Some Aran Calculations

Because Aran really looks like a fun class to play, and because I like statistics and calculations, I decided to kill some boredom by doing some Aran-calculations. =) The calculations are about what skill to max first for maximal damage output.

Note: The calculations are outdated. There are some numbers changed, the biggest being the damage distribution of one skill over several monsters. The exact numbers of that are unknown at the time, making these calculations worthless for now. Therefore, I've put the old calculations in a spoiler. =)

 Spoiler

Second Job

The first one is for the second job skillbuild. In the 2nd job, the Aran has 3 main skills which increases the amount of damage. The info is taken from the Aran Skill Tables.

Polearm Mastery
Description: [Mastery Level : 20] Raise the proficiency and accuracy while using a polearm. This skill will only be applied while using a polearm.
Requires: Level 3 Triple Swing, Completing a Level 31 Quest
Max Level: 20

Level 1: 15% Mastery, Accuracy +1
Level 20: 60% Mastery, Accuracy +20


Triple Swing
Description: [Mastery Level : 20] Press the attack key three times to attack your enemy three times.
Requires: Level 20 Double Swing
Max Level: 20

Level 1: 196% damage, Attacks 12 enemies
Level 20: 250% damage, Attacks 12 enemies


Combo Smash
Description: [Mastery Level : 20] Throw a polearm at your enemy. Can only be used when the Combo Counter is higher than 30. [To invoke : ↓ → + Skill Key]
Requires: Level 1 Combo Ability, Completing a Level 45 Quest
Max Level: 20

Level 1: 320% damage, Attacks 4 enemies, 450 Range
Level 20: 700% damage, Attacks 10 enemies, 450 Range


The software I used for the calculations is Wolfrom Mathematica 7.0. For the boring details, open the Spoiler. =)

 Spoiler

The input is this:

Short Explaination:
* dam is the average damage depending on the amount of mastery.
* Double, Triple and Smash are the formula for the skills Double Swing, Triple Swing and Combo Smash respectively. Mastery is the formula for Polearm Mastery.
* SPSmash is the damage if you have tot[i] amount of sp, where you put [i]i points in Triple Swing, j points in Combo Smash and tot-i-j points in Polearm Mastery. With alot of lines to prevent the skills to go over 20 SP each.
The damage is when you use Triple Swing 10 times, or at 10 monsters (resulting in getting 30 combo) and then using Combo Smash.
* The lowest table is finding the highest amount of damage for a single amount of SP s, also showing it how much i and j you've used plus 1, because I run it from 0 to 20 instead of 1 tot 20. Then running a table over it to get past all the 60 SP till all the 3 skills are maxed.

Note: I haven't taken into account that you need to be a certain level to unlock certain skills, but by saving SP at those points, you get the same amount of damage at the level the skill is unlocked.

And here is the output:
From left to right: SP in Triple Swing +1, SP in Combo Smash +1, Amount of Damage


The results for the build with the most damage:

#	Triple Swing	Combo Smash	Polearm Mastery
1	1	0	0
2	2	0	0
3	3	0	0
4	3	0	1
5	3	0	2
6	3	0	3
7	3	0	4
8	3	0	5
9	3	0	6
10	3	0	7
11	3	0	8
12	3	0	9
13	3	0	10
14	3	0	11
15	3	0	12
16	3	0	13
17	3	0	14
18	3	0	15
19	3	0	16
20	3	0	17
21	3	0	18
22	3	0	19
23	4	0	19
24	5	0	19
25	6	0	19
26	7	0	19
27	8	0	19
28	9	0	19
29	10	0	19
30	11	0	19
31	12	0	19
32	13	0	19
33	14	0	19
34	15	0	19
35	16	0	19
36	17	0	19
37	18	0	19
38	19	0	19
39	20	0	19
40	20	1	19
41	20	2	19
42	20	3	19
43	20	4	19
44	20	5	19
45	20	6	19
46	20	7	19
47	20	8	19
48	20	9	19
49	20	10	19
50	20	11	19
51	20	12	19
52	20	13	19
53	20	15	19
54	20	15	19
55	20	16	19
56	20	17	19
57	20	18	19
58	20	19	19
59	20	20	19
60	20	20	20

The result is that the strongest way to distribute the first 60 SP is:

Level 30: 1 Triple Swing (1)
Level 31: 2 Triple Swing (3) 1 Polearm Mastery (1)
Level 32 to 37: 3 Polearm Mastery (19)
Level 38 to 42: 3 Triple Swing (18)
Level 43: 2 Triple Swing (20). Save 1 SP
Level 44: Save 3 SP
Level 45: 7 Combo Smash (7)
Level 46 to 49: 3 Combo Smash (19)
Level 50: 1 Combo Smash (20) Putting points in the other skills.

