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Thread: Cast and Recast     submit to reddit submit to twitter

  1. #121
    An exploitable mess of a card game
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    Is this accounting for the haste?

  2. #122
    Chram
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    ... No. >.>

    Kept checking to make sure I wasn't forgetting anything, and somehow completely blanked on that. Rechecking values...

    Test:

    Protect II with 30/1024 haste (including belt):
    5 if 10/1000, 4 if 20/1000
    Result: 5

    Protectra III with 101/1024 haste (including belt):
    15 if 10/1000 or less, 14 if 11/1000 or more
    Result: 14

    Curaga IV with 60/1024 haste (including belt):
    10 if 11/1000, 9 if 12/1000
    Result: 10

    Cura III with 30/1024 haste (just belt):
    48 if 10/1000, 47 if 11/1000
    Result: 47

    ** Cura III with 51/1024 haste (test with assumption of 31/1024 for belt, +20/1024 from shoes):
    47 if 10/1000, 46 if 11/1000
    Result: 47

    So it's either 11/1000 fast cast recast time and 30/1024 haste, or 10/1000 fast cast recast time and 31/1024 haste. The latter seems more likely, giving it 2% Fast Cast.

  3. #123
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    Quote Originally Posted by Motenten View Post
    Fast Cast of Witful Belt:

    4% recast, so presumed 8% Fast Cast
    Did you factor out the 3% Haste on the belt itself?

    Edit: Damn you page 7! DAMN YOU!! 2% makes more sense, 8% sounded really high.

  4. #124
    xXNyteFyreXx420Sharingan
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    I could just be blind, but I don't see a test with any other Fast Cast gear there to rule out the possibility of it being 3%. 3% would make more sense given the haste and quick cast values. Unless I'm unaware of some flooring in the recast equations, the difference should be obvious with just the belt and a 5% FC piece and casting say, Reraise or Klimaform.

  5. #125
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    The last test might indicate that. With 3% FC, that would be roughly 15/1000 recast? That would land you at 46s after the haste value given.

  6. #126
    xXNyteFyreXx420Sharingan
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    Last I saw, we'd determined that Fast Cast is only applied to recast in whole percentage increments. As such, 2% and 3% would provide the same 1% reduction in recast time. Has that understanding changed?

  7. #127
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    That is the current understanding (iirc) and 3% Fast Cast would fit with the rest of the belt.

  8. #128
    Chram
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    Ahh. I see what you're saying. Yes, I can check for that later tonight.

  9. #129
    Chram
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    Protectra
    Witful Belt + Orison Locket (5% FC)
    With either 30 or 31/1024 haste:
    14 if 30/1000, 13 if 40/1000
    Result: 13
    At least 38/1000 total recast, meaning 40/1000=4%.

    That puts Witful at 3% FC.

  10. #130
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    Hi there, I'm trying to follow this thread and summarize the way FC works with spell recasting. Forgive me if some other summary like what is below is available in this thread. Can we all agree on the following

    Casting Delay
    1) Casting time delay reduction caps at a maximum of 80%
    2) The varying sources (Grimoire, Fast Cast, Elemental Celerity, -Casting Delay Gear) all appear to stack together additively in one pool.

    Recast Delay
    1) Recast delay reduction caps at a maximum of 80%.
    2) The varying sources are consolidated into different groups of modifiers which appears to be in its simplest form, ([Original Recast Value] x [Job Ability modifier value] x [Haste/Slow modifier value] x [Fast Cast modifier value]).

    Fast Cast
    1) Fast Cast values from all various sources (job Traits and Gear) stack together in the same modifier pool.
    2) The total value of that modifier cannot exceed 40%.
    3) It's value is rounded down, odd pieces by themselves are less potent than when they are paired together (and thus eliminate the fractional value).

    Haste
    1) Haste/Slow from all sources (Gear and Magic) stack together in the same modifier pool.
    2) The total value of that modifier cannot exceed the current capped value of 68.75


    Here's what I am unclear of

    1) Do sources of gear with "reduces x's recasting time" (blu gloves, blm body, Magian recast staffs, etc) exist as their own modifier or are they added into a another group? Which group then?
    2) How does the JA modifier work? Are individual ability values added together, or multiplied? If multiplied, then in what order?

