# Thread: How to Evaluate/Compare Different Damage Bonuses Reliably

1. ## How to Evaluate/Compare Different Damage Bonuses Reliably

Damage Equation with Critical Hits

Or
How to evaluate/compare different damage bonuses reliably

I often see discussions about critical hit multipliers, critical hit chance, and offence % bonus. Those discussions always seem biased one way or another with people using nothing but their impressions or gut feeling while affirming that one is better than the other. I will attempt to show here how to calculate the effect of such factors in an objective manner.

The damage equation, taking into account offence, critical hits and devastating critical hits, is as follows:
(I derive this equation in a following post in this thread for those who are interested)
Dc = Dn*(1+F) * (1 + C*M + V*N)
where:
• Dc = Average damage including crits and offence
• Dn = Average damage before Crits and Offence bonus
• F = Offence % increase in damage (in decimal, i.e. 25% = 0.25)
• C = Critical hit Chance (in decimal, i.e. 10% = 0.1)
• M = Critical hit multiplier bonus, applied to average damage (i.e. if the Crit Multiplier is 1.50 then M = 0.50, i.e. M = CritMult - 1)
• V = Devastate Crit Chance (in decimal)
• N = Devastate Crit Multiplier bonus applied to average damage (i.e. for a Devastate Multiplier of 2.2, N = 1.2, i.e. N = DevMult - 1)
Edit: In the next post, I've added a second version of these equations, which takes Multipliers that apply to Max damage.

Instead of D for damage, one can substitute d for dps in the above equation, by dividing it by the time period during which that damage was dealt.
dc = dn*(1+F) * (1 + C*M + V*N)
where:
• dc = Average dps including crits and offence
• dn = Average dps before crits and offence bonus

Now, in a discussion of which is better, increasing the offence % F, or increasing the % crit chance C, or increasing the crit multiplier bonus M, or increasing the % devastate crit chance V, or increasing the devastate crit multiplier N, one must increase only one of those variables at a time while keeping the others constant.

Increasing the Offence %

In this example, we'll assume the character has +30% Offence, i.e. F = 0.30. Increasing offence by 1% will result in:

Dc2 = Dn*(1+0.30+0.01) * (1 + C*M + V*N)
Dc1 = Dn*(1+0.30) * (1 + C*M + V*N)

The increase in damage (and dps) with 31% offence as compared to your current damage with 30% offence, is obtained as follows:

% Increase = Dc2/Dc1 – 1 ( or [Dc2-Dc1]/Dc1 )

= [Dn*(1.31) * (1 + C*M + V*N)] / [Dn*(1.30) * (1 + C*M + V*N)] - 1
= 1.31/1.30 – 1 = 0.00769 (or 0.769%)

Therefore, for the character with +30% offence, increasing offence by 1% will increase damage (or dps) by about 0.77%.

Is this a small or large increase?
1/30 = 0.033
This means a relative increase in the Offence % of 3.3%, to get 0.77% extra damage.

Increasing the offence % did not require us to know what the values of C, M, V and N are, since they get cancelled out whatever their values are. But to analyze the effect of an increase in one of those variable, we have to know what these four values are to start with, since the results will vary depending on their values.

For the sake of this demonstration, we will assume common values for them:

We assume that:
• C (the critical hit chance) versus an opponent of level 65 is 15.0%, i.e. C = 0.150
• V (the devastate hit chance) is such that it agrees with a critical hit chance of 15% versus an opponent's level of 65, i.e. D = 0.050 (5.0%) (meaning this character has a Critical Rating of 4550)
• The Critical Hit Multiplier applied to average damage is 1.50, and hence M, the critical hit multiplier bonus (above normal hit) is 0.50 (1.50–1)
• The Devastate Critical Hit Multiplier applied to average damage is 2.0, and hence N, the devastate critical hit multiplier bonus (above normal hit) is 1.0 (2.0–1)

Assumptions:

We therefore assume the following for these examples:

F = 0.30, C = 0.150, M = 0.50, V = 0.050, N = 1.0 (and, implicitly, an opponent level of 65)

Given the above, we will take +1% offence as our yardstick and calculate how much increase in one of the above 4 variables, when applied by itself, is equivalent to +1% offence.

In other words, we want to know:
• How much % increase in Critical Hit Chance corresponds to +1% offence?
• How much increase in Critical Hit Multiplier corresponds to +1% offence?
• Etc...

Since +1% Offence for this character results in +0.769% damage, we will find the % increases in the other variables which produce +0.769% damage too.

When we're done, we'll have a much better idea about answering questions such as:
• "What is best, +5% offence or +30% Critical Multiplier?", or
• "What is best, +2% Crit Chance or +50% devastate critical multiplier?" etc...

Increasing the Critical Hit Chance

Assume we increase the Crit Chance by k. The damage equation thus becomes:

Dc2 = Dn*(1+F) * (1 + (C+k)*M + V*N)
Dc1 = Dn*(1+F) * (1 + C*M + V*N)

% Increase in damage = Dc2/Dc1 – 1
= (1 + (C+k)*M + V*N) / (1 + C*M + V*N) - 1

What is the value of k that makes the increase in damage equal to +0.769% (+0.00769)?

0.00769 = (1 + (C+k)*M + V*N) / (1 + C*M + V*N) - 1

Solving for k, we find:

k = 0.00769*(1 + C*M + V*N) / M

Substituting with our data from above:

k = 0.00769*(1 + 0.15*0.50 + 0.050*1.0) / 0.50 = 0.0173 (or 1.73%)

Hence, for a character with the above stats to get the equivalent of +1% offence (i.e. +0.769% damage), we would need an increase of +1.73% in Critical Hit Chance. (I.e. instead of a Critical Hit Chance of 15.0% we would need a 16.73% Crit Chance.)

Is this a small or large increase?
1.73/15.0 = 0.115
This means a relative increase in the Crit Chance of 11.5%, to get the 0.77% extra damage (the equivalent of +1% offence, which was a relative increase of 3.3% in offence).

Increasing the Critical Hit Multiplier

Assume we increase the Critical Hit Multiplier bonus by m. The damage equation thus becomes:

Dc2 = Dn*(1+F) * (1 + C*(M+m) + V*N)
Dc1 = Dn*(1+F) * (1 + C*M + V*N)

% Increase in damage = Dc2/Dc1 – 1
= (1 + C*(M+m) + V*N) / (1 + C*M + V*N) - 1

What is the value of m that makes the increase in damage equal to +0.769% (+0.00769)?

0.00769 = (1 + C*(M+m) + V*N) / (1 + C*M + V*N) - 1

Solving for m, we find:

m = 0.00769*(1 + C*M + V*N) / C

Substituting with our data from above:

m = 0.00769*(1 + 0.15*0.50 + 0.050*1.0) / 0.15 = 0.0577 (or 5.77%)

(Notice that: m = k * M / C)

Hence, for a character with the above stats to get the equivalent of +1% offence (i.e. +0.769% damage), we would need an increase of +5.77% in Critical Hit Multiplier bonus. (I.e. instead of a Critical Hit Multiplier of 1.50, it should be 1.558)

Is this a small or large increase?
0.0577/0.5 = 0.115
This means a relative increase in the Crit Multiplier bonus of 11.5%, to get the 0.77% extra damage (same as the relative increase in Crit Chance).