As an extra check, what will be the difference at level 45 between 19 Mastery, 20 Triple Swing and 7 Polearm Smash; and 19 Mastery, 7 Triple Swing and 20 Polearm Smash:

20 Triple, 7 Smash: (100% + 140% + 250%) *10 + 440% = 4900 + 440 = 5340% after 10 attacks + Smash
7 Triple, 20 Smash: (100% + 140% + 211%) *10 + 700% = 4510 + 700 = 5210% after 10 attacks + Smash

As you can see, the difference isn't that great, it's only 2.4952% stronger, and this is only if you do it perfectly. Some factors which can make it less perfect:
*You don't get at exactly 30 combo, because of a big mob. If you still use Combo Smash as fast as possible, this means that the Triple Swing damage goes up a bit and the Max Triple build is a bit stronger.
*Combo Smash hits less monsters then Triple Swing, especially at lower levels. This way the +440% or +700% doesn't count for every monster you would hit with Triple Swing, making the Max Triple build a bit stronger.
*Combo Smash hits more monsters then Triple Swing, because of the range. This way the Triple Swing damage doesn't count for these extra monsters, making the Max Smash build a bit stronger.

Also note that you most like train in very in maps with very high spawn, and therefore you get to 30 combo very fast (3 to 4 Triple Swings) or even higher combo.

Third Job

Next is the third job skillbuild. This one is a bit more complex then the 2nd job, because instead of 3 damage-increasing skills, you have 4 now. And instead of one effective way to train (Getting your combo to 30 and use Polearm Smash), you have three: The old 2nd job way, getting your combo at 100 and use Phantom Peril, or don't use a finisher at all and get your combo as high as possible so you take advantage of Critical Combo.

First the four skills, this time taken from Strategywiki

Full Swing
Description: [Mastery Level : 20] Use Double Swing and Triple Swing together for a more powerful attack.
Requires: Level 20 Triple Swing
Max Level: 20

Level 1: Extra Double Swing: 74% damage, MP -6, Attacks 12 enemies. Triple Swing Damage: 278% damage, MP -8, Attacks 12 enemies.
Level 20: Extra Double Swing: 110% damage, MP -12, Attacks 12 enemies. Triple Swing Damage: 350% damage, MP -14, Attacks 12 enemies.

Note: From what I've heard from KMS players, Full Swing - Double Swing and Full Swing - Triple Swing are combined in 1 skill Full Swing. So when you put 1 point in Full Swing, it counts as 1 point in both Full Swing skills, therefore I combined both skills in 1 skill, as Strategywiki does.


Snow Charge
Description: [Mastery Level : 20] Grants the ice element to the Polearm. The enemy is slowed for a duration after being attacked.
Max Level: 20

Level 1: MP -25, 100% damage, 10 Seconds, Slows enemies by -21, Slow for 5 sec., 13% Elemental
Level 20: MP -35, 110% damage, 200 Seconds, Slows enemies by -40, Slow for 20 sec., 100% Elemental

Note: In the calculations, I'm only looking at neutral monsters, ignoring the slow-effect and the duration of the skill.


Combo Peril
Description: [Mastery Level : 30] The soul of a wolf is summoned to attack the enemy twice. Can only be used when the Combo Counter is greater than 100. [To invoke : ↓ → + Skill Key]
Requires: Level 10 Combo Smash
Max Level: 30


Level 1: 510% damage, Attacks 4 enemies, 600 Range, Attacks 2 Times
Level 30: 800% damage, Attacks 10 enemies, 600 Range, Attacks 2 Times


Combo Critical
Description: [Mastery Level : 20] After every attack, receive a 10% chance to increase the critical attack rate and hit.
Requires: Level 10 Combo Ability
Max Level: 20


