SWTOR Mechanics Basics: Understanding Expected Damage
Preface for 3.0: This article has been updated for 3.0. Nothing substantive changed in the information presented here due to 3.0.
- 1 Intro
- 2 Chance to Hit
- 3 Type of Hit
- 4 Target’s Armor
- 5 Reviewing the Two Roll System
- 6 Combining the Three Factors to Calculate Expected Damage
- 7 Summary
Last time – and it was quite awhile ago – we examined how Tooltip Damage values were calculated, and I mentioned that tooltips do not tell all of the story. Here I will try to outline more of the story, although there will be a third article on the subject that examines DoTs, stacks and other oddities.
To start, I want to introduce the concept of expected damage. Let’s assume an attack does 3,000 damage and has a 90% chance to hit, a 33% chance to critically hit for 5,250. How much damage should we expect from one use of this attack?
If we recorded 10 uses of this attack we could expect the following:
Given the table above we expect 10 uses of the attack to do 33,750 damage and a single use of the attack does, on average, 3,375 damage. This is expected damage; it is the amount of damage, on average, we expect from the attack. Notice not a single hit actually did 3,375 damage, but we still assert that an average hit will do 3,375 damage.
In SWTOR, there are three factors that influence the expected damage of an ability given specific tooltip damage. In other words, after your tooltip damage range has been calculated these three factors will be applied: Chance to Hit, Type of Hit and the Target’s Armor. Understanding these three factors allows us to calculate our expected damage and helps us make better decisions on gearing our characters. While the information discussed here is applicable for characters of any level, I have focused this on Elder Game scenarios.
Chance to Hit
Your chance to hit depends on your Accuracy and your target’s Defense Chance. Any Accuracy above 100% Accuracy will reduce your target’s Defense Chance. Let’s examine these two factors:
In SWTOR, Accuracy is the likelihood that your attack will successfully hit your target. Your Character Sheet only shows a summary of your Melee/Ranged Basic Accuracy and Force/Tech Accuracy:
You may not know but all classes have three different Accuracy values, and Dual Wielding classes have five. The values are:
- Melee/Ranged Basic Accuracy
- Off-Hand Melee/Ranged Basic Accuracy (Dual Wielders Only)
- Melee/Ranged Special Accuracy
- Off-Hand Melee/Ranged Special Accuracy (Dual Wielders Only)
- Force/Tech Accuracy
You can see all of these values by mousing over the Accuracy in your Character Sheet; a new tooltip will open that provides more detail and shows the Special Accuracy.
This shows the Melee Accuracy from a Marauder/Sentinel. Notice there are four different Accuracy values. As you can see, the base value for Melee/Ranged Basic Accuracy is 90% and the base value for Melee/Ranged Special Attacks is 100%. With the exception of your basic attack, all of your abilities are either Melee/Ranged Special Attacks.
Off-Hand base values are 57% and 67% for Basic Attacks and Special Attacks, respectively. Off-Hand Accuracy receives the same bonus as the Main Hand.
Next, your Force/Tech Accuracy is effectively the same as your Special Attack Accuracy. Its base value is 100% and it receives the same bonuses.
Accuracy Rating is a stat found on gear specifically Enhancements and potentially Earpieces, Implants, and Augments. In the picture above, Skills/Buffs total 4%. This includes the 1% Accuracy Buff from reaching max affection with your melee tank companion. The remaining 3% comes from a skill in one of the skill trees; however, with the release of 3.0 we no longer have access to this talent.
In SWTOR, Defense Chance increases the likelihood that you will successfully avoid an attack. When a target successfully defends against an attack all damage is negated. In combat logs this is recorded as any of the following: Miss, Dodge, Parry. Each NPC and Player has a Defense Chance. You can easily see your Defense Chance on your Character Sheet. Everyone has a base Defense Chance of 5%.Beginning in 2.0, Champion NPCs and above (including Operation’s Bosses) have a 10% Defense Chance for all attacks. And, Elite NPCs have a 5% Defense Chance against all attacks.
By hovering over the Defense Chance, you will see:
Applying Chance to Hit to Expected Damage
If your Special and Force/Tech Accuracy is 110% or more, you can effectively ignore this factor when calculating expected damage as the extra 10%+ Accuracy will negate the Operation Boss’s 10% Defense Chance. In the case of Off-Hand hits as well as your basic attack, you will need to adjust your Tooltip Damage by this factor: Accuracy * (1-Defense Chance).
Type of Hit
The second factor that determines your expected damage is the type of hit, including a critical hit, a shielded hit, or a normal hit. Critical hits do increased damage, shielded hits do reduced damage and normal hits are unaffected. The likelihood of a critical hit is based on your Critical Chance while the likelihood of a shielded hit is based on your target’s Shield Chance. Both of these chances are easy to see on your Character Sheet.
Any hit that is not a critical hit or shielded hit will be a normal hit. Once it has been determined that you successfully hit your target, the game determines the type of hit.
Critical Chance vs. Shield Chance
In the event that Critical Chance plus Shield Chance is greater than 100%, Critical Chance will override the Shield Chance. For example, if Critical Chance was 50% and Shield Chance was 60%, Shield Chance would effectively be reduced to 50%. Notice there is no opportunity for a normal hit in this scenario.