Increasing the Devastating Critical Hit Chance

Assume we increase the Devastate Crit Chance by v. The damage equation thus becomes:

Dc2 = Dn*(1+F) * (1 + C*M + (V+v)*N)
Dc1 = Dn*(1+F) * (1 + C*M + V*N)

% Increase in damage = Dc2/Dc1 – 1
= (1 + C*M + (V+v)*N) / (1 + C*M + V*N) - 1

What is the value of v that makes the increase in damage equal to +0.769% (+0.00769)?

0.00769 = (1 + C*M + (V+v)*N) / (1 + C*M + V*N) - 1

Solving for v, we find:

v = 0.00769*(1 + C*M + V*N) / N

Substituting with our data from above:

v = 0.00769*(1 + 0.15*0.50 + 0.050*1.0) / 1.0 = 0.00865 (or 0.865%)

Hence, for a character with the above stats to get the equivalent of +1% offence (i.e. +0.769% damage), we would need an increase of +0.865% in Devastate Critical Hit Chance. (I.e. instead of a Devastate Critical Hit Chance of 5.0% we would need a 5.87% Dev Crit Chance.)

Is this a small or large increase?
0.00865/0.05 = 0.173
This means a relative increase in the Dev Crit Chance of 17.3%, to get the 0.77% extra damage.

Increasing the Devastate Multiplier

Assume we increase the Devastate Critical Hit Multiplier bonus by h. The damage equation thus becomes:

Dc2 = Dn*(1+F) * (1 + C*M + V*(N+h))
Dc1 = Dn*(1+F) * (1 + C*M + V*N)

% Increase in damage = Dc2/Dc1 – 1
= (1 + C*M + V*(N+h)) / (1 + C*M + V*N) - 1

What is the value of h that makes the increase in damage equal to +0.769% (+0.00769)?

0.00769 = (1 + C*M + V*(N+h)) / (1 + C*M + V*N) - 1

Solving for h, we find:

h = 0.00769*(1 + C*M + V*N) / V

Substituting with our data from above:

h = 0.00769*(1 + 0.15*0.50 + 0.050*1.0) / 0.05 = 0.173 (or 17.3%)

(Notice that: h = v * N / V)

Hence, for a character with the above stats to get the equivalent of +1% offence (i.e. +0.769% damage), we would need an increase of +17.3% in Devastate Multiplier bonus. (I.e. instead of a Devastate Multiplier of 2.0, it should be 2.173)

Is this a small or large increase?
0.173/1.0 = 0.173
This means a relative increase in the Devastate Multiplier bonus of 17.3%, to get the 0.77% extra damage.

Result

For the hypothetical character whose current stats are:
• F = 0.30 (Offence % = 30.0%)
• C = 0.15 (Critical Hit Chance = 15.0%)
• M = 0.50 (Critical Hit Multiplier = 1.50, or bonus = 0.50 or 50%)
• V = 0.05 (Devastate Crit Chance = 5.0%)
• N = 1.00 (Devastate Crit Multiplier = 2.0, or bonus = 1.0 or 100%)
The following are all equivalent, and lead to an increase in dps of 0.769% :
• +1.00% Offence
• +1.73% Critical Hit Chance
• +5.77% Critical Hit Multiplier
• +0.87% Devastate Crit Chance
• +17.3% Devastate Crit Multiplier
If this character is offered a 1% increase in one of these 5 stats, he would best choose to put it in Devastate Crit Chance. If not possible, then in Offence. If not possible then in Critical Hit Chance. If not possible then in Crit Multiplier, and lastly in Devastate Crit Multiplier.

But that is only valid for this hypothetical character.
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Last edited by Alad.; Sep 14 2011 at 12:25 AM.

2. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

PART 2

Here I would like to derive simple formulas so as to be able to compare any of the 5 variables mentioned with any of the other 4.

Definitions:

• F = Current Offence % (in decimal)
• f = Additional Offence % bonus (in decimal)
• C = Current % Critical Hit Chance (in decimal)
• k = Additional Critical Hit Chance bonus (in decimal)
• M = Current Critical Multiplier Bonus, based on Avg of skill damage range (in decimal) (CMB = CM-1)
• m = Additional Critical Multiplier bonus, based on Avg of skill damage range (in decimal)
• V = Current Devastate Crit Chance (in decimal)
• v = Additional Devastate Crit Chance bonus (in decimal)
• N = Current Devastate Crit Multiplier Bonus, based on Avg of skill damage range (in decimal) (DCMB = DCM-1)
• h = Additional Devastate Crit Multiplier bonus, based on Avg of skill damage range (in decimal)
Note 1: The Critical Multipliers used in the formulas are those that multiply Average damage. If the multipliers figures you have are ones that are applied to Max damage, they need to be adjusted by multiplying them by the factor: MaxDmg/AvgDmg of the skill damage range.

Note 2: M and N are the Critical Damage Bonuses, in excess of the normal, average damage (i.e. Multiplier applied to Average Damage - 1)

Note 3:
If you are certain that the Crit Multipliers are applied to Max damage for your class, you have to adjust the Crit Multiplier bonuses being considered, m and h, by multiplying them by the factor: MaxDmg/AvgDmg.

Note 4: See below (the green equations) for versions of these equations which directly take Multipliers and Multiplier bonuses that are based on Max skill damage.

Comparing bonuses

You can compare any of the 5 bonuses mentioned above to one of the others above by calculating how much increase in damage each bonus will produce:

1. First calculate the value of X
2. Then calculate the value of R depending on which bonus is under consideration:
X = Crit contribution to damage = 1 + C*M + V*N
R = % increase in damage or dps
• R = f/(1+F) (bonus is f: an increase in offence %)
• R = k*M/X (bonus is k: an increase in Crit Chance %)
• R = m*C/X (bonus is m: an increase in Crit Multiplier %)
• R = v*N/X (bonus is v: an increase in Devastate Crit Chance %)
• R = h*V/X (bonus is h: an increase in Devastate Crit Multiplier %)
Note that all the bonuses I mention are direct % bonuses, not Ratings of any kind. If you want to compare Rating bonuses, you need to first find out what % that added Rating will add to your relevant % stat.

Let us use these formulas to answer the 2 questions asked at the start of this article, assuming the hypothetical character whose stats are defined in Part 1.

"What is best for my character, +5% offence or +30% Critical Multiplier?"

+5% offence gives the following increase to dps: (f=0.05)

R = f/(1+F) = 0.05/(1+0.30) = 0.0385 (i.e. 3.85% increase in dps)

+30% Critical Multiplier gives: (m=0.30)

R = m*C/X
X = 1 + C*M + V*N = 1 + 0.15*0.5 + 0.05*1.0 = 1.125
R = 0.30*0.15/1.125 = 0.04 (i.e. 4.0% increase in dps)

Hence, for this character, a +30% increase in Crit Multiplier is slightly superior to +5% offence.

"What is best, +2% Crit Chance or +50% devastate critical multiplier?"

+2% Crit Chance gives: (k=0.02)

R = k*M/X = 0.02*0.5/1.125 = 0.0088 (i.e. +0.88% dps)

+50% Devastate Crit Multiplier gives: (h=0.5)

R = h*V/X = 0.5*0.05/1.125 = 0.0222 (i.e. +2.22% dps)

Therefore, for this character, a +50% in Devastate Crit Multiplier is superior to a +2% Critical Hit Chance.

