RE: Master List of Game Formulae (Full Version)

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Kaelin -> RE: Master List of Game Formulae (9/7/2011 20:46:03)

@ArchMagus: That is the formula used for post-sweep (as seen in WF, but doubled in that game). AQ uses a different standard in the interim. Also, the multiplier for boss is not quite two. I have revised my sweep standards to include the discussion of monster rewards, both pre-sweep and post-sweep, so hopefully that'll clarify things a bit.

@TRB1965: I have added a spreadsheet that addresses the issue of the AQ daily caps, and I have also included columns for AQ post-sweep (or at least what it appears to be post-sweep) and WF.

@Razen: I have gone in an tried to answer your questions. Refer to [17], [18], and [21] for ~complete information.



marzx -> RE: Master List of Game Formulae (10/4/2011 20:16:50)

Removed post because my question was answered in a roundabout way during an earlier discussion concerning the weapon damage formula.



Watashig -> RE: Master List of Game Formulae (1/31/2012 23:33:21)

[13] Standard Monster Defense

Does this give the value before monster DEX/LUK? 200 DEX/LUK gives ~30 blocking, standard 130 monster has 80 AMD, and the formula gives me ~50. It looks like it all falls together nicely, but perhaps a clarification is needed?



Kaelin -> RE: Master List of Game Formulae (2/17/2012 8:18:32)

Sorry for the slow response...

I gave Defense (before accounting for monster stats) rather than AMD, since monsters are prone to use DEX and LUK values that don't fit the neat "DEX is secondary, capping at 200" and "LUK is tertiary, capping at 200" scheme. Granted, lots of monsters don't use standard Defense either, but they can usually be recognized as using modifications in multiples of 5.

I've added a note to the guide that hopefully clarifies this point.

[EDIT]: Okay, I've capitulated and added an AMD formula for the "default" monster build. You're going to want to enter this one into Excel or OpenOffice.



Avoleii Evanesca -> RE: Master List of Game Formulae (3/31/2012 23:56:46)

Since this guide is about game formulas, I'd like to reference about certain formulas that are apparently not yet included here.
(Unless it's just hidden within the great jumble of words in the guide and I just can't see it)Could it be possible to add in the "Common Damage Multipliers" the damage penalties that spells, skills or specials receive when associated with status conditions like burn, frozen, poisoned, etc..? I'm assuming it's *0.6X damage since so far that's the recent norm, unless the staff chooses it by by random everytime. But I'm very sure that there must be a standard for such penalties?
Also(If there is a set standard) the damage compensations for attacks locked to an element. So far, I've noticed *1.9X damage for same element at around ~lvl130 taking the Chillax Crusader and Guardian Block armors as reference, but then again it appears to be randomly chosen, else, scaled by level.








Kaelin -> RE: Master List of Game Formulae (4/23/2012 4:26:10)

Slow response, but here we go:

There's not a fixed compensation for being locked into elements. The multipliers depend on the armor's Resistance distribution and the choice of elements (and how much of each element is used), and not all the necessary information is available publicly. Level also indirectly affects the multipliers. Basically it's not possible right now, and even when it becomes possible, it probably won't be practical to include.

As for multipliers, the use of them depends on certain factors: the power of the attack being used (spells are stronger than Melee/Ranged weapon specials, which in turn are stronger than Magic weapon specials), the duration of the status, the save penalty/bonus, and (in some cases) the status effect's intensity. I may include some descriptions to assist here when I have the time, but they would not fit into the usual multiplier discussion.



Nex del Vida -> RE: Master List of Game Formulae (4/25/2012 22:00:03)

Not quite sure what happened, but the table of gold/XP caps is slightly wrong. My L91 character's cap is, according to the chart, 194150 gold--and yet he's currently at 199104 and still gaining.



Watashig -> RE: Master List of Game Formulae (4/25/2012 22:30:01)

@Avoleii Evanesca/Kaelin: Perhaps this information is what's needed for the element-locking-compensation.



Kaelin -> RE: Master List of Game Formulae (5/13/2012 0:40:45)

Nex: 194150 gold is the daily X-G gold cap for L88. I think you mistook row 91 for level 91.

Avoleii/Watashig: In terms of element-locking, the particular link works to a partial extent, although it does not fully explain how Chillax's regular attack works, which is locked in such a way that hits multiple elements. Furthermore, it does not explain what do to when element-locking results in an SP/MP cost reduction instead of a damage multiplier (although that information, like the information IMR gave, is embedded in the Armor spreadsheets). I'll see what I can do about that partial explanation later on, although I expect those standards to change in the future anyway.

