*Preface for 3.0: This article has been updated for 3.0. Nothing substantive changed in the information presented here due to 3.0.*

[toc]

### Intro

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:

Use # | Result | Damage |

1 | Normal Hit | 3,000 |

2 | Normal Hit | 3,000 |

3 | Critical Hit | 5,250 |

4 | Normal Hit | 3,000 |

5 | Critical Hit | 5,250 |

6 | Miss | 0 |

7 | Normal Hit | 3,000 |

8 | Critical Hit | 5,250 |

9 | Normal Hit | 3,000 |

10 | Normal Hit | 3,000 |

Total Damage |
33,750 |

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

**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.**

*expected damage*### 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:

#### Accuracy

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.

#### Defense

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)]*

### Target’s Armor

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.

### Summary

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.

## 45 replies on “SWTOR Mechanics Basics: Understanding Expected Damage”

I was under the impression Defense was rolled, and only subtracted if Accuracy is greater than 100%.

For cases where accuracy is less than 100%, this would mean

to_hit = hit_chance * chance_to_not_dodge.

In other words; Accuracy * (1 – Defense).

A concrete example, with Accuracy 0.9, Defense 0.1

By your method; 0.9 – 0.1 = 0.8.

By my method; 0.9 * (1 – 0.1) = 0.81.

Minor difference, but important. Which is correct?

I believe my method is correct. As evidence under your methodology, we would expect Off-Hand attacks to hit exactly as often as their listed Accuracy. I just reviewed a log for my Merc. I had a total of 154 OH attempts, and 47 misses. This is an effective hit rate of 69.5%, yet my listed Accuracy is 77.43%. Thus, I believe the target’s 10% Defense Chance reduces my effective OH Accuracy to 67.43%. My observed value is much closer to this. Based on this, it is statistically possible that your method could be correct, but it is far more likely that my method is correct.

Actually, his method is closer to your effective hit rate:

0.7743* (1 – 0.1) = 0.6968 or 69.68%, which is only 0.18% off of your effective hit rate instead of your method’s 2.07% off.

His method is what I’ve been told before.

Hmm, this is interesting. I guess I am confused by “…Defense was rolled, and only subtracted if Accuracy is greater than 100%”. In his example, Defense still hinders Chance to Hit even if it does not exceed.

I see three possible scenarios:

1: Accuracy – Defense = Chance to Hit

2: Accuracy * (1- Defense) = Chance to Hit

3: Accuracy * if[Accuracy > 1 , Defense – (Accuracy -1) , (1 – Defense)]

I had interpreted John Adams method as #2, which I feel most confident is not correct. If #2 was correct, I would expect to see some MH & Force/Tech attacks miss. I just combined a number of logs for my Merc, and got 14,428 such data points. Not a single miss. My Accuracy is 110.43%, so method 2 would indicate Chance to Hit is 99.387%. With 14,000+ attempts I would expect 88 misses, but not a single one was observed.

To compare method 1 and 3, I created this spreadsheet. https://docs.google.com/spreadsheets/d/16r5qp5AQ4mb1VeRIsZIDqk8wXgEnerp-OK5f_Ni-zK0/edit#gid=0

With my amalgamated combat log, I had 4,448 OH attempts and observed 1,386 misses. This equates to Chance to Hit rate of 68.84%; my OH Accuracy is 76.67%. This scenario is modeled in row 57 of my spreadsheet. Using method 1, we would expect Chance to Hit to be 66.7%. Using Method 3 we would expect Chance to Hit to be 69.0%. Clearly, method 3 more closely equals my observed data. So it does seem method 3 is more accurate, and potentially, correct. This surprises me as it is very complex for a marginal difference.

Apologies, i oversimplified to focus on the case i was most interested in. My precise formulas is:

h(accuracy, defense) = (min(1, min(1, accuracy) * (max(1, accuracy) – defense)))

The outer minimum handles the case where accuracy – defense > 1 (i assume you can’t have a to_hit chance greater than 1).

I think this is the same as your method #3.

Simplifying your formula may make comparison easier:

Accuracy * if[Accuracy > 1 , (Defense – Accuracy + 1) , (1 – Defense)]

Yes it is. When I first modeled these in excel I used the ‘outer minimum’, but in the version I published I omitted the extra formula as it is already complex enough. Thanks again for pointing this out.

Thank you for taking the time to answer my question.

Also, thank you for the excellent articles. I’m looking forward to future ones.

Hopefully, it doesn’t take me so long to write the next one.

Nice article! Thank you very much for the info. Is that your character name on POT5? Maybe I’ll see you around sometime.

Yeah Oofalong is my Marauder on Pot5. Unfortunately, I don’t get to play him as much as I’d like. Oofalong is also my SWTOR forum user name. I am one of the noobs who named everything the same thing. I was even the Oofalong Legacy for a while until we got the free name change.