The above questions are just examples. Please do not conclude that Devastate Crit Multiplier is always superior to Crit Chance, or vice versa. It all depends on the value of the bonus and on your character's current stats.

I hope this article will help make some dps bonus comparisons easier, at least with regard to those 5 common bonuses.

Caveat: Applying the formulas to one skill as opposed to overall dps

When considering the effects of different bonuses on one particular skill, for example to determine whether changes to a skill represent a buff or a nerf, it is important to know the Crit Chances and Crit Multipliers for that particular skill, not just your overall data. It is a fact that some skills have higher crit chances and/or higher crit multipliers than other skills.

Having said that, you will recognise that you are using a bunch of such skills while fighting, each having hidden bonuses to critical hit chances and multipliers. The % Crit Chances and Multipliers you will use in the above formulas will therefore most probably be approximations, at best, causing the results you obtain from these formulas to be equally approximate, but still a lot better than gut feelings.

Modified Formulas, taking into account Crit Multipliers that are based on Max damage

OK. I went ahead and modified my formulas to take into account Multipliers that apply to Max damage, rather than Average damage. (I'll try to add them to the original post if there's space left there).

Dc = Dn*(1+F) * [1 + C*(g*Mx-1) + V*(g*Nx-1)]

X = 1 + C*(g*Mx-1) + V*(g*Nx-1)

R =
f / (1+F)

R =
k*(g*Mx-1) / X

R =
m*g*C / X

R =
v*(g*Nx-1) / X

R =
h*g*V / X

where:
• Dc: Average damage or dps including Offence% and Crit damage bonuses
• Dn: Average damage or dps before Offence% and Crit damage bonuses
• F: Offence % bonus to damage (in decimal)
• C: Critical Hit %Chance (in decimal)
• V: Devastating Critical Hit %Chance (in decimal)
• Mx: Critical Hit Multiplier, based on max of skill damage range
• Nx: Devastating Hit Multiplier, based on max of skill damage range
• g: Max/Avg damage ratio, based on your class' skill damage ranges (= 2*Max/(Min+Max) )
• X: Crit Factor (damage increase due to crits)
• R: % increase in average dps (Dc) due to f, k, v, m or h
• f: Additional bonus to offence% (in decimal)
• k: Additional bonus to Crit Chance% (in decimal)
• v: Additional bonus to Devastate Crit Chance% (in decimal)
• m: Additional bonus to Crit Multiplier, based on max of skill damage range
• h: Additional bonus to Devastate Crit Multiplier, based on max of skill damage range

Important:
Note a very important change in the above formulas compared the ones I originally posted: Mx and Nx are the full crit multipliers, whereas in the original formulas M and N were equivalent to (Mx-1) and (Nx-1) respectively, i.e. they were the damage multiplier bonuses in excess of 1.

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Last edited by Alad.; Sep 14 2011 at 05:21 AM. Reason: Added new formulas that use Crit Multipliers based on Max damage

3. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Derivation of the Damage Formula

Critical Hit Chance is a certain probability that, instead of landing a normal hit, you land a critical hit that does bonus damage determined by the Critical Hit Multiplier.

For example, if the Crit Chance is 10% and the Crit Multiplier is 1.50, you have one chance out of every 10 hits (if the game's Random Number Generator is functioning properly), to land a Critical Hit. If you would normally do 100 damage on a normal hit, you would then do 100*1.50 = 150 damage on the critical hits.

The Critical Hit Multiplier is so named because it is used to multiply the damage you would have normally done, had it not been a critical hit. The portion above 1 can be called the Critical Hit Multiplier Bonus, or Critical Hit Damage Bonus, in this case it is 0.50, or 50%. (Lotro gear always refers to Multiplier bonuses in %. Simply divide by 100 to obtain the decimal multiplier bonus.)

Devastating Critical Hits are exactly the same as Critical Hits, except that they have a lower chance to occur, and when they do, they do even more damage than a critical hit. For example, if your Critical Hit Rating is around 4550, your Critical Hit Chance will be 15.0% and your Devastating Critical Hit Chance will be 5.0%. Whereas your damage bonus would be around 50% on a Critical Hit, it would be around 100% for the Devastating Hit. I.e. the Multiplier for the Devastating Hit will be 2.0 instead of 1.5.

One could write a formula that describes the expected value of damage, given the probability to crit and to devastate, as follows:

Suppose your crit chance is C, and your devastate chance is V. This means the probability that you will land a normal hit is (1-C-V).

If your normal damage is D, your crit multiplier is (1+M) and your devastate multiplier is (1+N) (where M and N are the crit damage *bonuses*), then your damage can be subdivided into 3 parts:
Normal hits: D*(1-C-V)
Critical hits: D*C*(1+M)
Devastating hits: D*V*(1+N)
The total average expected damage, crits included, would then be:

Dc = D*(1-C-V) + D*C*(1+M) + D*V*(1+N)

= D*(1-C-V + C + C*M + V + V*N)
= D*(1 + C*M + V*N)

Your normal (i.e. non-crit) average damage, D, is being enhanced by other sources, one of which is your Offence %.

D = Do*(1+Z)*(1+F)

Where F is your offence %, and Z represents all other damage-boosting factors, which we consider to remain constant for the purpose of this discussion; and Do is your raw average damage before any enhancements.

Hence, Dn, your normal average damage not counting Offence bonus and crits can be expressed as:

Dn = Do*(1+Z)

Our final damage equation thus becomes:

Dc = Dn*(1+F)*(1 + C*M + V*N)

Regarding Critial Magnitudes:

In this equation, the Critical Multipliers are applied to your average damage. There used to be evidence in Lotro, and there still is, that the Critical Damage is calculated by applying the multiplier to the max damage in the skill's damage range. If such is the case, there is a simple solution to adapt Crit Multipliers for use in the equation, once they are known with certaintly:

Since the skill's damage range is known, let's assume a min/max ratio of 70%, i.e. min = 0.7*max
Average damage is therefore (min+max)/2 = 1.7*max/2 = 0.85*max
If the multipliers you know are applied to max damage, then they should be divided by 0.85 (in this example) before they are used in the above damage equation.

Determining the Crit Multipliers

The problem is not in doing the above simple conversion, but in determining the values of the Critical Magnitudes, which for some obscure reason are being held secret by Turbine.

The only proper way to try to determine those magnitudes is to make sure there is as little interference with the damage magnitude as possible while performing a long series of logged hits on a mob that has zero mitigation to the kind of damage you are using and who preferably is the same level as your character.

Very Important: None of your skill/trait effects should buff your damage unexpectedly, as this will only make it impossible to determine the multipliers (you may need to remove all your class traits).

You should also preferably use a plain weapon (not a legendary one) with zero bonuses to damage.

The last time I did such tests, on several classes, was on the training dummy in Archet, when it still had a few thousand morale. It now dies pretty fast with its low morale, but it may still be useful.

The numbers I had collected at the time showed 1.50 multiplier for skill crits, and 2.0 for skill devastates (not auto-attacks), applied to max damage. Note that almost every class has at least one skill which has an extra high crit multiplier, reaching 3.0 in some cases.