I have added some notes about damage reductions to balance out stuff that causes status effects.



I will update this guide to reflect any XP/gold-related changes. There is no need to post a request, formula, or other information. Please wait until Saturday (June 9) to post concerning any missing or incorrect information.



Duskstar -> RE: Master List of Game Formulae (6/8/2012 7:29:21)

Sorry - I didn't see your post, instead hit reply right at the top of the thread on the other page :/

I started making something in Excel for the new Caps etc, and here's a table I made in the process, this is without the *1.1 X-G boost. The ratio basically shows how many levels you can get from capping, and as a point of interest, 115 is the point that you stop being able to gain a level a day, and is also the same 125 for X-Gs. 

Level	Gold Cap	Exp to Level	Exp Cap		Ratio (C:L)

0	2000		110		6000		54.54545
1	2022		121		6066		50.13223
2	2047		133		6140		46.16541
3	2073		146		6220		42.60274
4	2102		161		6307		39.17391
5	2133		177		6400		36.15819
6	2167		195		6500		33.33333
7	2202		214		6606		30.86916
8	2240		236		6721		28.47881
9	2281		259		6844		26.42471
10	2325		285		6976		24.47719
11	2372		314		7117		22.66561
12	2423		345		7268		21.06667
13	2476		380		7429		19.55
14	2534		418		7603		18.189
15	2596		459		7788		16.96732
16	2663		505		7988		15.81782
17	2734		556		8201		14.75
18	2810		612		8430		13.77451
19	2892		673		8675		12.89004
20	2980		740		8939		12.07973
21	3074		814		9221		11.32801
22	3175		895		9525		10.64246
23	3283		985		9850		10
24	3400		1083		10199		9.41736
25	3525		1192		10575		8.87164
26	3659		1311		10978		8.37376
27	3804		1442		11411		7.91331
28	3959		1586		11876		7.48802
29	4125		1745		12376		7.09226
30	4305		1919		12914		6.72955
31	4497		2111		13492		6.39128
32	4705		2323		14114		6.07576
33	4928		2555		14784		5.7863
34	5168		2810		15504		5.51744
35	5426		3091		16279		5.26658
36	5705		3400		17114		5.03353
37	6004		3740		18013		4.81631
38	6327		4114		18981		4.61376
39	6675		4526		20024		4.42422
40	7050		4979		21149		4.24764
41	7453		5476		22360		4.08327
42	7889		6024		23667		3.92878
43	8359		6626		25076		3.78449
44	8865		7289		26596		3.64879
45	9412		8018		28236		3.52158
46	10002		8820		30005		3.40193
47	10639		9702		31916		3.28963
48	11326		10672		33978		3.18385
49	12068		11739		36205		3.08416
50	12870		12913		38610		2.99001
Level	Gold Cap	Exp to Level	Exp Cap		Ratio (C:L)
51	13736		14204		41208		2.90115
52	14672		15625		44016		2.81702
53	15683		17187		47050		2.73753
54	16777		18906		50330		2.66212
55	17959		20797		53877		2.59061
56	19238		22876		57713		2.52286
57	20621		25164		61862		2.45835
58	22117		27680		66350		2.39704
59	23736		30448		71207		2.33864
60	25488		33493		76464		2.28298
61	27385		36842		82154		2.2299
62	29439		40527		88316		2.17919
63	31663		44579		94988		2.13078
64	34072		49037		102215		2.08445
65	36681		53941		110044		2.04008
66	39509		59335		118528		1.99761
67	42574		65268		127721		1.95687
68	45895		71795		137686		1.91777
69	49496		78975		148489		1.8802
70	53401		86872		160203		1.84413
71	57636		95559		172907		1.80943
72	62229		105115		186686		1.77602
73	67211		115627		201634		1.74383
74	72618		127190		217854		1.71282
75	78485		139908		235455		1.68293
76	84853		153899		254559		1.65407
77	91766		169289		275297		1.6262
78	99271		186218		297813		1.59927
79	107421		204840		322263		1.57324
80	116272		225324		348816		1.54806
81	125886		247856		377659		1.5237
82	136331		272642		408993		1.50011
83	147679		299906		443038		1.47726
84	160011		329897		480034		1.4551
85	173414		362887		520243		1.43362
86	187983		399175		563949		1.41279
87	203821		439093		611463		1.39256
88	221042		483002		663125		1.37292
89	239767		531302		719302		1.35385
90	260133		584432		780399		1.33531
91	282285		642876		846855		1.31729
92	306383		707163		919148		1.29977
93	332601		777880		997802		1.28272
94	361129		855668		1083386		1.26613
95	392174		941234		1176522		1.24998
96	425963		1035358		1277889		1.23425
97	462742		1138894		1388227		1.21893
98	502781		1252783		1508344		1.20399
99	546374		1378061		1639122		1.18944
100	593841		1515867		1781522		1.17525
Level	Gold Cap	Exp to Level	Exp Cap		Ratio (C:L)
101	645532		1667454		1936595		1.16141
102	701829		1834200		2105488		1.14791
103	763150		2017619		2289451		1.13473
104	829950		2219381		2489850		1.12187
105	902725		2441320		2708176		1.10931
106	982019		2685451		2946058		1.09704
107	1068425		2953997		3205274		1.08506
108	1162588		3249396		3487764		1.07336
109	1265216		3574336		3795649		1.06192
110	1377081		3931770		4131244		1.05073
111	1499026		4324946		4497079		1.0398
112	1631971		4757441		4895914		1.02911
113	1776923		5233185		5330768		1.01865
114	1934979		5756504		5804937		1.00841
115	2107340		6332154		6322021		0.9984
116	2295318		6965370		6885954		0.9886
117	2500345		7661907		7501036		0.979
118	2723988		8428097		8171963		0.96961
119	2967955		9270907		8903866		0.96041
120	3234119		10197998	9702357		0.9514
121	3524521		11217797	10573563	0.94257
122	3841395		12339577	11524186	0.93392
123	4187182		13573535	12561546	0.92544
124	4564550		14930888	13693649	0.91714
125	4976415		16423977	14929244	0.90899
126	5425966		18066375	16277897	0.90101
127	5916688		19873012	17750063	0.89317
128	6452392		21860313	19357176	0.88549
129	7037245		24046345	21111736	0.87796
130	7675803		26450979	23027410	0.87057
131	8373049		29096077	25119146	0.86332
132	9134429		32005685	27403286	0.8562
133	9965902		35206253	29897705	0.84922
134	10873984	38726879	32621951	0.84236
135	11865801	42599567	35597404	0.83563
136	12949150	46859523	38847449	0.82902
137	14132555	51545476	42397665	0.82253
138	15425344	56700023	46276033	0.81616
139	16837721	62370026	50513162	0.80989
140	18380846	68607028	55142538	0.80374
141	20066932	75467731	60200796	0.7977
142	21909340	83014504	65728021	0.79177
143	23922689	91315954	71768068	0.78593
144	26122975	100447550	78368926	0.7802
145	28527702	110492305	85583106	0.77456
146	31156024	121541535	93468073	0.76902
147	34028904	133695689	102086713	0.76358
148	37169283	147065258	111507849	0.75822
149	40602268	161771784	121806805	0.75295
150	43741791


