Wednesday, May 22, 2013

Ragnarok Online 2 Assassin and Thief Skills Analysis


Table of contents
  • Introduction and purpose
  • Theory basis
  • Combo Points and Combo Training / Mastery
  • Consuming Skills
  • Generating Skills
  • Utility Damage Skills
  • Buffs
  • Usage Ratio
  • Conclusion
  • Word from the Author
Introduction and purpose
This is an in-depth analysis of the Assassin and Thief skills, providing an overview of how much damage each skill(point) will provide with the intention of optimizing Assassin DPS builds and build paths.
The information presented will be extensive and detailed. If you spot any errors, please let me know and I’ll correct them.

Theory basis
To build this theory we have to take two things in consideration:
Frequency of skills and DPS
Whilst in theory a skill may have a 0 second cast time and a 1 second after-cast delay, in practice there will be delays, either by lag or player reaction time. To rule these factors out for this theory, they will simply be ignored and henceforth we will presume that every skill takes exactly 1 second to perform, i.e. after 10 seconds, 10 skills will have been performed.
Skill Damage
In RO2, skill damage are displayed as a percentage of Attack Damage: “Obtain 1 Combo Point. Attack enemy to inflict attack damage of 25%”
From this point on, I will refer to the percentages of attack damage as Attack Damage Percentage, or ADP, which will be the basis for determining how much damage one will do.
Our ratio: ADP/S
Because we earlier stated that we will presume we will perform 1 skill per second, we can extend the use of this number to ADP per skill, or ADP per second: ADP/S. To value a spended skill point, i.e. a level in a skill, I shall list the ADP value of a level of a skill and the increase in ADP/S per level. The latter is important, as this will take cooldown into account, while the former will not. For Thief or Assassin skills, cast time is not an issue as it is always instant.
Combo Points and Combo Training / Mastery
The Thief / Assassin mechanic in RO2 is “Combo Points”. One can generate up to 5 combo points using a Generation Skill (discussed in detail later on) and then consume them using a Consumer Skill (discussed in more later on.)
Relevance of Deadly Blow
To grasp what combo points are for, let’s take a quick look at the two consumer skills:
  • Deadly Blow: Consume all combo points for 7% ADP per point.
  • Shadow Explosion: Requires and consumes 5 combo points
Shadow Explosion is a (the) high damage burst skill with a high cooldown, therefore having 5 combo points at the time this skill can be used is trivial. That leaves us with Deadly Blow to evaluate the damage value of combo points.
To illustrate the generation and consumption of points we will use Double Attack (25 ADP) and Deadly Blow (25 ADP + 7 ADP per point.) Assume that one would only use Deadly Blow in a series of 6 attacks: this would result in doing 6 * 25 = 150 ADP. Now consider doing a DB after obtaining 5 points: 5 * 25 + 1 * 25 + 5 * 7 = 185 ADP. Proper mathematical proof aside, as you can see, using Deadly Blow after obtaining 5 combo points in a series of attacks is the most efficient way of dealing damage using these two skills.
Combo Training / Mastery
“Combo Training (Passive)
Description: Use skills that obtain combo points to obtain additional 1 combo point with 5%/10%/15% probability.”
The Combo Training skill is by far the hardest Thief / Assassin skill to rate for ADP/S. First of all, it does not really add any real damage. After all it simply offers you the chance of reaching 5 combo points faster. This in turn, however, does allow you to use the optimized damage from a 5 point Deadly Blow more often, increasing your overall damage.
To calculate the value of combo points, let us consider the ADP per skill for this scenario: 5 Double Attacks + 1 Deadly Blow = 185 ADP / 6 skills = 30.83 ADP. The base damages for these skills were 25 ADP each, so let’s subtract 150, leaving us with 5.83 ADP per obtained and consumed combo point, thus per skill, and use that as our basis.