I am desperately looking for fresh/recent Crit Multiplier data for the different classes, especially a positive confirmation as to whether Crit Multipliers are applied to max damage or to whatever damage is rolled on the hit (and hence to average damage). I have been observing some non-uniform crits on several classes which seem to imply the crits apply the multiplier to average damage now, but I must admit I've also observed a few uniform numbers in the same runs, which left me uncertain and I still haven't had the time to get to the bottom of this issue.

Any info is most welcome, especially with supporting data or even video captures. The Combat Analysis plugin is an excellent tool to use for that. I wish its author could build in some special functionality to help calculate those pesky multipliers.

Last edited by Alad.; Sep 12 2011 at 01:39 AM.

4. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Great post, really useful numbers.

Do you think you could setup a spreadsheet where you put in the relevant variables and it outputted the results as you've got in those final dot points? That would allow people to customise it for their own character without going through the maths themselves .

Also shows how epic that Baingrist bonus would have been if it actually worked, it's probably a >5% increase in DPS for 1/3 of the time which is pretty huge for a clicky.

5. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by PsychobabbleJJ
Great post, really useful numbers.

Do you think you could setup a spreadsheet where you put in the relevant variables and it outputted the results as you've got in those final dot points? That would allow people to customise it for their own character without going through the maths themselves .

Also shows how epic that Baingrist bonus would have been if it actually worked, it's probably a >5% increase in DPS for 1/3 of the time which is pretty huge for a clicky.
The Baingrist bonus of +5% Devastate Chance for 1 min every 3 mins, is indeed a nice bonus by itself.

The spreadsheet would be trivial to make The hardest part of this is figuring out your effective Crit Multipliers.

7. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Great work (+rep), but I think you are missing one important point. Crit's are always based off the top end damage of the skill, but regular attacks aren't. This means that crit modifiers will have a bigger impact than you math predicts. I took a brief look at my characters, and depending on the skill and class, low end damage is 60-75% of top end damage. I think this means that you need 80-87% of the crit and dev related modifiers to match 1% offense than what you gave in the examples. I'll let you work out the details though. I don't think it will be too hard to incorporate this into your formula, but I think it is important if you are looking for exact numbers.

8. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Looks like expectation to me. As someone else has indicated already criticals take the maximum of the damage range. The other issue I would raise is that your normal damage should really be taken as some uniform distribution over the damage range.

As a simplified example suppose an attack deals 101-150 damage. For simplicity sake suppose critical and dev critical multipliers are just 1.5 and 2. The crit chance is 15% and dev crit chance is 5%.

You have a 5% chance of dealing 300 damage.
You have a 15% chance of dealing 225 damage.
You have 85% chance of dealing anywhere between 101-150 damage.

The criticals are simple. For the uncritted damage you can work out that the probability of deal each damage in that range is 0.80/50. In essence, you have the following:

101 damage: 0.016
102 damage: 0.016
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149 damage: 0.016
150 damage: 0.016
225 damage: 0.15
300 damage: 0.05

To work out the expected value, you simply multiply each damage with its associated probability. Next you add up all the results.

6275*0.016 + 225*0.15 + 300*0.05 = 100.4 + 33.75 + 15 = 149.15

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It's a bit strange and if you mess around with the crit chances a bit. Imagine if you have 100% crit chance then you get 0% normal and dev crit so it simple becomes 225. Basically if you ALWAYS crit when you attack, you are expected to deal 225 damage which is correct.

Another example suppose you have no crit chance and no dev crit chance then the expect value works out to be 125.5. Basically if you never crit or dev crit and only get normal attacks, you average around 125.5 damage.
Last edited by defrule; Sep 12 2011 at 10:03 AM.

9. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

There is a problem with your formula. Your critical chance is the sum of your criticals and devastates. You have a critical chance of 15%. Devastate chance of 5%. You will get 10% critical results. 5% Devastate.

Put it in other terms. Your Devastate chance can never be higher than your Critical chance. It they are the same - then every Critical is a Devastate. Devastate are a type of Critical.

Since Criticals long before Devastates, I suspect internally a 15% critical and 5% Devastate are stored as Critical - 15%, Devastate - 33%. The game does two rolls. 15% chance for a Critical. 33% chance of promotion to a Devastate. Devastate is displayed as - 15% x 33% = 5%.

If you play with your gear, changing Critical chance - both Critical chance and Devastate Chance will move together.
Last edited by Yula_the_Mighty; Sep 12 2011 at 10:58 AM.

10. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by Yula_the_Mighty
There is a problem with your formula. Your critical chance is the sum of your criticals and devastates. You have a critical chance of 15%. Devastate chance of 5%. You will get 10% critical results. 5% Devastate.

Put it in other terms. Your Devastate chance can never be higher than your Critical chance. It they are the same - then every Critical is a Devastate. Devastate are a type of Critical.

Since Criticals long before Devastates, I suspect internally a 15% critical and 5% Devastate are stored as Critical - 15%, Devastate - 33%. The game does two rolls. 15% chance for a Critical. 33% chance of promotion to a Devastate. Devastate is displayed as - 15% x 33% = 5%.

If you play with your gear, changing Critical chance - both Critical chance and Devastate Chance will move together.
I did read somewhere that they function separately, 15% and 5% meaning 20% of some form of crit but it was empirical evidence and I don't think any dev has explicitly stated which way it goes.

11. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by defrule
I did read somewhere that they function separately, 15% and 5% meaning 20% of some form of crit but it was empirical evidence and I don't think any dev has explicitly stated which way it goes.
You could test it. It would take a while. I am pretty sure I saw an analysis that seemed to indicate that 15% Critical chance and 5% Devastate chance worked out to be 10% Critical and 5% Devastate. The mix was 2 Criticals for every Devastate instead of the 3 Criticals for every Devastate that you are expecting.

One thing to remember - you can not always believe what a developer says - they will often make a statement with out any data to confirm the game works the way they think does. This is especially true of complicated features like skill interaction and the combat system. They are full of bugs. Or work differently than they think.

I run into this a lot in my software work. I read the design document and the code comments. I start reading the code. The code does not work the way the human readable text says. The game does not care what the documentation says. It reads the code as being the final word. A common problem is a code update without changing any of the documentation because the software designer is in a hurry to get it done.

The OMG - I got 100 bugs in my intray. Thursday we are going to build again. My sup is going to clock me if I do not get a significant number of fixes for these bugs ubmitted to the build.
Last edited by Yula_the_Mighty; Sep 12 2011 at 11:32 AM.

12. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by Yula_the_Mighty
You could test it. It would take a while. I am pretty sure I saw an analysis that seemed to indicate that 15% Critical chance and 5% Devastate chance worked out to be 10% Critical and 5% Devastate. The mix was 2 Criticals for every Devastate instead of the 3 Criticals for every Devastate that you are expecting.

It's pretty short, and mostly consists of me complaining about the testing methodology.

Last edited by moebius92; Sep 12 2011 at 11:17 PM.

13. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by shazbaat
Great work (+rep), but I think you are missing one important point. Crit's are always based off the top end damage of the skill, but regular attacks aren't. This means that crit modifiers will have a bigger impact than you math predicts. I took a brief look at my characters, and depending on the skill and class, low end damage is 60-75% of top end damage. I think this means that you need 80-87% of the crit and dev related modifiers to match 1% offense than what you gave in the examples. I'll let you work out the details though. I don't think it will be too hard to incorporate this into your formula, but I think it is important if you are looking for exact numbers.
Thank you for giving me rep without reading the entire post!

