize)
    FC recast reduction = 20/100 (RDM89 FC5, AF1+1 head)
    RDM Composure = * 1.25 (or +25%)

    IF order = Fast Cast > Composure, with n fractional bits after Fast Cast...
    9 fractional bits = 6.3984375 ... * 1.25 = 7.998046875
    20 fractional bits = 6.3999996185 ... * 1.25 = 7.9999995232
    33 fractional bits = 6.3999999999 ... * 1.25 = 7.9999999999
    34 fractional bits = 6.4 ... * 1.25 = 8 (supposedly...)

    IF order = Composure > Fast Cast, with n fractional bits after Composure...
    0 fractional bits = 10 ... * (1 - 20/100) = 8

    In-game menu recast = "0:08" (8 seconds)

    There was a bit of confusion earlier on this page due to my miss-reading this post:
    Quote Originally Posted by Yugl View Post
    99 RDM + Composure + Deodorize => 8s recast
    This meant exactly as written, without any Fast Cast gear, but I didn't notice initially.
    Later I was informed that the result was supposed to be 7s recast... which is why I changed my conclusion in my previous post.
    However, now the test server is back up again, I have tested it to actually be 8s, as mentioned above.

    Also, for FC > Composure, 34 fractional bits appears to give the correct answer in OpenOffice Calc, but I think it's only due to a software limitation with large fractional values.
    I have used 20 fractional bits as a reasonably safe precision amount, which demonstrates the point fine anyway.
    So, the only real possibility here is that Composure is calculated first...

    Correct order = Composure > Fast Cast

    ---
    So there's still much more testing to do before the recast time calculation order can be figured out completely.
    Some of it is going to be very complicated such as testing Haste <> Composure... ; ;
    The only thing that looks 100% certain is that Fast Cast is calculated last, which is kinda a surprise.

    Sorry for another ridiculously long post again... :P

  10. #110
    Hydra
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    Here's a summary of the above post, as it was pretty long and not very straight to the point...

    Here are the tested recast time calculation orders for two terms.

    Haste > Fast Cast
    Hasso|Seigan > Haste
    Light Arts > Haste
    Composure > Fast Cast


    Here are the current possibilities for the whole recast calculation order, with all five known recast terms:

    1st: Hasso|Seigan -or- Arts|Stratagem -or- Composure
    2nd: Hasso|Seigan -or- Arts|Stratagem -or- Composure
    3rd: Hasso|Seigan -or- Arts|Stratagem -or- Composure -or- Haste
    4th: Composure -or- Haste
    5th: Fast Cast


    Here are the current possibilities for fractional bit resolution of the recast value held after each term:

    SAM Hasso|Seigan = 0 ~ 2
    SCH Arts|Stratagem = 9 ~ unknown
    RDM Composure = 0 ~ unknown
    Haste = 7
    Fast Cast = n/a, effectively 0 (as long as FC is definitely the last term in the calculation order)


    As long as this fractional bit stuff is the correct way to go about this, then the rest just needs to be narrowed down.

  11. #111
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    Considerations and Preparation
    1. Previous tests with exiled consistently caused me to cast faster, so this was inapplicable
    2. Latency will become a greater issue if you use third-member chat triggers rather than if you use game hour
    3. Two characters with AutoExec that have access to BLM and RDM (And Thunder IV on both)
    4. Place this line within the AutoExec file. This file causes your character to cast anytime the game hour is XX:X9. In other words, every 10 ticks.
    5. I took Radec's suggestion and used mobs that we can kill in one hit. We used East Ronfaure and Abyssea-Vunkerl for this test.
    6. Base tests had (N=15) each roughly. Other tests had (N=3-5) roughly. The reason for this is because the base tests yielded patterns that allowed for the proceeding tests to yield convincing results (This will become obvious as you read through).

    Preliminary tests
    Thanks to Suter for assisting with these tests.

    1. Base test: Initial Casting
    We used RDM without any gear to check for discrepancies that arise when we know we have the same level of fast cast. We found that there was a distinct pattern:
    Pattern 1: My character would initiate casting earlier. I would always land the cast first.
    Pattern 2: Both characters initiate casting at the same time. He would always land the cast first.

    2. Base test: Land time
    In order to better understand the base cast rate environment, we also used mobs that had enough HP to survive two nukes.
    When Pattern 1 occurs: Either I land noticeably faster OR we land at relatively the same time. In the latter case, despite me landing first (Since it is Pattern 1), his name appears in the log first.
    When Pattern 2 occurs: We appear to cast at the same time. Yugl appears in the log first.