    Please, can someone shead some light on this?

  11. #131
    Sea Torques
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    Quote Originally Posted by Nausi View Post
    Recast Delay
    1) Recast delay reduction caps at a maximum of 80%.
    2) The varying sources are consolidated into different groups of modifiers which appears to be in its simplest form, ([Original Recast Value] x [Job Ability modifier value] x [Haste/Slow modifier value] x [Fast Cast modifier value]).
    There is no known cap on recast reduction.

    The order of the terms is important, but not currently pinned down.

    Quote Originally Posted by Nausi View Post
    2) How does the JA modifier work? Are individual ability values added together, or multiplied? If multiplied, then in what order?
    See the second link.

    Recast calculations apparently involve a lot of binary. Despite my intent to, I haven't read through all of the testing carefully enough to explain how it's done.

  12. #132
    Groinlonger
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    Nausi ~

    In general, that is the appropriate model for for recast time calculation. The exact model remains elusive to this point. What's missing is the order of calculation of terms, and the exact method of calculation for each step. These are both important in predicting the discretization error that will occur in extreme cases. If you're not familiar with discretization error, it's error that is produced due to the limitation of a digital computer's ability to represent numbers. Digital computers can only represent specific real numbers which are different depending on how the computer decides to represent these numbers.

    This is a little bit copy/paste from something I sent to TS, but I think it may help clear things up for people who have been having trouble putting it all together (some of my previous posts on the matter are jumbled or outright wrong.)

    First, consider a byte that is being used to represent integers. The possible values are the integers equal to and between 0 and 255. Now choose an odd integer from this number space, say 201. Dividing this number by 2 would result in 100.5 in real number space. However, because this number does not exist within the binary number space a byte can represent, the resulting value will be truncated to 100. This is what is meant by discretization error. This is probably exactly what occurs with Fast Cast before it is used in recast calculations. The values for each piece of of Fast Cast gear or trait are stored as integers. The integers are summed, and then divided by 2. Odd values of Fast Cast will thus experience truncation (which is what has been observed.)

    Additionally, integers are not the only way computers can represent numbers. Floating point is a format used to represent decimals, and could potentially be used in this calculation somewhere. The numbers any floating point system can represent are also discrete, and the error is even more difficult to predict.

    Now, to complicate things further, the order in which calculations are performed has an impact on the error that is produced. In integer number space, for example, (1÷2)*2 = 0 while (1*2)÷2=1.

    We know at least the following at this point ~

    • All terms are stored as integers not floating points.
    • Stored recast times correspond to 0.25 seconds per unit.
    • The final term is converted to an integer byte (8 bits) and corresponds to 1.00 seconds per unit.
    • The numerator for Fast Cast recast division is 2 and then 100 (remember this value is first divided in half).
    • The numerator for Haste recast division is 1024.


    Now, I'm not really interested in finding out the interim calculation order or specifics as I don't consider it very useful information. It's also entirely possible to accidentally convert an integer to a floating point and vice versa when programming just depending on your syntax, thus there are a great number of ways this calculation could actually be occurring. If someone is intent in solving it, then I recommend the following.

    *Stick to conventional ways that computers represent numbers

    There are only a few choices for this. IEEE 754 formats for 16, 32, and 64 bit floating point numbers and 16, 32, and 64 bit integer numbers. I think it's same to assume that none of the intermediate calculations are carried out in any other formats (finding out custom bit lengths etc.) because that would require physically constructing their own server hardware and computer engineering standards to do so. That seems unlikely.

    *Assume integer math at first

    Floating point calculations require more computational time. Good programmers know this and try to avoid them when appropriate.

    I'd like to rewrite the recast time page. Currently it's a bit too technical and difficult to follow, but I've kind of forgotten which terms are lumped together, and how many separate terms there are.

  13. #133
    Groinlonger
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    Well, despite what I said earlier about not wanting to do this, I can't seem to stop thinking about it. I'm going to look into the following possible exact methods outlined below.