The basis assumes Combo Training level 0: you will always need 5 generation attacks and 1 finisher. Now let’s assume Combo Training level 1, a prerequisite skill for your assassin skills, so you will always have this. Level 1 gives you 5% chance to generate an additional combo point when using a Generation Skill. This means you will now (on average) need less than 5 attacks to do your 5 point Deadly Blow. To be exact:
  • Chance of 5 points after 3 attacks: 0.007250
  • Chance of 5 points after 4 attacks: 0.171475
  • Chance of 5 points after 5 attacks: 0.821275
Which results in an average of 4.814 attacks needed to obtain 5 points. Instead of needed 5+1 skills for 35 ADP, we now only need 4.814 + 1 skills, bringing the combo point to 6.02 ADP/S (from 5.83 on lvl 0.) Calculating these numbers for every level (5%, 10%, 15%) we can display the ADP/S for this skill:
  • 6.02 (+0.187)
  • 6.19 (+0.172)
  • 6.35 (+0.160)
As you can see, the overall theoretical damage increase given by each point in Combo Training is quite low.
Consuming Skills
In this section I will briefly list all consumer skills and their ADP and ADP/S increases per level.
Deadly Blow
Consumes all combo points.
Cooldown: instant
  • 17 + 7/point
  • 19 + 7/point (+2)
  • 21 + 7/point (+2)
  • 23 + 7/point (+2)
  • 25 + 7/point (+2)
Shadow Explosion
Requires and consumes 5 combo points.
Cooldown: 20s.
  • 67 (+3.35)
  • 72 (+0.25)
  • 76 (+0.25)
  • 81 (+0.25)
  • 85 (+0.25)
Generating Skills
In this section I will briefly list all point generating skills and their ADP and ADP/S increases per level.
Double Attack
Generate 1 combo point.
Cooldown: instant
  • 17
  • 19 (+2)
  • 21 (+2)
  • 23 (+2)
  • 25 (+2)
Dark Illusion
Generate 1 combo point.
Hiding required.
Always crits. This makes this skill somewhat hard to calcute as we do not take critical rate into account in this model.
Cooldown: instant
  • 17
  • 19 (+2)
  • 21 (+2)
  • 23 (+2)
  • 25 (+2)
Cross Impact
Generate 1 combo point.
Cooldown: 8s
  • 17 (+2.125)
  • 19 (+0.25)
  • 21 (+0.25)
  • 24 (+0.375)
  • 26 (+0.25)
Grimtooth
Up to 3 enemies: values listed for 3 enemies and single target hit.
Generate 1 combo point.
Cooldown: 10s
  • 48 (+4.8) or 16 (+1.6)
  • 54 (+0.6) or 18 (+0.2)
  • 60 (+0.6) or 20 (+0.2)
  • 66 (+0.6) or 22 (+0.2)
  • 72 (+0.6) or 24 (+0.2)
Shadow Strike
Generate 3 combo points.
Cooldown: 20s
  • 28 (+1.4)
  • 32 (+0.2)
  • 35 (+0.15)
  • 38 (+0.15)
  • 42 (+0.2)
Utility Damage Skills
In this section I will briefly list all other skills and their ADP and ADP/S increases per level.
Dagger Throwing
Ranged attack, primarily used to lure mobs.
Cooldown: 8s
  • 18 (+2.25)
  • 21 (+0.375)
  • 23 (+0.25)
  • 25 (+0.25)
Meteor Assault
Up to 3 enemies: values listed for 3 enemies and single target hit.
Cooldown: 3s
  • 51 (+17) or 17 (+5.67)
  • 60 (+3) or 20 (+1)
  • 69 (+3) or 23 (+1)
Shadow Fang
Up to 10 enemies. This skill description is rather vague and I have never verified the real coefficients per enemy hit. The effect seems greatest between 3 and 6 enemies, so I will list values for 6, 3 and 1 enemy.
Cooldown: 0s
  • 54 (+54) or 27 (+27) or 9 (+9)
  • 60 (+6) or 30 (+3) or 10 (+1)
  • 72 (+12) or 36 (+6) or 12 (+2)
Shadow Assault
Leap and 3 second knock down.