One other thing, I see you've done cumulative Exp already, but how would I go about working out the amount of days capped to reach the new level, or basically, how would I get the average daily cap from one level to another?



Kaelin -> RE: Master List of Game Formulae (6/8/2012 23:20:06)

I've already done an XP list (posted on Thursday, in fact), so there's no need to make one (it also has cumulative XP rolled in). I haven't uploaded a table for daily caps yet, but as I stated in the guide (in the Edit Log section) and in my previous post, I'll update things when I have the chance. Please do not try to supply this information yourself, because it can have errors (your list does not round XP for XP-to-level to the nearest 10 as it should) or it may not fit the format I want to use for the guide. In most cases, I have already have tables, but I need to make some revisions or format changes here or there.

I will need another day to get this guide up to date, so please be patient. It should be ready by Sunday (server time). If you still see problems at that point, then please let me know.



[EDIT]: Okay, the guide should be up to date.

[EDIT]: Rolled stat price training update. The guide gets a slight bit shorter.

[Small EDIT]: For kicks, I've simplified/factored the HP/MP formulas. They aren't much shorter, but they should be easier to use. If you've got something like 50 END at L90, it should be reasonable enough to perform a calculation of [(90/20 + 1)(50 + 100)]. Even if the division is "hard" for you, it's easy to take a calculator to divide 90/20, add 1, and then multiply 150 (that last sum should be easy to do in your head!)