    Code:
    R = [[([(r*(100-[f/2]))/100]*(1024-h))/1024]/4]
    or

    Code:
    R = [[([(r*(1024-h))/1024]*(100-[f/2]))/100]/4]
    Code:
    R	Final Recast
    r	Base recast
    f	Fast Cast
    h	Haste
    The values for r are simply the base recast listed in the game multiplied by four. The parenthesis and brackets denote strict order of operations while the brackets also indicate where truncation to a whole integer would occur.

    The first model is Fast Cast > Haste, the second is Haste > Fast Cast.

  14. #134
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    Hey Mojo, I'm not sure if you've read this, but Mougurijin has determined that it's Haste > Fast Cast. link

  15. #135
    Groinlonger
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    I did read that, but he assumed floats were used there, and in a way that may not be possible without designing your own hardware and engineering standards (i.e., the arithmetic used was not consistent with any IEEE 754 standard.) So I am skeptical of the results unless I have misinterpreted them (which is very possible!)

    Neither of the two methods I suggested work. However, there are several other ways that it could be done using just integers (by grouping some terms before truncating by the product of their denominators) which I am looking at currently.

  16. #136
    Groinlonger
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    I've been able to get something working quite well using integer math. My data is as follows.

    Code:
    Fast Cast	Haste	Spell		Result	A	B	C	D	E	F	G	H	I
    4		150	Reraise		50	50	50	49	51	49	49	50	48	50
    4		150	Regen		10	10	10	9	10			10		10
    2		150	Regen		10	10	10	9	10			10		10
    6		150	Protectra III	14	14	13	14	14			14		13
    2		150	Curaga IV	9	9						8		
    6		150	Protect II	4	4								
    6		150	Cure III	4	4								
    6		150	Deodorize	6	6								
    6		150	Curaga IV	8	8								
    6		150	Regen		9	9								
    6		150	Protectra III	14	14								
    6		150	Protectra IV	14	14								
    6		150	Reraise		49	49								
    18		150	Protect II	4	4								
    18		150	Deodorize	6	6								
    18		150	Curaga II	7	7				
    18		150	Curaga III	8	8				
    18		150	Protectra III	13	13				
    18		150	Protectra IV	13	13				
    18		150	Reraise		46	46				
    30		150	Cure II		3	3				
    30		150	Protect IV	4	4				
    30		150	Deodorize	5	5				
    30		150	Protectra III	12	12				
    30		150	Protectra IV	13	13				
    30		150	Reraise		43	43				
    
    A	[[hf]4]
    B	[[[f]h]4]
    C	[[[h]f]4]
    D	[fh4]
    E	[[h]f4]
    F	[[f4]h]
    G	[[4]hf]
    H	[[h4]f]
    I	[[f]h4]
    The Fast Cast and Haste values are self explanatory. The result is what I observed, and the numbers in the columns marked A through I are what the model predicted given the truncation order to the right of the letter below. It's kind of shorthand notation, f = fast cast, h = haste, 4 = final division by 4. Everything in brackets would be multiplied by terms I supposed earlier and then truncated by division of the product of their bases.

    The table is mostly empty. That's because after a few spells, if the model had thrown an error, I simply discarded it and stopped checking for values as it was already flawed. The model that worked for everything I lumped Fast Cast and Haste together, truncated with division by their common base, and then truncated again by division by 4.

    Code:
    R = [[(r*(100-[F/2])*(1024-h))/(1024*100)]/4]
    
    R	Final Recast
    r	Base recast
    f	Fast Cast
    h	Haste
    The list of spells used were not random. I selected spells such that the smallest possible change in r would produce a change in R. I did this because spells with such r values are the most likely to throw an error between observed and predicted recast times. I couldn't test every such critical r value as that would have required changing jobs, leaving town, or access to spells that I don't have, but none of the ones I did test threw any errors, and I tested three combinations of Haste and Fast Cast.

    Either way, this model agrees with observations I made before, and seems much more realistic than anything else suggested. It needs more testing though. Every time I think I have this figured out, something breaks it. It only covers Haste and Fast Cast, but I'll work on it more later.