    Given the patterns found in (1) and (2), I decided to focus on tests where we begin casting at roughly the same time. Both pattern (1) and (2) show the ability to land at the same time, but the difference in initiating the cast time and variance in land time found in pattern (1) makes it unreliable. However, Pattern (2) seems both consistent in initiation and landing.

    3. Elemental Celerity

    Comparison 1
    Yugl (RDM): Fast Cast (Trait) + Warlock Hat NQ (10% FC)
    Suter (BLM): Elemental Celerity (Trait)
    Expected: Suter lands first S:(1-0.5) v Y:(1-0.4)
    Result: Yugl lands first. Elemental Celerity is not 50%

    Comparison 2
    Yugl (RDM): Fast Cast (Trait)
    Suter (BLM): Elemental Celerity (Trait)
    Expected: Unknown. At this point, we only know that Elemental Celerity is not 50%.
    Result: Patterns (1) and (2) manifested.

    Comparison 3
    Yugl (RDM): Fast Cast (Trait) + Augur Feet (3% FC)
    Suter (BLM): Elemental Celerity (Trait)
    Expected: Yugl lands first assuming Comparison (2) leads us to believe Elemental Celerity is 30%. S:(1-0.3) v Y:(1-0.33)
    Result: Yugl lands first. Elemental Celerity is roughly 30%.

    4. Affinity Cast Time Reduction

    Comparison 1
    Yugl (RDM): Fast Cast (Trait) + Pajama Staff (14% CTR for Thunder) + Augur Feet (3% FC) + Atma of Tusked Terror (5% FC) [Total: 52% in Cast Time Reduction]
    Suter (RDM): Fast Cast (Trait) + Warlock Hat NQ (10% FC) + Duelist Body NQ (10% FC) + Loq Earring (2% FC) [Total: 52% in Fast Cast]
    Expected: H0: If Elemental Cast Time Reduction is additive rather than multiplicative, we should see patterns (1) and (2) emerge. H1: If Elemental Cast Time Reduction is multiplicative, then Suter should cast faster.
    H0: S:(1-0.5) v Y:(1-(0.3 + 0.14 + 0.03 + 0.05))
    H1: S:(1-0.5) v Y:(1-0.38)*(1-0.14)
    Result: Patterns (1) and (2) emerged.

    Comparison 2
    Yugl (RDM): Fast Cast (Trait) + Pajama Staff (14% CTR for Thunder) + Augur Feet (3% FC) + Atma of Tusked Terror (5% FC) + Stoicheon Medal (3% Elemental Magic Cast Time Reduction) [Total: 52% in Cast Time Reduction]
    Suter (RDM): Fast Cast (Trait) + Warlock Hat NQ (10% FC) + Duelist Body NQ (10% FC) + Loq Earring (2% FC) [Total: 52% in Fast Cast]
    Expected: H0: If Elemental Cast Time Reduction is additive rather than multiplicative, Yugl should cast faster. H1: If Elemental Cast Time Reduction is multiplicative, then Suter should cast faster. Notice that there are multiple versions of each since it is unknown how Elemental Magic Cast Time Reduction functions
    H0a: S:(1-0.5) v Y:(1-(0.3 + 0.14 + 0.03 + 0.05+0.03))
    H0b: S:(1-0.5) v Y:(1-(0.3 + 0.14 + 0.03 + 0.05))*(1-0.03)
    H1a: S:(1-0.5) v Y:(1-0.38)*(1-0.14)*(1-0.03)
    H1b: S:(1-0.5) v Y:(1-0.41)*(1-0.14)
    Result: Yugl casted faster consistently. And remember, I am specifically looking at Pattern (2) scenarios unless I expect Pattern (1) to occur.

    5. Elemental Magic Cast Time Reduction

    Comparison 1
    Yugl (RDM): Fast Cast (Trait) + Stoicheon Medal (3% Elemental Magic Cast Time Reduction) + Duelist Body +2 (12% FC) + Atma of the Tusked Terror (5% FC) [Total: 50% in Cast Time Reduction]
    Suter (RDM): Fast Cast (Trait) + Warlock Hat NQ (10% FC) + Duelist Body NQ (10% FC) [Total: 50% in Fast Cast]
    Expected: H0: If Elemental Cast Time Reduction is additive rather than multiplicative, we should see patterns (1) and (2) emerge. H1: If Elemental Cast Time Reduction is multiplicative, then Suter should cast faster.
    H0: S:(1-0.5) v Y:(1-(0.3 + 0.12 + 0.03 + 0.05))
    H1: S:(1-0.5) v Y:(1-0.47)*(1-0.03)
    Result: Patterns (1) and (2) emerged.