TRB1965 -> RE: Master List of Game Formulae (7/8/2012 23:26:32)

@Kaelin - any updates on the daily cap formulas? When calculated as stated above (I get the same numbers as you), they are a little bit.

The formula says a level 120 x-guardian should experience cap at 10,672,592. My level 120 X-guardian capped at somewhere between 10,509,397 and 10,559,386. And he's not the only one. In the Erebus war there was pretty much a consensus that everyone was capping somewhere between 96% and 98% of the listed values. But there was no consistency to it, so it appears to be a rounding issues somewhere, but I tried every way I can of rounding the formula and it's various components and found nothing that works.



Golden Emperor -> RE: Master List of Game Formulae (7/20/2012 17:15:31)

[11] Monster Encounter Levels

According to your formula the lowest level monster I can encounter is 97.75.

1) I still encounter bun-bards at lvl 95 in random battles, why is that?

2) Are numbers rounded normally, down, or up?


@TRB1965 I'm having the same issues as you, the thing is, the cap always seems to be lower than stated, I wonder if it is because numbers are always rounded down (eg 97.75 rounded to 97)?



Dev -> RE: Master List of Game Formulae (7/25/2012 19:26:16)

AQ Daily EXP Cap: (3*1.055^Lvl+24+3*1.055^(Lvl^1.085))*200 (*1.1 for X-Guardians)
AQ Daily Gold Cap: (1.055^Lvl+8+1.055^(Lvl^1.085))*200 (*1.1 for X-Guardians)

WF Daily EXP Cap: (3*1.055^Lvl+24+3*1.055^(Lvl^1.085))*400
WF Daily Gold cap: (1.055^Lvl+8+1.055^(Lvl^1.085))*400






ugauga -> RE: Master List of Game Formulae (8/2/2012 15:25:29)

I have a doubt about rounding numbers. I will use the number 123,45 as example:

Round off the contents in the brackets to the nearest integer.
123,45 = 123

"[ ]" = Round down the contents in the brackets to the nearest integer.
123,45 = 123 (same result than Round Down?)



Duskstar -> RE: Master List of Game Formulae (8/14/2012 11:55:00)

quote:

Damage Reduction: (Expected Status Attempt Rate) * [50 - (Enemy's Save Bonus)] * (Effect Value)

In section 23, I'm just wondering about the above. That can be re-arranged by:

Damage Reduction = (Expected Status Attempt Rate) * [50 - (Enemy's Save Bonus)] * (Effect Value)
Damage Reduction / (Effect Value) = (Expected Status Attempt Rate) * [50 - (Enemy's Save Bonus)]
(Effect Value) = (Expected Status Attempt Rate) * [50 - (Enemy's Save Bonus)] * Damage Reduction

Which to me looks like if the enemy get's a negative save bonus, so basically a save penalty, the value of the effect should be greater, and hence, using DoT effects like Poison as an example, the Poison effect can either deal more damage, or last longer, in return for Poison being easier to inflict. If it's supposed to be + then I have no problem, or if I have arranged it wrong, then please do say :)



Dragoon23 -> RE: Master List of Game Formulae (9/16/2012 4:28:12)

For your Monster MP:

Monster HP = (MonsterSetHP + END*1.5) * Random Number Between 0.950-1.050
Monster MP = (MonsterSetHP + INT*1.5) * Random Number Between 0.950-1.050

^ is that suppose to be setHP or setMP since right above it you mention sethp/mp:

MonsterSetHP/MP = Each monster has a set amount of HP/MP they get as a "base" amount (Example: a Frogzard has a set HP of 30). The "END" and "INT" below are the values belonging to the monster rather than the player.



Kaelin -> RE: Master List of Game Formulae (9/16/2012 4:51:18)

ugauga: Yes, sometimes rounding off (to the nearest) give the same result as rounding down.

Duskstar: Yes, if an enemy receives a negative save bonus, it means the effect has a higher chance of inflicting, which makes the impact of the status effect stronger.

"Effect Value" is basically in the equation to stand for how much impact a status effect will have (once it is inflicted). For one turn of paralysis, this would be 1.4, since that is the expected damage a player would do (in terms of Melee units) in their free turn. Weaker status effects (like -50 DEX for one turn, or a Blind worth -10 BtH) would receive a small multiplier, and thus the damage reduction for them would be much less.

The reason my equation is arranged the way it is is to dictate how much of a penalty the weapon (or spell, or pet, or whatever) takes in order to produce the given effect given the other parameters. Certainly if you want to know how power a status effect is rated to be, you can rewrite your equation in the way you have, but the equation is written in a way to explain how calculations are handled (I think) by the Knights.