  17. #137
    Groinlonger
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    More data

    Code:
    f	h	Spell		Result	Predicted
    8	150	Cure III	4	4
    8	150	Deodorize	6	6
    8	150	Barfira		8	8
    8	150	Curaga IV	8	8
    8	150	Regen		9	9
    8	150	Protectra	12	12
    8	150	Protectra II	13	13
    8	150	Protectra III	13	13
    8	150	Protectra IV	14	14
    8	150	Regen IV	19	19
    8	150	Stoneskin	24	24
    8	150	Cura II		32	32
    8	150	Cura III	40	40
    8	150	Reraise		49	49
    10	150	Cure III	4	4
    10	150	Deodorize	6	6
    10	150	Barfira		8	8
    10	150	Protectra	12	12
    10	150	Protectra II	12	12
    10	150	Protectra III	13	13
    10	150	Protectra IV	14	14
    10	150	Stoneskin	24	24
    10	150	Cura II		32	32
    10	150	Cura III	40	40
    Same idea as before, trying values likely to throw errors. None thrown. I'll try some BLM spells as their spells have many unique r values and would fit well with the WHM testing I've done already.

    For testing purposes (can be updated further.)

    Code:
    Spell		Recast	r
    Shell		5	20
    Protect II	5.25	21
    Cure II		5.5	22
    Protect IV	5.75	23
    Cure III	6	24
    1 BLM		6.5	26
    75 RDM		7	28
    4 BLU		7.25	29
    Deodorize	8	32
    9 BLM		9	36
    1 BLU		9.75	39
    Barfira		10	40
    Curaga II	10.25	41
    Curaga III	10.5	42
    Curaga IV	10.75	43
    15 BLM		11	44
    16 BLU		11.25	45
    17 BLM		11.5	46
    18 BLU		11.75	47
    Regen		12	48
    19 BLM		12.25	49
    21 BLM		13	52
    23 BLM		13.5	54
    26 BLU		14	56
    30 BLU		14.25	57
    26 BLM		14.5	58
    Protectra	15	60
    28 BLM		15.25	61
    30 BLM		15.75	63
    Protectra II	16	64
    32 BLM		16.5	66
    Protectra III	17	68
    36 BLM		17.75	71
    Protectra IV	18	72
    38 BLM		18.5	74
    40 BLM		19	76
    44 BLU		19.25	77
    18 BLU		19.5	78
    42 BLM		19.75	79
    Haste		20	80
    44 BLM		20.25	81
    46 BLM		21	84
    48 BLM		21.75	87
    51 BLM		22.5	90
    38 BLU		23	92
    53 BLM		23.25	93
    60 BLU		23.75	95
    Regen IV	24	96
    57 BLM		24.5	98
    59 BLM		25.25	101
    75 BLM		26	104
    62 BLM		26.5	106
    63 BLM		27.25	109
    64 BLM		27.75	111
    65 BLM		28.5	114
    66 BLM		29.25	117
    Stoneskin	30	120
    68 BLM		30.75	123
    69 BLM		31.5	126
    70 BLM		32	128
    71 BLM		32.75	131
    72 BLM		33.25	133
    50 BLU		33.75	135
    73 BLM		34	136
    58 BLU		34.5	138
    73 BLM		34.75	139
    74 BLM		36	144
    75 BLM		37.25	149
    61 BLU		39	156
    Cura II		40	160
    50 BLM		41.5	166
    52 BLM		42.25	169
    54 BLM		42.75	171
    58 BLM		43.75	175
    62 DRK		44	176
    60 BLM		44.5	178
    37 NIN		45	180
    71 BLU		49	196
    Cura III	50	200
    70 DRK		52	208
    61 BLU		56	224
    Reraise		60	240
    71 DRK		180	720