Cooldown: 20s
  • 26 (+1.3)
  • 29 (+0.15)
  • 32 (+0.15)
  • 35 (+0.15)
  • 38 (+0.15)
Buffs
In this section I will briefly list all buffs and what they will do for the ADP/S of and Assassin. Before I get to the skills however, we will have to address critical strikes. To again simplify our model, we will assume that critical strikes deal twice as much damage as a normal attack. I have found no evidence for this claim, nor can I find any other numbers to back this up, hence we will use this as an assumption. To express the effect of critical strikes, let’s assume that 25 critical hits out of 100 hits increased our damage by 25 hits (i.e. 25 out of those 100 hit twice.) On average, one might say that every percent of critical chance will result in 1% extra damage.
Genocide Mark
30 minute party buff
  • 0.4% (+0.4%)
  • 0.8% (+0.4%)
  • 1.2% (+0.4%)
  • 1.6% (+0.4%)
  • 2.0% (+0.4%)
Shadow Cloak
30 minute self buff
  • 1% (+1%)
  • 2% (+1%)
  • 3% (+1%)
  • 4% (+1%)
  • 5% (+1%)
Shadow Form
Increases Attack Damage and Movement Speed by a percentage, thus increases all damage output.
self buff
  • 6% (+6%)
  • 12% (+6%)
  • 18% (+6%)
  • 24% (+6%)
  • 30% (+6%)
Poisoning Weapon
30% to apply a Damage over Time debuff.
Assuming you applied this debuff on an enemy you will inflict
  • 5 ADP/S (+5)
  • 5.5 ADP/S (+0.5)
  • 6 ADP/S (+0.5)
  • 6.5 ADP/S (+0.5)
  • 7.5 ADP/S (+1)
Shadow Fiend
Generating Skills have a chance to inflict extra 22 ADP. The listed values assume that 75% of used skills are Generating skills, hence the number is 0.75 * percentage * 22.
  • 0.66 (+0.66)
  • 1.32 (+0.66)
  • 1.98 (+0.66)
Hiding
Stealths the thief and causes the first attack to be done to deal double damage.
Can only be used out of combat.
  • 40% slowed
  • 20% slowed (+0)
  • 0% slowed (+0)
Cloak Hiding
Improves movement speed while in hiding.
  • 10% (+0)
  • 20% (+0)
  • 30% (+0)
Usage Ratios
In this section, I will address the usage ratio problem.
Some considerations
  • For Shadow Fiend, I took into account the fact that roughly 75% of used skills skill be point generating skills. This however, should be applied to all generating and consuming skills.
  • Point generating skills may eventually “use” the generated points in the form of a consumer. Therefore it would make sense to include consumer damage in generator damage.
  • ADP/S is a ratio when one would use that skill and that skill only. It is only natural that using other skills will drop the actual ADP/S of a skill. For example: assume a series of 5 Double Attacks followed by a Deadly Blow. If one could invest 4 skill points, where should one invest those points? The presented ADP/S for each investment seems to be +2, but if skill usage is taken into account one would soon see that a skill point invested in Double Attack would result in +10 ADP over the series while the skill point in Deadly Blow only results in +2.
Full Single Target Combo
Consider the 2 finishers: Deadly Blow (17~25 + 35) and Shadow Explosion (67~85) As can be seen, Shadow Explosion deals more damage at level 1 than Deadly Blow at level 5, but keeping its cooldown in mind you could say that for every Shadow Explosion, one would do 3 Deadly Blows during the 20 second cooldown (explosion > 4.5x > blow > 4.5x > blow > 4.5x > blow > 4.5x > explosion) – for more details on the 4.5 I used, visit the Combo Training section higher up.