    Comparison 2: FLAWED COMPARISON!
    Yugl (RDM): Fast Cast (Trait) + Stoicheon Medal (3% Elemental Magic Cast Time Reduction) + Duelist Body +2 (12% FC) + Atma of the Tusked Terror (5% FC) + Augur Feet (3% FC) [Total: 50% in Cast Time Reduction]
    Suter (RDM): Fast Cast (Trait) + Warlock Hat NQ (10% FC) + Duelist Body NQ (10% FC) [Total: 50% in Fast Cast]
    Expected: Here is where the problem emerges (Didn't realize this until I made this post). The above set puts me at 50% FC and 3% Elemental CTR. This means that regardless of the order, casting will favor me. Unfortunately, Suter's Fast Cast options were limited. However, Comparison (2) under Affinity Cast Time Reduction should serve as substitute for this comparison.
    Result: Yugl casted faster consistently.

    6. Findings
    Elemental Celerity is 30%
    Affinity Cast Time Reduction is additive with Fast Cast
    Skill (Such as Element/Enhancing Magic) Cast Time Reduction is additive with Fast Cast

  12. #112
    Hydra
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    That's some nice testing, and the test method looks pretty solid to me.
    I'm glad to see affinity cast time reduction stacks additively with fast cast, the same as with recast time.

    It would be interesting to know if Divine Benison also stacks additively with fast cast for cast time, although now the cast timers for those spells have been reduced in a recent update testing that might be a bit difficult?

    Otherwiki has Elemental Celerity trait as: tier I = -15% @ BLM50, tier II = -25% @ BLM90, with no intermediary tiers between those levels.
    I don't think -25% would work in your "Comparison 2" test though...

    Thunder IV base cast time = 8.5 seconds
    -1% = -0.085 seconds
    -5% = -0.425 seconds
    Thunder IV -25% = 6.375 seconds
    Thunder IV -30% = 5.95 seconds

    A consistent 425 milliseconds higher latency than your test partner seems very unlikely, and should be easily noticeable, so Otherwiki definitely seems wrong on their -25% value.

    Impact should give more accurate results with it's 12 second cast time, if both testers have it, although I guess it would have been a pain to keep recasting it.

    Flare has the highest cast time of the elemental magic spells at 19 seconds, but I guess you need something you can cast on RDM too for these tests.
    If you are planning to test lower tier(s) of Elemental Celerity though, I think Flare would give the most accurate results.

    I assume SCH Arts and Stratagems are much less likely to stack additively with Fast Cast, but Addle might be more likely?
    Atma of the Foe Flayer would make testing Addle a lot simpler if you plan on testing that too.

  13. #113
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    I've heard SCH and Fast Cast were multiplicative in the past (I believe this was based on recast?). I can check though. Addle will require me to obtain the atma, but that is doable if I get red proc support with that. Since this test was made progressively (Literally had the person sit while I made the AE code and then had to teach them have to DL/Use the code), I was a bit constrained. Now that the method is 'there', future tests should run smoother assuming he has Twilight cloak.

  14. #114
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    Can someone please tell me what I'm doing wrong...

    Goading Belt = 51/1024 haste
    Walahra Turban = 50/1024 haste
    Nashira Seraweels = 20/1024 haste

    Thundaga III [34s] + (Goading Belt + Walahra Turban + Nashira Seraweels)
    IF haste is 120/1024 = 30s
    IF haste is 121/1024 = 29s
    Result = 29s

    Wind Breath [29.5s] + (Goading Belt + Walahra Turban + Nashira Seraweels)
    IF haste is 121/1024 = 26s
    IF haste is 122/1024 = 25s
    Result = 26s

    Goading Belt + Walahra Turban + Nashira Seraweels = 121/1024 haste.

    BLM99/sch49
    Firaga III recast time = 31.5 seconds
    Dark Arts = -10% (*0.9) recast time for Black Magic
    Haste = 121/1024 (Goading Belt + Walahra Turban + Nashira Seraweels)

    Calculation order = Dark Arts > Haste, with n fractional bits after Dark Arts...
    9 fractional bits = 28.349609375 ... * (1 - 121/1024) = 24.999704361
    12 fractional bits = 28.3498535156 ... * (1 - 121/1024) = 24.9999196529
    13 fractional bits = 28.3499755859 ... * (1 - 121/1024) = 25.0000272989

    IF order was Haste > Dark Arts, with n fractional bits after Haste...
    7 fractional bits = 27.7734375 ... * 0.9 = 24.99609375
    10 fractional bits = 27.77734375 ... * 0.9 = 24.999609375
    11 fractional bits = 27.7778320313 ... * 0.9 = 25.0000488281

    In-game menu recast timer = 0:25 (25 seconds)

    So...
    Haste fractional bit resolution was previously determined to be: 7 fractional bits
    The calculation order was also previously determined to be: SCH Arts|Stratagem > Haste

    This means the recast held after Dark Arts needs to be stored with at least 13 fraction bits, which in this example would mean at least an 18 bit integer...