Level 1: +1% Probability, +1% Critical Damage, Stacks 1 Times
Level 20: +6% Probability, +10% Critical Damage, Stacks 6 Times

Note: The amounts are different from the Aran Skill Tables. The Aran Skill tables are the first version of the skills, while most skills have been finetuned to the versions at Strategywiki.
From what I've heard from other KMS players, Critical Combo has a base Crit-chance of 10%, and a base Crit damage of +100%. That means that at level 1, the maximal amount of criticals would be 10% + 1%*1 = 11% crit chance for 100% + 1%*1 = +101% damage. At level 20, the max crit chance is 10% + 6%*10 = 70% crit chance for 100% + 10%*10 = +200% damage. That's a huge amount, way higher then the Critical skills from other classes.

Here are the boring calculations again:

 Spoiler

The input for the skills:

*Triple, Crit, Slash, Peril and Snow are the formula for respectively Triple Swing with Full Swing, Critical Combo, 2nd job Polearm Slash, Phantom Peril and Snow Charge
*Crit has an interesting formula, because it's depended on the amount of combo you have.
*Dam is the average damage range, I gave my example a damage range of 1000~600.

Here we are calculating again which build does the most damage:

*SP1 calculates the damage using the Polearm Slash method, SP2 using the Phantom Peril method and SP3 the Critical Combo method.
*SP1, SP2 and SP3 calculates how much damage you do when you put i points in Full Swing, j points in Critical Combo, k points in Snow Charge and tot-i-j-k points in Phantom Peril. With alot for lines to prevent them to prevent skills go over their max level. All three also take into account that with the first 10 attacks, you have no criticals, with the 2nd 10 attack the criticals stack 1 time, ect. Because SP1 uses 30 attacks while SP2 and SP3 uses 100 attacks, the damage of SP1 is multiplied with 10/3.
*Lazy1, Lazy2 and Lazy3 calculates which build does the most damage when you have n[/n] amount of SP to distribute, using method 1, 2 or 3. Then running a table over it for all the 90 SP when all skills are maxed.
*VeryLazy calculates of the three builds calculated at Lazy1, Lazy2 and Lazy3, which one does the most damage.

It was a very long calculation, and my fairly fast computer took 48 minutes to calculate it. Therefore, I have the results in a graph:

The blue dots are method 1 (Combo Smash). The red dots are method 2 (Phantom Peril) and the yellow lines are method 3 (Critical Combo).
*Method 1 (blue) has the build: Max Full Swing -> Max Snow Charge -> Max Critical Combo. Critical doesn't increase the damage that much, because you'll never get past 30 combo.
*Method 2 (red) has the build: 1 Full Swing -> 1 Phantom Peril -> Max Full Swing -> Max Snow Charge -> Max Critical Combo -> Max Phantom Peril.
* Method 3 has a strange increase around 15-20 SP. Plus the calculated build is strange: First it raises Full Swing to 15, while at 16 SP, it completely reverts it to 16 Critical Combo. Because I assume you don't want to waste SP Resets just to do a bit more damage the first 5 levels, I also plotted the green dots. This is the damage when you max Critical Combo first.
- After that, you get a mix of skills for maximal damage output, because with the big amount of damage due of criticals, Snow Charge increases the damage about the same % as Triple Swing. So after maxing Critical Combo, you get 12 Snow Charge -> 1 Full Swing, 1 Snow Charge till you have 8 Full Swing, 20 Snow Charge -> Maxing Full Swing.

As you can see, 3 skills are lineair, but Critical Combo is quadratic. It explains the green/yellow dots at the beginning, and the red dots from 40 - 50 SP.

But, these calculations are the perfect example again. And the biggest factor which doesn't make it perfect is, that in method 3, you don't always have above 100 combo, you have a 'startup time' of the first 100 combo before you can deal damage with the criticals of awesomeness. Therefore, I decided to run more calculations, hurray! This time, we compare 2 builds:

*Build 1: Max Triple Swing -> Max Snow Charge -> Max Critical Combo
*Build 2: 1 Triple Swing -> Max Critical Combo -> 12 Snow Charge -> 1 Snow Charge and 1 Full Swing 8 times, till you have 20 Snow Charge and 8 Full Swing -> Max Full Swing.