This brings us to the full combo (or rotation) discussion. I briefly discussed the ratio between Deadly Blow and Shadow Explosion, so let us stick with these numbers:
  • Shadow Explosion: 5% (1 in 20)
  • Deadly Blow: 15% (3 in 20)
Now that we know how often these skills are used, we can redefine the amount of ADP an invested skill point would give us:
  • Shadow Explosion: 0.1675 ADP/S for the first and 0.0125 ADP/S for each subsequent level.
  • Deadly Blow: 0.3 ADP/S for each subsequent level
One could conclude that if one had 1 point to spare, it would be better to put it in Deadly Blow 5 than to unlock or level Shadow Explosion.
As for generating skills, let me first annotate them on whether you will be using them:
  • Double Attack: no cooldown, 25 ADP
  • Grimtooth: 10s cooldown, 24 ADP
  • Cross Impact: 8s cooldown, 26 ADP
  • Dark Illusion: 3s cooldown, 25 ADP, stealth (thus out of combat) only
  • Shadow Strike: 20s cooldown, 42 ADP, generates 3 points!
If we are to generate points, Double Attack seems the obvious choice over Grimtooth, Cross Impact and Dark Illusion. Shadow Strike brings more damage and 3 points, at the cost of a 20 second cooldown.
Let’s consider Double Attack and Shadow Strike as our generating skills and add them to the 20 skill rotation:
  • Shadow Explosion: 5% (1 in 20)
  • Deadly Blow: 15% (3 in 20)
  • Shadow Strike: 5% (1 in 20)
  • Deadly Blow: 75% (15 in 20)
Small note: 15 + 3 points are generated without taking Combo Training into regard. Even at level 1 this skill will generate an addition 0.75 combo points for this series, bringing the average to 18.8 combo points. Level 3 will grant us 17.25 + 3 = 20.25 combo points. One would almost think Gravity thought this through when they designed it.
The resulting ADP/S per level is as follows:
  • Shadow Strike: 0.07 ADP/S for the first and 0.01 ADP/S for each subsequent level.
  • Double Attack: 1.5 ADP/S for each subsequent level
Combo Point values for this combo
As it turns out, Shadow Explosion deals 8.4~12 ADP per combo point if you were to use the same 25 ADP as its base damage and as you all know: Deadly Blow deals 7. When using the 1/3/1/15 ratios I used above you would end up on average 8.25 ADP per obtained combo point and Combo Training makes it so you obtain these combo points faster. With the ratios above, i.e. 16 generating attacks, you would generate an additional 3.9% / 7.5% / 10.9% points (this is based on the chances of getting to 5 combo points faster, refer back to the Combo Training section.) This brings the numbers for Combo Training to
  • 0.32 ADP/S
  • 0.30 ADP/S
  • 0.28 ADP/S
Conclusion
A brief recap:
  • ADP: Attack Damage Point or Attack Damage Percent, based on the percentage damage a skill inflicts.
  • ADP/S: ADP per Skill: the amount of ADP the skill or level of the skill will contribute to the total DPS when the skill is used in a rotation.
  • Usage Ratio: The assumed occurrence of a skill within a rotation, usually based on a 20 skill rotation.
Before I present the final numbers, I want to address one issue left untouched:
Single Target vs Multi Target
To better understand the point I am about to make, please view this list. Assume the Assassin is facing a group of 3 enemies:
  • Grimtooth: 7.2 ADP/S (+1 combo point) (0.5 mana / s)
  • Meteor Assault: 23 ADP/S (1 mana / s)
  • Shadow Fang: 36 ADP/S (5 mana / s)
A quick calculation learns that the single target rotation above with the 4 skills on level 5 will yield 682 ADP, so 34.1 ADP/S. As you can see, this number gets VERY close to using Shadow Fang (your best AoE option) in terms of simple DPS. Furthermore, the single target rotation will use 43 mana to execute 20 skills while 20 Shadow Fangs consumes 100 mana.
Naturally, when facing more than 3 enemies, Shadow Fang will prove to be stronger, but in this case, when facing up to 3 enemies the Single Target Damage Rotation is in favour.