    Is there something wrong with the way I'm calculating the recast ?
    Here's the method I use...

    = TRUNC ( [Spell base recast] * [SCH Arts|Stratagem] * 2 ^ [n fraction bits] ) / 2 ^ [n fraction bits] * [Haste]

    Which for my example looks like...

    Firaga III Base Recast > Dark Arts > Haste > Result Recast
    = TRUNC ( 31.5 * 0.9 * 2 ^ 12 ) / 2 ^ 12 * (1 - 121/1024) = 24.9999196529
    = TRUNC ( 31.5 * 0.9 * 2 ^ 13 ) / 2 ^ 13 * (1 - 121/1024) = 25.0000272989

    Is there something wrong with this ?
    I believe it's exactly the same as what Montenten suggested to do in this post on the previous page of this thread ?

  15. #115
    Chram
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    If you're using Excel, I do it like this:

    Bits: #
    BitUnit: 1 / Power(2, Bits)

    RecastUnits = (example) 1024 (for haste)
    timeUnits = (example) 121 (Goading Belt + Walahra Turban + Nashira Seraweels)

    Recast at a certain resolution: floor(BaseRecast * (RecastUnits - timeUnits) / RecastUnits, BitUnit)

    Comparing with your method, seems to yield the same results.


    Things I noted:

    If it's calculated in order of Arts > Haste, and Arts recast is in units of /1024 (102/1024 for 10%), Arts only needs 6 bits to yield the observed result (7 bits also yields the observed result).

    If it's calculated in order of Haste > Arts, and Arts recast is in units of /1024, Haste needs 7 bits to yield the observed result.


    Was there a test to show that Arts recast is in units of /1000 instead of /1024?

  16. #116
    Hydra
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    I tested whether Arts uses /100 or /1024 earlier tonight, however I still couldn't tell you for definite which it is...


    Matching Arts is supposedly -10% (-102.4/1024)

    -101/1024 vs. -102/1024 -- Thunder V (45.5s) + Dark Arts -- 41s vs. 40s
    = 0:40

    -102/1024 vs. -10% -- There isn't any spell with a suitable base recast... :/

    -10% vs. -103/1024 -- Klimaform (180s) + Dark Arts -- 162s vs. 161s
    = 2:42 (162s)

    So, best I can say is matching arts is either -10/100 or -102/1024


    Opposing Arts is supposedly +20% (+204.8/1024)

    +204/1024 vs. +20% -- Klimaform + Light Arts -- 215s vs. 216s
    = 3:36 (216s)

    +20% vs. +205/1024 -- There isn't any spell with a suitable base recast again... :/

    +207/1024 vs. +208/1024 -- Aero IV + Light Arts -- 39s vs. 40s
    = 0:39

    So the best I can say for opposing arts is between +20/100 and +207/1024

    I've just realised a possible solution to this issue -- using gear that enhances Arts...
    So I'll see if it's possible to narrow it down properly.

    - Update -
    Well that idea didn't go too well, put simply, it's not possible to find out directly whether arts|stratagems is /100 or /1024.
    The only way to continue testing this is to include another recast time adjustment term, which makes things more complicated and the results less reliable...

  17. #117
    Hydra
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    !!
    Montenten, it seems you are right about SCH Arts being /1024 instead of /100

    I stumbled across this test which should only work with the /1024 system instead of /100, no matter what calculation order or precision you use...

    Fire II (18.5s) + Dark Arts + 40/1024 haste (Goliard body)

    WITH Dark Arts = -10/100 ...
    IF Dark Arts > Haste, with n fractional bits after Dark Arts...
    0 fractional bits = 16 ... * (1 - 40/1024) = 15.375
    20 fractional bits = 16.6499996185 ... * (1 - 40/1024) = 15.9996090084

    IF Haste > Dark Arts, with n fractional bits after Haste...
    0 fractional bits = 17 ... * (1 - 10/100) = 15.3
    7 fractional bits = 17.7734375 ... * (1 - 10/100) = 15.99609375
    20 fractional bits = 17.77734375 ... * (1 - 10/100) = 15.999609375