Then we compare the three methods again, but only the strongest one as calculated in the previous spoiler.

First comparison is, when following Build 2, how high does your combo need to be to get more damage using Method 3 compared to using Method 1 (30 combo -> Polearm Slash). The results:

SP	Combo
1 to 17 SP	Never
18 and 19 SP	173
20 SP	132
21 SP and higher	118

So when for example you've put 20 SP following Build 2, you need to have to reach higher then 132 combo to be stronger then the Polearm Slash method.


Next comparison is Method 3 (Critical Combo) using Build 2 (Critical Combo first Build) versus Method 1 (Polearm Slash) using Build 1 (late-Critical Combo Build). So when you're an Aran following Build 2, how high does your combo has to be to outdamage an Aran follwing Build 2 and Method 1. The results:

SP	Combo
1 to 19	Never
20	854
21 to 34 SP	408-405
35 to 41 SP	358-353
42	320
43	320
44	294
45	251
46	251
47	235
48	208
49	196
50	186
51	176
52	168
53	160
54	154
55	147
56	141
57	135
58	131
59	126
60	121
61 and higher	118

From 21 to 41, it goes slowly down because both builds max Snow Charge at this moment, which multiplies both damages with the same numbers, resulting in the same damage ratio.
After 41, Method 3 starts with Full Swing while Method 1 does Combo Critical now. And after 61 SP, you get the same results as the first calculation, because now all 3 skills are maxed.


Last one: We compare using Method 2 (Phantom Peril) using Build 1 (late-Critical) versus Method 3 (Critical Combo) using Build 2 (Critical first). Because according to the graph in the spoiler, Method 2 is stronger then Method 1 after 56 SP, we only look after 56 SP.

The results:

SP	Combo
56-61	130
62	139
63	140
64	141
65	141
66	142
67	143
68	144
69	145
70	146
71	147
72	148
73	148
74	149
75	150
76	151
77	152
78	153
79	154
80	155
81	156
82	157
83	158
84	159
85	160
86	161
87	162
88	164
89	165
90+	166

After 90 SP, both builds have all 4 skills maxed.

Conclusion
If you think you can't make it past the 'hell levels' 70-77, go with Build 1 and use the Polearm Slash Method 1 till 56 SP = level 88. After that, use the Phantom Peril Method or if your think your average Combo will exceed the values of the last table, go for the no finisher method.

If you want to go for Critical First, use the Build 2, and use the Polearm Slash method till at least 19 SP = level 76. After that, if your number exceeds the number from the first table (which isn't that high, after level 77 it's only 118), don't use a finisher. After that, when you're maxing Phantom Peril (which is from level 90 till 100), use the numbers from the last table to see if using Phantom Peril or not is beneficial.

[i]Build 1:
Use the 30 combo -> Polearm Slash method
Level 70: 1 Triple Swing (1)
Level 71-76: 3 Triple Swing (19)
Level 77: 1 Triple Swing (20), 2 Snow Charge (2)
Level 78-83: 3 Snow Charge (20)
Level 84-87: 3 Critical Combo (12)
Use Phantom Peril now as your finisher instead of Polearm Slash, for combo's higher then the last table
Level 88: 1 Phantom Peril (1) 2 Critical Combo (14)
Level 89 & 90: 3 Critical Combo (20)
Level 91-99: 3 Phantom Peril (29)
Level 100: 1 Phantom Peril (30) and putting points in the other skills.

Build 2:
Use the 30 combo -> Polearm Slash method
Level 70: 1 Triple Swing
Level 71-76: 3 Critical Combo (18)
Don't use a finisher after this point if your combo get's higher then the first table
Level 77: 2 Critical Combo (20) 1 Snow Charge (1)
Level 78-80: 3 Snow Charge (13)
Level 81-85: 1.5 Snow Charge (20), 1.5 Full Swing (8)
Level 86-89: 3 Full Swing (19)
Use Phantom Peril as your finisher at this point when your combo doesn't exceed the amount as in the last table
Level 90: 1 Full Swing (20) 2 Phantom Peril
Level 91-99: 3 Phantom Peril (29)
Level 100: 1 Phantom Peril (30) and putting points in other skills.

That's it.

This is the first time posting something for this, so sorry for the sloppiness and my not so perfect English. =( But I hope I helped some of you.