Skill ADP/S including Usage Ratio
                        Per level       Level 1
Skill           Ratio   ADP/S   inc %   ADP/S

Deadly Blow     15%     0.30    1.3%    2.55
Shadow Expl     5%      0.25    1.1%    3.35

Double Attack   75%     1.50    6.6%    12.75
Dark Illusion   0%      0.00    0.0%    0.00
Cross Impact    40%     0.80    3.5%    6.80
Shadow Strike   5%      0.20    0.9%    1.40

Dagger Throwing 40%     0.80    3.5%    7.20
Shadow Assault  5%      0.15    0.7%    1.30

Genocide Mark   100%            0.4%    0.00
Shadow Cloak    100%            1.0%    0.00
Shadow Form     100%            6.0%    0.00
Poisoning Weap  100%    0.50    2.2%    5.00
Shadow Fiend    80%     0.70    3.1%    0.70
Combo Training  80%     0.29    0.9%    0.29 (Shadow Expl 1)
Combo Training  80%     0.33    1.0%    0.33 (Shadow Expl 5)

Meteor Assault  15%     1.35            7.65
Shadow Fang     100%    3.00            27.00
Grimtooth       50%     3.00            24.00
How to read:
  • Ratio: the assumed ratio this skill will be used in a rotation.
  • ADP/S: the ADP per Skill spending 1 skill point in this skill will yield. For instance: if a rotation would use both Double Attack and Cross Impact on level 1, investing one skill in either would result in an increase of the listed ADP/S.
  • Increase: the increase in ADP/S overall, based on a lvl 1 rotation of 5x Double Attack > Deadly Blow.
  • Level 1 ADP/S: the ADP per Skill from spending 1 skill point to unlock this skill. Do note it will replace the other basic skill within this category, i.e. Cross Impact or Shadow Strike would replace one Double Attack
While these numbers seem odd (Shadow Strike will result in higher total ADP when used in a rotation than Cross Impact) keep in mind that these numbers are the values based on Usage Ratio, i.e. if you were to consider investing your next skill point, the highest value in the list over the skills you are using in your rotation would likely be your best investment.
Conclusion
When looking at the ADP/S increases, a few skills get high marks. Double Attack and Shadow Form seem to be must level skills, providing around 6% damage increase per spent skill point. When looking at the finishers it turns out to be more worthwhile to invest in Deadly Blow than it would be to invest in Shadow Explosion and as it turns out it appears that the buffs provide big damage increases per point spentas well. While Shadow Fiend provides a higher per-level increase than Poisoning Weapon, the latter gives a huge damage increase on the first skill point spent and is (based on ADP) the skill a thief should get as soon as possible.
Assuming the Assassin would have all skills on level 1 and uses all of them, either as a buff or in a rotation, the priority of investing skill points would be as follows:
  • Shadow Form Buff
  • Double Attack (Thief)
  • Shadow Fiend Buff
  • Poisoning Weapon (Thief)
  • Shadow Cloak Buff
  • Combo Mastery Buff (Thief)
  • Deadly Blow (Thief)
  • Shadow Explosion
  • Shadow Strike
  • Genocide Mark Buff (Thief)
Now again, these are assuming you already have unlocked these skills and you are using them. Unlocking will overrule upgrading as it will increase the total ADP of a rotation (buffs are an exception.)
Word from the Author
If you made it this far, you must be as crazy in the head as I am
So, this all began because I once joined a discussion on whether Combo Training was worth the points or not. We tried to express combo points as damage and soon figured out that this was rather hard and somewhat depending on your Shadow Explosion skill level. The first thing to consider was that it’s not really 5% per level. After all, generating an additional point when you already have 4 stacked up is a bit useless, so instead we calculated how many attacks you would need on average to reach 5 combo points. We found out that the skill gave roughly the same damage increase as Deadly Blow does, at least for the second point. The third point would rank a little lower, but still around the same increase.
I hope you found this information useful, you can use it as a theoretical backing for your skill builds or as a guide on build order. Either way, thanks for reading.