    WITH Dark Arts = -102/1024 ...
    IF Dark Arts > Haste, with n fractional bits after Dark Arts...
    0 fractional bits = 16 ... * (1 - 40/1024) = 15.375
    4 fractional bits = 16.625 ... * (1 - 40/1024) = 15.9755859375
    5 fractional bits = 16.65625 ... * (1 - 40/1024) = 16.0056152344
    20 fractional bits = 16.6572265625 ... * (1 - 40/1024) = 16.0065536499

    IF Haste > Dark Arts, with n fractional bits after Haste...
    0 fractional bits = 17 ... * (1 - 102/1024) = 15.306640625
    6 fractional bits = 17.765625 ... * (1 - 102/1024) = 15.9960021973
    7 fractional bits = 17.7734375 ... * (1 - 102/1024) = 16.003036499
    20 fractional bits = 17.77734375 ... * (1 - 102/1024) = 16.0065536499

    In-game menu recast timer = 0:16 (16 seconds) !!

    No matter which way around or how many fractional bits you use with /100 system Dark Arts, it always adds up to 15 seconds, not 16.
    So only the /1024 system can be correct!

    - Update -
    I pretty much had the entire calculation order sorted out for a short time, but since then I've kept finding problems.

    I'm beginning to wonder if it's possible if Composure or even Hasso|Seigan are /1024 system instead of % (/100).
    Composure should be +256/1024 (25%) and Hasso|Seigan should be +512/1024 (50%).
    But it seems, based on my previous tests, that Composure now has to be something very slightly different to +256/1024...

    I'm now trying to test between +256/1024 and +257/1024 composure, as unlikely as +257/1024 sounds.
    It's a little awkward testing this as I have to assume I don't know which way around Composure <> Fast Cast is again, but I think I've figured out some tests to try.
    Does anyone think +257/1024 sounds even possible for Composure though? O.o

  18. #118
    Hydra
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    OK, I managed to narrow Composure down to +256/1024, so it is simply +25% (*1.25).
    +255/1024 is definitely too low, +257 is definitely too high.

    Haste [7 fractional bits] > Fast Cast
    Composure [4+ fractional bits] > Fast Cast (more than 4 fractional bits makes no difference at all if composure is the very first term used)

    Composure > Haste > Fast Cast...
    This has problems, but Haste > Composure > Fast Cast is looks far more impossible.

    Here's probably the most problematic test at the moment:

    Dia III (7s), Composure, -15/100 FC recast (RDM89 FC5), 60/1024 haste (Goliard body, Nashira legs)

    In-game menu recast time = 0:07

    If haste is limited to 7 fractional bits, then neither Composure > Haste > Fast Cast, nor Haste > Composure > Fast Cast work with any number of fractional bits after Composure...
    Either way round with 7 fractional bits after Haste will give a result of 6 seconds...
    It only adds up to 7s with Composure > Haste > Fast Cast, with recast after Haste having at least 9 fractional bits...

    7 fractional bits after Haste was already proven earlier though...

  19. #119
    An exploitable mess of a card game
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    Considerations and Preparation
    1. I conducted this test with Swanseatom, so I decided to check for the patterns found here. The patterns surfaced once again. Moreover, he says he sees himself casting a bit earlier during the times that I see us both casting at roughly the same time. This leads me to believe that the game predetermines who will cast first and if you are determined to cast first, you will see yourself cast slightly earlier. Otherwise, you will appear to cast at the same time. Try this for yourself and see if you get the same results!

    Elemental Celerity and Fast Cast

    Comparison 1
    Yugl (RDM): Fast Cast (Trait) + Duelist Body+2 (12% FC) + Augur's Feet (3% FC)
    Swanseatom (BLM/RDM): Elemental Celerity (Trait) + Fast Cast Sub (Trait)
    Expected: Assuming FC and Elemental Celerity stack additively, patterns (1) and (2) should emerge
    Result: Patterns emerge.

    I could not do more testing than this since Swan did not have his other CTR gear with him. However, the appearance of patterns is quite evident considering the pattern has appeared with two different players. Furthermore, if they were multiplicative, I should have endlessly casted faster. Thus, I attribute the emergence of patterns to FC and Elemental Celerity stacking additively.

    Conclusion
    Fast Cast and Elemental Celerity stack together additively.

  20. #120
    Chram
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    Just a gear test note:

    Fast Cast of Witful Belt:

    4% recast, so presumed 8% Fast Cast

    Verifying amount:

    Cura III, no haste
    48 seconds if 40/1000 FC, 47 seconds if 41/1000 FC
    Result: 48 seconds

    Protectra III with 2% (20/1024) haste [Blessed Pumps]
    16 seconds if 39/1000 FC, 15 seconds if 40/1000 FC
    Result: 15 seconds

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