Hahaha, no worries…RL has taken precedence in my household lately, so I’m also not on as much as I like. I’ll keep an eye out for you. I typically am on my Merc (Geejzo) or my Mara (Rebzogi). Take care, and hope to see you.

Under “Applying Type of Hit to Expected Damage”, there’s a typo. It currently reads:

“30% * 5,250 + 70% * 3,000 = 2,856″

but it should read

30% * 5,250 + 70% * 3,000 = 3,675”

which makes sense, since with no shield chance and 100% hit rate, the expected damage MUST be greater than the base damage of 3000.

Tried posting exactly the same couple of hours ago but somehow lost it & then got involved in guild ops runs. Other than that another great article.

sorry must have been a typo. I will get this fixed

thanks for pointing this out

Ok, my question is, why are some of my hits 5000 dmg and some 11000 dmg? Its really the same move (Force Sweep), they are always criticals, yet some hit 5k-6k and some hit 10k-11k I don’t get it. This makes the difference parsing, I compared my parsing with other people with Dot-smash and they did almost identical rotations but their moves simply hit for more and we had really almost identical gear, this is the aspect of the game which I don’t get.

post a link to your combat log

Hi,

don’t know why but torparse.com is acting crazy for me. This is one of them, not the latest though http://torparse.com/a/622096/6/0/Overiew

Wait, this one is a bit more recent http://www.torparse.com/a/643798 its the one from 18:25 to 18:33

For the first 10k damage attack, you have the Singularity buff, which increased damage of Force Sweep by 33%. This is done before the critical multiplier, which is causing your damage to almost double.

18:25:57.464 Merovejec’s Force Sweep critically hits Operations Training Dummy for 9762* kinetic damage, causing 9762threat!

18:25:57.657 Merovejec loses Singularity.

Second time, you do not have Singularity and only do 5.6k damage:

18:26:09.181 Merovejec’s Force Sweep critically hits Operations Training Dummy for 5616* kinetic damage, causing 5616threat!

You can see this repeated in the 3rd and 4th times (once with Singularity, once without):

18:26:18.399 Merovejec’s Force Sweep critically hits Operations Training Dummy for 9345* kinetic damage, causing 9345threat!

18:26:18.588 Merovejec loses Singularity.

18:26:27.728 Merovejec’s Force Sweep critically hits Operations Training Dummy for 4801* kinetic damage, causing 4801threat!

Hi all,

thnx for the hints, will try to adapt the rotation. However cant get Singularity up everytime cause I don’t have Force Exhaustion. Still the other guys attacks did more dmg in general (Dispatch, Slash etc)

The downside of using DotSweep spec is that only every other Sweep will have the Singularity buff:

http://dulfy.net/2014/02/11/swtor-sentinel-dps-class-guide/#5

4.7 Rotation Strategy

“Unfortunately without Force Exhaustion only every other Force Sweep benefits from Singularity,”

Your rotation looks fine. Just realize that every other Sweep will do almost double damage.

Depends if you are in berserk or not you get 100% bonus damage from berserk in dotsmash

Not 100% bonus damage, but 33.33% damage increase before Critical Multiplier:

From Singularity’s description:

Zen in Shii-Cho form grants 3 stacks of Singularity, reducing the focus cost and increasing the damage dealt by your next Force Sweep by 33.33%.

If you active berserk is 3×33.3 so its almost 100% 🙂

In 2.0, BioWare stated that all champion bosses, including ones in Flashpoints and Operations have a 10% defense chance for Force/Tech. All elite bosses have a 5% defense chance for Force/Tech:

http://www.swtor.com/patchnotes/2.0-rothc/rise-hutt-cartel-and-scum-and-villainy

”

Enemies of Elite toughness now have 5% Force and Tech defense, and enemies of Champion toughness have 10% Force and Tech defense. This gives greater chance of resisting Force and Tech attacks, and increases the importance of Accuracy when fighting Elite enemies.”

Thanks, I remembered hearing this at the time, but I couldn’t find the specifics so I didn’t quote it. I will update the article.

Can you elaborate on this part please?

“If you have combat fly-text turned, you will see the damage types are color-coded. White Damage is Energy and Kinetic, and this damage type is mitigated by armor. The Yellow damage is Internal and Elemental damage, and is not mitigated by armor. 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.”

So far, I have been under the impression that the flytext color denoted the type of the attack, not the type of the damage. (E.g. white = weapon attack (melee/ranged/special); yellow = Force/Tech). For example, Demolition Round/Heatseeker missle has yellow flytext but it deals kinetic damage according to the tooltip. (As you can see in this link: http://www.swtor-spy.com/skill-tree-calculator/commando/23/ ) So it’s a Tech attack with kinetic damage that is mitigated by armor, hence the yellow text.