The most common manifestation of this is when hits have a 100% Critical Chance. This phenomenon applies to incoming hits as well. Specifically, tanks will never be able to shield a critical hit.
Determining the Magnitude of a Critical Hit
Your Critical Multiplier represents the increased damage done by a critical hit. Here we see a Critical Multiplier of 72.96%.
Thus, a critical hit will do all of the damage of a normal hit and then 72.96% more damage or 172.96% of the damage of a normal hit.
Your Critical Multiplier has a base value of 50%. This amount is increased via your Surge Rating and other buffs. For example, reaching max affection with your melee DPS companion will grant you +1% to your Critical Multiplier. Typically, there will be a skill in your skill tree that “…increases the critical strike damage…” of one or more attacks. The quoted text indicates the skill will increase your Critical Multiplier.
Applying Type of Hit to Expected Damage
As a rule, NPCs do not have a shield, so for Elder Game content there are two possible outcomes a normal hit and a critical hit. The magnitude of the hit – given you actually hit – equals a weighted average of the two possible outcomes.
For example, if we have an attack that does base damage of 3,000 and a 30% Critical Chance and a 75% Critical Multiplier, how much damage should we expect? To start, we can calculate the damage of a critical hit; it is 3,000 * 175% = 5,250. Our Critical Chance tells us this should happen 30% of the time. The remaining 70% will be a normal hit of 3,000. We can do a weighted average of the two outcomes to determine the magnitude of hit:
30% * 5,250 + 70% * 3,000 = 3675
While doing this weighted average approach is always valid, the process can be simplified with this formula:
Normal Hit * [1 + (Critical Chance * Critical Multiplier)]
The third factor affecting expected damage is the target’s armor. Specifically, armor will mitigate some of the Energy and Kinetic damage dealt.
Please note that damage type is independent of attack type. Often, but not always, the Tooltip for each attack will list what type of damage it deals.
Operation’s Bosses have 35% Armor Damage Reduction. Thus, only 65% of the damage from Energy and Kinetic hits will actually damage the boss.
Reducing a Target’s Armor
In 3.0, SWTOR expanded the availability of the Sundered debuff, which reduces the targets armor rating 20%. We can effectively think about this as the 35% Armor Damage Reduction being reduced to 28%.
However, behind the scenes the Armor Rating is changed which lessens the Armor Damage Reduction. This is a linear relationship between Armor Rating and Armor Damage Reduction.
Reviewing the Two Roll System
I did not expressly present SWTOR’s two-roll combat system even though the pieces of it are explained in the Chance to Hit and Type of Hit sections. It is worth reviewing in its entirety. The two-roll system governs all combat in SWOTR, including NPCs’ attacks on player characters. The first roll determines whether or not your attack will hit your target. The probability of a hit is increased based on your Accuracy. And, the probability of a miss is increased by your target’s Defense Chance. Assuming your attack hits the target a second roll occurs. This roll determines if you do a critical hit, a shielded hit, or a normal hit. Critical Chance will override Shield Chance when their sum is greater than 100%.
Combining the Three Factors to Calculate Expected Damage
Like last article, I am going to use Rail Shot as my example.
Recall the three components that affect Tooltip Damage are Weapon Damage, Damage Bonus & Base Level Damage. We previously established the following:
- Main Hand Weapon Damage ranging from 679 to 1,262
- Damage Bonus of 2,222
- Base Level Damage of 542
- Off-Hand Weapon Damage ranging from 204 to 379
The average total Main Hand damage is:
(679 + 1,262)/2 + 2,222 + 542 = 3,735
And, the average Off-Hand damage is:
(204 + 379)/2 = 292
Since we are estimating the expected damage we can average the minimum and maximum weapon damage values.
Next, let’s assume the following:
- Main Hand Special Accuracy of 110%
- Off-Hand Special Accuracy of 77%
- Critical Chance of 30%
- Critical Multiplier of 75%
- Target’s Armor Mitigation of 35%
Our expected damage from the Main Hand is equal to:
3,735 * [1 + (30% * 75%)] * (1 – 35%) = 2,974
Our expected damage from the Off-Hand is equal to:
[ 77% * (100% – 10%)] * 292 * [1 + (30% * 75%)] * (1 – 35%) = 161
By adding these two amounts together, we get 3,135 which is the expected damage of a single use of Rail Shot. Again, we are unlikely to see this specific amount register in our combat log, but this should be the value if we average every Rail Shot in our Combat Log. Notice these three factors are multiplicative so it does not matter what order we put them in.
We can combine our tooltip damage calculations with the three expected damage factors to determine, on average, the outcome of an attack. It is important to model each individual attack as many attacks have unique factors such has a higher Critical Chance or the ability to bypass a percent of the target’s armor. Altogether this allows us to understand the best attacks to use and the best stats for our gear.
About the author
Oofalong is a well known theorycrafter from <The Chandrian> guild on the of The Shadowlands server and has contributed immensely to both the theorycrafting community on the SWTOR official forums and previously on mmo-mechanics.com. He aspires to help others understand the game’s mechanics and bring civility to SWTOR forums everywhere.