Dragoon23: Thank you!



Duskstar -> RE: Master List of Game Formulae (9/24/2012 16:39:55)

Okay, I guess I kind of read it the wrong way, and so got confused. Thanks for clarifying that :)

Also, because I noticed you didn't have it, I've got a weapon special B/R and SLS formula which rolls the proc rate in as well:

SBR: =(ROUND((((((0.8*((((«Weapon Base»+(«Weapon Random»/2))*(100+(3*«Power Level»)))+((((MROUND(MIN(((2.1462*«Power Level»)+10.399),200),5))/8)*(100+(6.6*«Power Level»)))/2))/100))+(0.2*(ROUND(((((-0.00000349*(«Power Level»^3))+(0.000552*(B3^2)))+(0.0801*«Power Level»))+1.67),2)*(«Weapon Base»+(«Weapon Random»/2)))))-((1-(20/100))*((((«Weapon Base»+(«Weapon Random»/2))*(100+(3*«Power Level»)))+((((MROUND(MIN(((2.1462*«Power Level»)+10.399),200),5))/8)*(100+(6.6*«Power Level»)))/2))/100)))*100)/((20/100)*(«Weapon Base»+(0.5*«Weapon Random»)))),0)/100) {{this is the bit which rolls in the proc rate}}*((1 - 0.91*(1-«Proc Rate»))/«Proc Rate»)/(1.5*0.91)

I had *0.9 first, but 0.91 just rounded up nicer.

However, I appreciate that the rest of it is more than extremely messy, so I'll see if I can simplify it in any way. The SLS one's much nicer:

SLS: =ROUND((100+(«Power Level»*6.6)),0)/100*((1 - 0.9*(1-«Proc Rate»))/«Proc Rate»)/(1.5*0.9)

I don't know if you want them or not, but I've noticed you don't have it, so there you go :)



Kaelin -> RE: Master List of Game Formulae (10/9/2012 21:47:23)

I'll be looking at this issue (and updating things for the cap raise) within a few days.



Flamey123 -> RE: Master List of Game Formulae (12/31/2012 3:14:27)

What's the difference between Weapon Special Hit Rate and Special Rate?

EDIT - THANKS Watashig :)



Watashig -> RE: Master List of Game Formulae (12/31/2012 3:23:14)

The former is the frequency in which the weapon special hits or misses. The latter is the frequency in which the weapon special occurs, or procs.



Flamey123 -> RE: Master List of Game Formulae (12/31/2012 4:04:38)

quote:

(Weapon Base) * (Armor Base) + (Weapon Random) * (Armor Random) / 2 + (Stat Damage) * (Armor Stat) / 2


Over here, which part(s) is divided by 2?
Is it (Weapon Base) * (Armor Base) + (Weapon Random) * (Armor Random) / 2
or is it (Weapon Random) * (Armor Random) / 2



Watashig -> RE: Master List of Game Formulae (12/31/2012 4:07:31)

Remember the order of operations, which is in the beginning:

quote:

2) Order of Operations:

As in all mathematics, expressions are simplified in the order below.
[a] Parentheses: Anything inside parentheses takes priority. When there are multiple layers of parentheses, simplify the innermost layers first.
[b] Exponents: Exponents come next. Work left to right.
[c] Multiplication and Division: Both of these operations are done next. Work left to right.
[d] Addition and Subtraction: Both of these operations are last. Work left to right.

Example:
3 - 4 * (5 + 3 ^ 3) / 8
= 3 - 4 * (5 + 27) / 8 <-- First we work inside the parentheses. The Exponent takes priority over the Addition.
= 3 - 4 * (32) / 8 <-- We do the addition in the parentheses.
= 3 - 4 * 32 / 8
= 3 - 128 / 8 <-- Multiplication and Division have priority over the Subtraction, so we work the Multiplication left to right.
= 3 - 16
= -13


It's the latter, because division comes before addition. So if I had a weapon with 16 base and 32 random, in an armor with 669% base/random, we'd have:

16 * 669% + 32 * 669% / 2 + stats
= 107.04 + 214.08 / 2 + stats
= 107.04 + 107.04 + stats
= 214.08 + stats



Flamey123 -> RE: Master List of Game Formulae (12/31/2012 4:11:41)

Thanks again, I took Ice Dragon Blade

EDIT : I got it, thanks for your time and help :D



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