I do talk quite a bit about the crit multipliers towards the end, and that they might still be (as i'm certain they were at some point), multiplying Max damage.

I hope it's clear that the numbers 1.50 and 2.0 that I give in my examples are understood to be just that, examples. And that the multipliers anyone should plug into these formulas should be those that multiply Average damage. Hence a small conversion may be required as I show in an example towards the end of my post (3rd post from the top).

14. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by defrule
As someone else has indicated already criticals take the maximum of the damage range.

The other issue I would raise is that your normal damage should really be taken as some uniform distribution over the damage range.

As a simplified example suppose an attack deals 101-150 damage. For simplicity sake suppose critical and dev critical multipliers are just 1.5 and 2. The crit chance is 15% and dev crit chance is 5%.

You have a 5% chance of dealing 300 damage.
You have a 15% chance of dealing 225 damage.
You have 85% chance of dealing anywhere between 101-150 damage.

The criticals are simple. For the uncritted damage you can work out that the probability of deal each damage in that range is 0.80/50. In essence, you have the following:

101 damage: 0.016
102 damage: 0.016
.
.
.
149 damage: 0.016
150 damage: 0.016
225 damage: 0.15
300 damage: 0.05

To work out the expected value, you simply multiply each damage with its associated probability. Next you add up all the results.

6275*0.016 + 225*0.15 + 300*0.05 = 100.4 + 33.75 + 15 = 149.15
Thank you for raising an "issue" that isn't one, since it seems you didn't bother to try out your data in my formulas. And thank you for you "simplified" example; that's the exact result that my much simpler and direct formula would calculate, without going through all the trouble you went through.

Demonstration:

Damage range: 101 - 150
C = 0.15
V = 0.05
Crit Multiplier applied to max damage = 1.50
Devastate Multiplier applied to max damage = 2.00
F = 0 (you're assuming offence % is already included in the damage mentioned)

Method 1: Using the formulas that take Crit Multipliers based on Average Damage

Step 1) Calculate Avg Damage, M and N after correcting for the Multipliers (my formulas expect the value of the multipliers that would be applied to average damage):
Damage Range = 101 - 150
=> Dn = Average Damage = (101+150)/2 = 125.5
Multiplier correction factor = Max/Avg = 150/125.5 = 1.19522
Crit Multiplier applied to Average damage = 1.50 x 1.19522 = 1.7928
=> M (Crit Multiplier Bonus) = 1.7928-1 = 0.7928
Devastate Multiplier applied to Average damage = 2.00 x 1.19522 = 2.3904
=> N (Dev Multiplier Bonus) = 2.3904-1 = 1.3904

Step 2) Plug the data into the formula: Dc = Dn * (1+F) * (1 + C*M + V*N)

Expected average damage:
Dc = 125.5*(1+0)*(1 + 0.15*0.7928 + 0.05*1.3904) = 149.15

Method 2: Using the formulas that take Crit Multipliers based on Max Damage

Step 1) Calculate Avg Damage and g (the multiplier correction factor)
Damage Range = 101 - 150
=> Dn = Average Damage = (101+150)/2 = 125.5
g = MaxDmg/AvgDmg = 150/125.5

Step 2) Plug the data into the formula: Dc = Dn * (1+F) * [1 + C*(g*Mx - 1) + V*(g*Nx - 1)]

Expected average damage:
Dc = 125.5 * (1+0) * [1 + 0.15*(150/125.5 * 1.50 - 1) + 0.05*(150/125.5 * 2.00 - 1)] = 149.15

Looks like expectation to me.
I didn't get that. Could you elaborate, please?
I did indeed expect people who would post in this thread to at least read my post.
Last edited by Alad.; Nov 10 2011 at 02:10 PM. Reason: Added calculation with new damage formula which takes Multipliers based on Max damage

15. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by Yula_the_Mighty
There is a problem with your formula. Your critical chance is the sum of your criticals and devastates. You have a critical chance of 15%. Devastate chance of 5%. You will get 10% critical results. 5% Devastate.
[...]
Since Criticals long before Devastates, I suspect internally a 15% critical and 5% Devastate are stored as Critical - 15%, Devastate - 33%. The game does two rolls. 15% chance for a Critical. 33% chance of promotion to a Devastate. Devastate is displayed as - 15% x 33% = 5%.
What evidence is there of this?
They could simply do one roll for the total i.e. 20%, to see if it's a crit or a devastate, and if the roll is in the 20% range, then do another roll to determine which of the two it is. Come to think of it, only a single roll would be enough by dividing up the possible outcomes into the proper proportions (3 ranges for normal hit, crit hit and dev crit hit). I suppose this is what they do for the 6 ranges in BEP + Partial BEP.

If you play with your gear, changing Critical chance - both Critical chance and Devastate Chance will move together.
Of course they do, how does that prove that the Dev% chance is included in the displayed Crit% chance?

Edit: I would be convinced that the displayed %dev chance is included in the displayed %crit chance if, for example, you could equip an item that adds +1% Dev Crit Chance, and see both displayed crit chances increasing by 1% as a result. The only item that has such a bonus, to my knowledge, is the sword Baingrist (adds +5% Devastate Crit Chance). Unfortunately I don't own this item, so if anyone has it perhaps they can tell us if %Crit Chance in the tooltip also increases by 5% when that buff is active.
Last edited by Alad.; Sep 13 2011 at 07:55 AM.

16. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by moebius92

It's pretty short, and mostly consists of me complaining about the testing methodology.
The link you gave goes to a screenshot. It's nice, mind you But it would be great to have the good link.

17. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Damage range: 101 - 150
C = 0.15
V = 0.05
Crit Multiplier applied to max damage = 1.50
Devastate Multiplier applied to max damage = 2.0
F = 0 (you're assuming offence % is already included in the damage mentioned)

Step 1) Calculate Avg Damage, M and N after correcting for the Multipliers (my formulas expect the value of the multipliers that would be applied to average damage):
Damage Range = 101 - 150
=> Average Damage = (101+150)/2 = 125.5
Multiplier correction factor = Max/Avg = 150/125.5 = 1.19522
Crit Multiplier applied to Average damage = 1.50 x 1.19522 = 1.7928
=> M (Crit Multiplier Bonus) = 1.7928-1 = 0.7928
Devastate Multiplier applied to Average damage = 2.00 x 1.19522 = 2.3904
=> N (Dev Multiplier Bonus) = 2.3904-1 = 1.3904

Step 2) Plug the data into the formula: Dc = Dn*(1+F)*(1 + C*M + V*N)

Expected average damage:
Dc = 125.5*(1+0)*(1 + 0.15*0.7928 + 0.05*1.3904) = 149.15
This may or may not work when you start trying to apply critical multiplier modifiers. In your first post, you apply a critical multiplier via the following formula:

Dc2 = Dn*(1+F) * (1 + C*(M+m) + V*N)

If you use M = 0.7928, this isn't going to work, because it's really <Multiplier correction factor> * (M + m), not <Multiplier correction factor> * M + m.

The link you gave goes to a screenshot. It's nice, mind you But it would be great to have the good link.

18. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by moebius92
This may or may not work when you start trying to apply critical multiplier modifiers. In your first post, you apply a critical multiplier via the following formula:

Dc2 = Dn*(1+F) * (1 + C*(M+m) + V*N)

If you use M = 0.7928, this isn't going to work, because it's really <Multiplier correction factor> * (M + m), not <Multiplier correction factor> * M + m.

Yes, I realise it could be a bit confusing But I think it does work, try it. Don't forget that the m that goes into this equation has to be based on average damage, and the m that comes out of the equation (as I was using it in the post you mention) is based on average damage too. So if you consider the case that multipliers are based on max damage, you'd have to adjust (decrease) the m that is the result of the calculation. I didn't do that in my example, because I started off with a multiplier that is based on average damage already, so the m that came out didn't need any adjustments. (I hope I'm making sense! LOL)

As I said earlier, this topic has interested me for a long time and I've been measuring multipliers for a few years in lotro on several classes. At some point, relatively recently (within the last year I'd say), the results I was getting seemed to suggest that crit damage was changed to be based on whatever damage the roll gave, since I wasn't getting crits of identical values any more. I'll have to do some more serious testing if I get the courage to do it. Or perhaps some other person will have done some recent rigourous testing already.

19. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

When I said this looks like expectation it was a good thing because what you are doing is much better than any parsing in game. It does look bad now that I read it again.

Basically:
$\large \bg_black E(X)=x_1p_1+x_2p_2+\cdots +x_kp_k$

We this in mind, all you have to do is this:
$\large \bg_black E(X)=x_{norm}p_{norm}+x_{crit}p_{crit}+x_{dev}p_{dev} \newline \newline \begin{matrix} x_{norm} & : & non-crit\;damage\\ x_{crit} & : & crit\;damage\\ x_{dev} & : & dev-crit\;damage\\ p_{norm} & : & probability\;of\;not\;critting\\ p_{crit} & : & probability\;of\;crit\\ p_{dev} & : & probability\;of\;dev-crit \end{matrix}$

Now I can put some stuff in to give
$\large \bg_black E(X)=\frac{a+b}{2}p_{norm}+bM_{crit}p_{crit}+bM_{dev}p_{dev} \newline \newline \begin{matrix} a & : & lowest\;damage\\ b & : & highest\;damage\\ M_{crit} & : & sum\;of\;crit\;multipliers\\ M_{dev} & : & sum\;of\;dev-crit\;multipliers \end{matrix}$

Now I'm just wondering, why is it necessary to deliberately factor out the average damage and introduce correctors? By simply using the above you get exact numbers with my example and at no point was any rounding needed. No need to go into the Max/Avg stuff which in this case seems to require rounding even when the example is perfectly doable in exact form, it just seems a bit too round about. You didn't quite get 149.15 exact did you, it rounded from what I see.

I admit though, I didn't really read your post in depth. It's probably the same thing with things defined differently but I'll check in the meantime.
Last edited by defrule; Sep 13 2011 at 10:26 AM.

20. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Thank you for raising an "issue" that isn't one, since it seems you didn't bother to try out your data in my formulas. And thank you for you "simplified" example; that's the exact result that my much simpler and direct formula would calculate, without going through all the trouble you went through.
The reason I spelled out the entire damage distribution is to illustrate the example as throughly as possible. There was no need to break down the normal damage from 101-150 because that is simply a uniform distribution so it just gives the average anyway.

If I was to shorten the whole thing it would be precisely what I wrote above
$\large \bg_black E(X)=\frac{a+b}{2}p_{norm}+bM_{crit}p_{crit}+bM_{dev}p_{dev} \newline \newline \begin{matrix} a & : & lowest\;damage\\ b & : & highest\;damage\\ M_{crit} & : & sum\;of\;crit\;multipliers\\ M_{dev} & : & sum\;of\;dev-crit\;multipliers \end{matrix}$

In short, the whole thing would have just been:
$\large \bg_black \begin{matrix} 125.5\ast0.8 & + & 225\ast0.15 & + & 300\ast0.05 & = & 149.15\\ Avg\ast{p_{nocrit}} & + & critdmg\ast{p_{crit}} & + & devdmg\ast{p_{dev}} & = & expected \end{matrix}$

21. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

This is great! Thanks for the posts. I read them, but have 2 questions.

1. How did you arrive at your formulas? It sounds like they were empirically derived from test data (implied by the term, "objective"). Or did you get some source code?

2. Do you have any sense whether these equations will hold for RoI?

Thanks!

22. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

As I said earlier, this topic has interested me for a long time and I've been measuring multipliers for a few years in lotro on several classes. At some point, relatively recently (within the last year I'd say), the results I was getting seemed to suggest that crit damage was changed to be based on whatever damage the roll gave, since I wasn't getting crits of identical values any more. I'll have to do some more serious testing if I get the courage to do it. Or perhaps some other person will have done some recent rigourous testing already.
I've done a lot of testing on this, and in every controlled experiment I've done, crits have been exactly the same every time. Here are some things likely to affect your damage solo:

- the level of the mob. Most mobs come in a level range, there might be 65's mixed with 66's for example.
- will or agi or might debuffs (depending on the class). For instance wolves like to put a might debuff on you which lowers damage of melee classes.
- For tactical classes your fate affects crit magnitude.
- if you are using an axe, the armor rend proc from the axe will increase your damage.
- procs from equipment like the turtle shell bracelet.

There's a whole bunch of other stuff too. I listed a bunch on the this post on the RK forums.

Also, if you know your crit multiplier exactly, you can figure out the mobs exact mitigations to specific damage types by comparing the <tooltip max damage>*<multiplier> to the actual damage you do to the mob. Unfortunately, it's extremely difficult to do a controlled experiment on raid boss mobs where this info would be most useful. It isn't too hard to figure out your crit multiplier exactly on a physical class, but nearly impossible on a tactical class because of the fate contribution to crit multiplier.

23. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by defrule
When I said this looks like expectation it was a good thing because what you are doing is much better than any parsing in game. It does look bad now that I read it again.
OK, got it.

$\large \bg_black E(X)=x_{norm}p_{norm}+x_{crit}p_{crit}+x_{dev}p_{dev} \newline \newline \begin{matrix} x_{norm} & : & non-crit\;damage\\ x_{crit} & : & crit\;damage\\ x_{dev} & : & dev-crit\;damage\\ p_{norm} & : & probability\;of\;not\;critting\\ p_{crit} & : & probability\;of\;crit\\ p_{dev} & : & probability\;of\;dev-crit \end{matrix}$
So far so good.