  18. #138
    Groinlonger
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    Code:
    f	h	Spell		Result	Predicted
    2	150	Protect IV	4	4
    2	150	Cure III	5	5
    2	150	Deodorize	6	6
    2	150	Curaga III	8	8
    2	150	Curaga IV	9	9
    2	150	Regen		10	10
    2	150	Protectra III	14	14
    2	150	Protectra IV	15	15
    2	150	Haste		16	16
    2	150	Stoneskin	25	25
    2	150	Cura II		33	33
    2	150	Cura III	42	42
    2	150	Reraise		50	50
    2	150	Aero		7	7
    2	150	Thunder		10	10
    2	150	Aeroga		11	11
    2	150	Firaga		12	12
    2	150	Water II	13	13
    2	150	Blizzaga	13	13
    2	150	Thundaga	14	14
    2	150	Fire II		15	15
    2	150	Stonega II	16	16
    2	150	Waterga II	17	17
    2	150	Thunder II	17	17
    2	150	Aeroga II	18	18
    8	150	Stone		5	5
    8	150	Aero		7	7
    8	150	Stonega		9	9
    8	150	Waterga		10	10
    8	150	Thunder		10	10
    8	150	Aeroga		11	11
    8	150	Stone II	11	11
    8	150	Protectra	12	12
    8	150	Water II	12	12
    8	150	Thundaga	14	14
    8	150	Fire II		15	15
    8	150	Blizzard II	16	16
    8	150	Waterga II	16	16
    8	150	Thunder II	17	17
    8	150	Aeroga II	17	17
    I'm pretty convinced at this point, unless someone turns up something that can refute it. Going to shift focus over to other recast sources to perhaps incorporate them into the final product.

  19. #139
    Groinlonger
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    I did some testing on SCH job abilities, but I don't have all of the extra gear, so it could use some additional verification.

    Testing I didn't record very well just showed it that Celerity/Alacrity overwrite Light/Dark arts (thus any gear that enhances light/dark arts will not do anything when those other Celerity/Penury are active.) The base appears to be 100, like Fast Cast, although the value is not divided for recast calculations.

    Code:
    s	f	h	Spell		Result	A	B	C	D
    10	15	0	Cure III	5	5	4	4	4
    10	15	0	Regen		10	10	9	9	9
    10	15	0	Stoneskin	25	25	24	25	24
    10	30	0	Protect II	4	4	3	3	3
    10	32	0	Protect II	3	3	3	3	3
    
    A	[[hfs]4]
    B	[[fh]s]4]
    C	[[s]fh]4]
    D	[[fh]4]s]
    The models A B C and D showing shorthand for the truncation order. Only one of them works.

    Code:
    R = [[(r*(100-[F/2])*(1024-h))*(100-s)/(1024*100*100)]/4]
    
    R	Final Recast
    r	Base Recast
    f	Fast Cast
    h	Haste
    s	Scholar
    More testing needs to be done on this, I didn't do much at all, just to show which one of those possible models it could be. There are many other ways to do it with just integers, although I assumed that the bases would stay with their numerators for each term when being truncated, and this is all of those possibilities.

    The value of s is an integer. Light/Arts is s = 10, gear that enhances it adds integer amounts (so relic head = +5, etc.) If Celerity/Penury are active, s = 50, and gear that enhances it adds integer amounts (relic +2 feet I think add 15.)

  20. #140
    Groinlonger
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    I forgot to test Manifestation/Accession. Confirmed all of the results from them that others had found. Adjusted to take this into consideration and narrowed down truncation order to the following.

    Code:
    R = [[(r*(100-[F/2])*(1024-h))*(s)/(1024*100*100)]/4]
    
    R	Final Recast
    r	Base Recast
    f	Fast Cast
    h	Haste
    s	Scholar
    
    	If Alacrity or Celerity or Manifestation or Accession process,s = (100-c)*(m)
    	If Alacrity or Celerity processes,c = 50 + bonuses from gear (integer values)
    	If Alacrity or Celerity don't process, c = 0
    	If Manifestation or Accession process,m = 2 if SCH main, m = 3 if SCH sub
    	If Manifestation or Accession don't process,m = 1
    
    	If neither Alacrity or Celerity or Manifestation or Accession process,s = (100-a)
    	If Light Arts or Dark Arts is active then
    	If spell matches grimoire, a = 10 + bonuses from gear (integer values)
    	If spell opposes grimoire, a = -20 (gear is ignored)
    	If no grimoires are active, then s = 100

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