My question is: Why is the flytext of Demolition Round / Arsenal Yellow when it deals kinetic damage? Does attack type (Force/Tech/Basic/Special) influence the color in any way?

Thanks.

Sorry, I don’t know what I was thinking here; I guess I too got confused by attack type and damage type.

White = Melee/Ranged Attacks

Yellow = Force/Tech Attacks

Between the fact that BW has changed the combat system over time and I have a bad memory I made the following SWTOR combat presentation to remind myself of the details:

https://docs.google.com/presentation/d/1fA9jLxQi0-eebkFUTRmOzS5QjU6wq-_kCqvDo9rca58/edit?usp=sharing

If you see any mistakes in my slide deck email me gmail.com — funkyj.

I don’t take much notice of the flytext me how does one know if it crits? Does “crit” come up?.

So if I’m understanding it correct than I always calculated the armorpen from skilltree’s wrong? For example a SS-slinger has 10% armorpen on all attacks. I assumed the expected damage after DR to be like this:

( 1 – 35% + 10% )

If I understand it correctly it should have been

( 1 – 35% * 90% )

/facepalm ….

Thanks for this guide oofalong. You just resparkeld my interrest in working on my spreadsheet which calculates the actual damage done by abilities. The idea is that when you upload combatlogs to torparse I could determine what the difference in damage would have been with different stats.

Its not 100% accurate ofc since parses contain lots of RNG but your guide should help me and others to gear up more efficiently 🙂

Correct, 10% armor pen would effectively reduce the Armor Mitigation by 3.5%. This looks like: [ 1 – (35% * (100% – x%))]. In your case x =10%. If you also added the Mercenary/Commando 20% debuff then x would become 30%. This is why I presented my formula this way.

I’m wondering if armour penetration isn’t calculated as:

(1 – f(7538.5 * (1 – 0.1)))

= (1 – f(7538.5 * 0.9))

= (1 – f(6784.7))

= (1 – 0.3264)

= 0.67357

where “f” is the function armour_rating -> damage_reduction, 7538.5 is the armour rating that gives 0.35 damage reduction, and the armour penetration in question is 0.1 (copying from the original post question).

This is compared to 0.685 using the above method.

I really don’t know, but i’m hoping Oofalong does.

You are correct here; there is an armor rating that gets reduced. Since I didn’t go into the the detailed calculation of Armor Rating, I sort of generalized the Armor Reduction calculation. I suppose I should fix this or go into more detail to ensure the best possible info.

damage reduction:

armour_rating / ( armour_rating + 240 * level + 800 )

The constants are “240” (multiplicative) and “800” (additive). I’m not sure if they are the same below level 51.

Your calculation and result and mine are the same. 🙂 So it does appear my suspicion was correct. Thank you for confirming it. I don’t get to ask these questions elsewhere, so i really appreciate your time.

Nitpick: Consulars and Inquisitors have a base defence of 10%.

Dumb question: For Carnage would it be worth it to have the same number of Acc pieces as non-Carnage marauders? Would the extra to-hit on your off-hand weapon be a dps increase?

Carnage takes 2-3 acc pieces where Anni and Rage take 4-5… offhand accuracy is insignificant as offhand damage is < 8% of your mainhand damage. Get mainhand to 100% acc and your set. I carry an extra set of implants w/ pwr-srg for carnage

My question is in regards to the Critical Chance vs Shield Chance. I do not understand why this is correlated. Isn’t the roll on a crit (attacker), separate from the roll on shield (receiver)? Thanks in advance.

The answer is that they are not separate – they’re decided in the same roll.

If you have 30% crit chance, and your target has 40% shield chance, then the chance of each outcome is:

30% critical hit (damage boosted by crit multiplier %)

40% shielded hit (damage reduced by target absorb %)

And so the remainder = (100 – 30 – 40) =

30% normal hit

If crit chance + shield chance > 100% then there is no chance of a normal hit, and crit pushes shield off the result table.

Is the Expected damage example a bit misleading in the Intro section? If chance to hit is 0.9, critical chance is 0.33 and we assume the two-roll system, wouldn’t the expected damage then be 0.9 * (0.33 * 5250 + 0.66 * 3000) = 3341 instead?

Stupid me: Of course the example is correct. 33% would refer to 1/3 (and 66% to 2/3), so I have a small rounding issue in my calculation. Forget my post.

Do you assume that chance to hit is normally distributed? In that case, have you done any confidence intervals?

I am not sure how Chance to Hit/Accuracy’s distribution matters although I would suggest its binomial distribution. I believe the Weapon’s damage is normally distributed.

In any event, I haven’t done any confidence intervals or hypothesis testing.