Now I can put some stuff in to give
$\large \bg_black E(X)=\frac{a+b}{2}p_{norm}+bM_{crit}p_{crit}+bM_{dev}p_{dev} \newline \newline \begin{matrix} a & : & lowest\;damage\\ b & : & highest\;damage\\ M_{crit} & : & sum\;of\;crit\;multipliers\\ M_{dev} & : & sum\;of\;dev-crit\;multipliers \end{matrix}$

Now I'm just wondering, why is it necessary to deliberately factor out the average damage and introduce correctors? By simply using the above you get exact numbers with my example and at no point was any rounding needed. No need to go into the Max/Avg stuff which in this case seems to require rounding even when the example is perfectly doable in exact form, it just seems a bit too round about. You didn't quite get 149.15 exact did you, it rounded from what I see.
If you read the way I derived the formula, you'll see I didn't actually factor out average damage (because I didn't start from your formulas! lol), I just applied the theory you lined up so elegantly in your first image, and considered that "crit damage is normal damage amplified by some multiplier". The equation I got looked clean and simple, with a nice and practical, easy to understand factor (1 + C*M + V*N) which represents the added contribution of crits to non-crit dps. And I was satisfied. (I'm an engineer, we're like that )

Of course you can also rewrite that equation to build in the assumption (I'm at that stage now until further notice) that crits are based on max damage. The only way to do that when speaking about your dps as a whole (which has no Min and Max), is to use the Min/Max ratio of the majority of the skills you commonly use, together with your average dps (there's no getting around that part because we're not just talking about one skill, but your overall dps and how it's affected by those bonuses). The ratio can be built into the formula directly, I agree. I just think the way it is now is simple and intuitive. (But I'll think about including versions with Min/Max built in).

As for the rounding, it is obviously due to my having calculated intermediate values, the Multipliers, which I chose to round to 4 decimals only. It's not a defect in the formula. You can include the Min and Max in the formula and get the precise result you got in your example without needing to round.

One last thing: Why are the M's in your last equation "sums" ?

I admit though, I didn't really read your post in depth. It's probably the same thing with things defined differently but I'll check in the meantime.
Well have you done it yet?
Last edited by Alad.; Sep 14 2011 at 12:00 AM.

24. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Those M's are sums because it's simple all the gear stuff and also the innate multiplier put together. For a champion with only the 50% crit legacy for instance, the Mcrit would be 1.5+0.5 = 2 and dev crit would be 2+0.5 = 2.5. (I don't think that legacy actually works on dev crits but whatever)

If my Wild Attack dealt 350-400 westernesse damage, I know my crits will deal 800 with the legacy and dev crits will deal 1000. Which will then be reduced by 7-9% by mob mitigations and then you have other external stuff to increase it.

Engineers grrrr... we're never going to agree.

Here something for people to play with, it roughly works I think. Probably a few cells you don't really need to care about in it.
Last edited by defrule; Sep 13 2011 at 09:59 PM.

25. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by defrule
Those M's are sums because it's simple all the gear stuff and also the innate multiplier put together.
I see. I wouldn't call this the "sum of multipliers" since there's only 1 multiplier. Perhaps "sum of critical damage bonuses/modifiers", or "sum of critical multiplier bonuses/modifiers".

Engineers grrrr... we're never going to agree.
LOL, what are you, then?

Here something for people to play with, it roughly works I think. Probably a few cells you don't really need to care about in it.
I promise to take a look at it later. (I did, and it looks ok )

In the meantime I have written a version of my formulas that take into account multipliers that are based on max damage. (As expected, they're a bit ugly, but only a bit). I'll make a new post with them, and try to add them to the original post if there's space left there.
Last edited by Alad.; Sep 13 2011 at 11:57 PM.

26. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Modified Formulas, taking into account Crit Multipliers that are based on Max damage

OK. I went ahead and modified my formulas to take into account Multipliers that apply to Max damage, rather than Average damage. (I'll try to add them to the original post if there's space left there).

Dc = Dn*(1+F) * [1 + C*(g*Mx-1) + V*(g*Nx-1)]

X = 1 + C*(g*Mx-1) + V*(g*Nx-1)

R =
f / (1+F)

R =
k*(g*Mx-1) / X

R =
m*g*C / X

R =
v*(g*Nx-1) / X

R =
h*g*V / X

where:
• Dc: Average damage or dps including Offence% and Crit damage bonuses
• Dn: Average damage or dps before Offence% and Crit damage bonuses
• F: Offence % bonus to damage (in decimal)
• C: Critical Hit %Chance (in decimal)
• V: Devastating Critical Hit %Chance (in decimal)
• Mx: Critical Hit Multiplier, based on max of skill damage range
• Nx: Devastating Hit Multiplier, based on max of skill damage range
• g: Max/Avg damage ratio, based on your class' skill damage ranges (= 2*Max/(Min+Max) )
• X: Crit Factor (damage increase due to crits)
• R: % increase in average dps (Dc) due to f, k, v, m or h
• f: Extra bonus to offence% (in decimal)
• k: Extra bonus to Crit Chance% (in decimal)
• v: Extra bonus to Devastate Crit Chance% (in decimal)
• m: Extra bonus to Crit Multiplier, based on max of skill damage range
• h: Extra bonus to Devastate Crit Multiplier, based on max of skill damage range

Important:
Note a very important change in the above formulas compared the ones I originally posted: Mx and Nx are the full crit multipliers, whereas in the original formulas M and N were equivalent to (Mx-1) and (Nx-1) respectively, i.e. they were the damage multiplier bonuses in excess of 1.
Last edited by Alad.; Sep 14 2011 at 05:08 AM.

27. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by anteku
This is great! Thanks for the posts. I read them, but have 2 questions.

1. How did you arrive at your formulas? It sounds like they were empirically derived from test data (implied by the term, "objective"). Or did you get some source code?

2. Do you have any sense whether these equations will hold for RoI?

Thanks!
Yes, they are empirically derived from common sense I.e. how crits should function. It's a simple issue really. And no, I don't have any access to source code.

As for RoI, I don't see why they shouldn't continue to work this way.

You're welcome!

28. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by shazbaat
I've done a lot of testing on this, and in every controlled experiment I've done, crits have been exactly the same every time. Here are some things likely to affect your damage solo:

- the level of the mob. Most mobs come in a level range, there might be 65's mixed with 66's for example.
- will or agi or might debuffs (depending on the class). For instance wolves like to put a might debuff on you which lowers damage of melee classes.
- For tactical classes your fate affects crit magnitude.
- if you are using an axe, the armor rend proc from the axe will increase your damage.
- procs from equipment like the turtle shell bracelet.

There's a whole bunch of other stuff too. I listed a bunch on the this post on the RK forums.

Also, if you know your crit multiplier exactly, you can figure out the mobs exact mitigations to specific damage types by comparing the <tooltip max damage>*<multiplier> to the actual damage you do to the mob. Unfortunately, it's extremely difficult to do a controlled experiment on raid boss mobs where this info would be most useful. It isn't too hard to figure out your crit multiplier exactly on a physical class, but nearly impossible on a tactical class because of the fate contribution to crit multiplier.
Thanks shazbaat. I've been playing my RK a lot these past months, and it's definitely not the easiest class to use to measure crit multipliers due to various damage buffs which pop up and screw the numbers.

There is something else that I haven't seen people talk about. The multipliers could very well be based on the average of the skill's damage range, rather than its max. The average of the range is still a constant, just as the max is. The multipliers deduced using this hypothesis would then be larger than those that everyone is calculating based on max (as I have been doing as well). Given that the only numbers we know for sure are the multiplier bonuses from buffs and gear, the only way to tell for sure whether multipliers apply to average or max of the range, is to add to them using gear, then check that the crits have actually increased by exactly the added amount. I admit, I haven't done such tests, but I suppose someone has already done them since we're all following this assumption.

For example:
A skill that does 600-1000 (800 avg) crits systematically at 2000.
You can either say the multiplier is 2.0 (based on max) or 2.5 (based on Avg).
The only way to tell what the multiplier is based on would be to add a known amount, say, 0.3 to the multiplier, by equipping items/buffs, and then redo the same tests and see whether the new crits are 2.3*max (2300) or 2.8*Avg (2240).

29. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Thanks shazbaat. I've been playing my RK a lot these past months, and it's definitely not the easiest class to use to measure crit multipliers due to various damage buffs which pop up and screw the numbers.

There is something else that I haven't seen people talk about. The multipliers could very well be based on the average of the skill's damage range, rather than its max. The average of the range is still a constant, just as the max is. The multipliers deduced using this hypothesis would then be larger than those that everyone is calculating based on max (as I have been doing as well). Given that the only numbers we know for sure are the multiplier bonuses from buffs and gear, the only way to tell for sure whether multipliers apply to average or max of the range, is to add to them using gear, then check that the crits have actually increased by exactly the added amount. I admit, I haven't done such tests, but I suppose someone has already done them since we're all following this assumption.

For example:
A skill that does 600-1000 (800 avg) crits systematically at 2000.
You can either say the multiplier is 2.0 (based on max) or 2.5 (based on Avg).
The only way to tell what the multiplier is based on would be to add a known amount, say, 0.3 to the multiplier, by equipping items/buffs, and then redo the same tests and see whether the new crits are 2.3*max (2300) or 2.8*Avg (2240).
Since I was on a champion when I did a lot of my tests, I knew the multiplier exactly. There is +50% from the champion legacy (which I didn't have at the time), and another +25% from the class trait for certain skills. I also had some dev mag settings slotted which contributed to the devastate multiplier. I killed a ton of stuff in thievery and mischief and found that the "weak" mobs had very close to zero mitigation. This meant that for instance my wild attack hit for almost exactly 1.5x the max damage on the tooltip.

I used the calculated mob mitigation as a check for my calculations. It didn't matter which mobs I fought, or what their mitigations were, it worked out that every skill resulted in the same mitigation for a mob. If the calculation was based off of average damage (or low end damage), this wouldn't have worked without making a different multiplier for each skill. This is because each skill has a different percentage range due to the way bonus damage is included in skills.
For instance when I did the tests remorseless strikes had a range on the tooltips of 654-896 while swift strike had a range of 257-407. So min/max damage for the first is 73% while for the second it is 63%. If crit damage were based off something other than max damage the numbers would not have worked out so nicely.

I have the spreadsheet, but it's basically a huge wall of numbers that would take a lot of explaining. I also would like to redo the tests without the racial bonus for swords slotted. This is because the sword bonus does affect skills, but is not included in the tooltip. I'd also like to find a better place than T&M because the wolves occasionally put a -might debuff on you that affects the outcome. It's one of those things on my to do list.

30. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

I agree, given that champ damage includes constants that are independent of weapon damage, the min/max ratios are different for different skills. So if you found the same multipliers repeatedly using several skills, it must be based on whatever you assumed the multiplier applies to, and that's max damage.

And yes, the sword damage racial trait doesn't show its effect on the tooltips. There's something else that doesn't show on the tooltip damage, and that's the Hope bonus, whether Area hope or from tokens. Be careful where you do those tests.

31. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

I tried to use the formula to recover the values which are displayed on the tooltip ingame (RoI values).

I use the following character
• Elf hunter lvl1
• agility = 29
• Fragile Shortbow with 1-3 Damage

Due to the agility I get a
• ranged offence = +20%
• Crit chance = 12.7%
• Dev chance = 4.2%

If I now look at Quick Shot, the tooltip shows the following:
• Without Bow: 120% of Ranged + 1 Damage
• With Bow: 4-5 Damage

Can anyone explain to me how I get a minimal damage of 4 with the formulas stated here? Feel free to use the worst-case scenario for all occurring rounding.

We were trying to verify those formulas from lotro-wiki, but they are not better than the ones stated here.
Last edited by .EoD.; Sep 27 2011 at 06:20 PM.

32. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by defrule
I did read somewhere that they function separately, 15% and 5% meaning 20% of some form of crit but it was empirical evidence and I don't think any dev has explicitly stated which way it goes.
From Yore:
Originally Posted by DangerDan
They are not a percent of a percent. If you have a 15% chance for a regular critical and a 4% chance for a devastating critical, you have a 19% chance to critical in one form or another. Both kinds of critical will allow you to use your crit-response skills.

33. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by .EoD.
I tried to use the formula to recover the values which are displayed on the tooltip ingame (RoI values).

I use the following character
• Elf hunter lvl1
• agility = 29
• Fragile Shortbow with 1-3 Damage

Due to the agility I get a
• ranged offence = +20%
• Crit chance = 12.7%
• Dev chance = 4.2%

If I now look at Quick Shot, the tooltip shows the following:
• Without Bow: 120% of Ranged + 1 Damage
• With Bow: 4-5 Damage

Can anyone explain to me how I get a minimal damage of 4 with the formulas stated here? Feel free to use the worst-case scenario for all occurring rounding.

We were trying to verify those formulas from lotro-wiki, but they are not better than the ones stated here.
Your damage numbers are so small, that rounding can create a big error. The only bonuses that matter here are the +20% and the +1 mentioned in the skill tooltip.

Suppose the bow minimum damage is actually 1.49, and it's rounded to 1 in the display. Suppose the +1 damage bonus shown in the skill tooltip is really 1.49, rounded to +1. And that the +1 gets added before you apply the +20% ranged damage bonus. You get:
(1.49 + 1.49) * 1.20 = 3.576, which is rounded to 4 in the tooltip.

Although I must admit, if the constant +1 from the tooltip should get added before the 120% multiplier, then the tooltip is misleading (should say "Ranged damage +1, +20%"). Of course this could also be a bug. Or a hidden bonus at low levels. Nice catch anyway! +rep

Now let's see if we can get to the number 5:
Suppose the bow max damage is really 2.5, rounded to 3. You'll have:
(2.5 + 1.49) * 1.20 = 4.788, which is rounded to 5.
In fact, the max damage on the bow could even be 3.08, rounded to 3, and you'll get:
(3.08 + 1.49) * 1.20 = 5.484, which is still rounded to 5.

PS:
I logged my hunter to try figuring those skill damages. There are most certainly hidden values that get added. I tried to find relationships to explain them, but couldn't. Sometimes the same amount is added to the min and max of the skill, sometimes (if you switch bows) it's a different amount. Each skill gets added a different amount. So that seems to be a mystery. Or a bug, hopefully only in the skill tooltips with no bow equipped.
Last edited by Alad.; Sep 30 2011 at 06:17 AM.

34. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by scrubmonkey
From Yore:
Originally Posted by DangerDan
They are not a percent of a percent. If you have a 15% chance for a regular critical and a 4% chance for a devastating critical, you have a 19% chance to critical in one form or another. Both kinds of critical will allow you to use your crit-response skills.
Thanks for that link. That post from a Dev clears up the situation. DevCrits% is not included in Crit%.

35. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Your damage numbers are so small, that rounding can create a big error. The only bonuses that matter here are the +20% and the +1 mentioned in the skill tooltip.

Suppose the bow minimum damage is actually 1.49, and it's rounded to 1 in the display. Suppose the +1 damage bonus shown in the skill tooltip is really 1.49, rounded to +1. And that the +1 gets added before you apply the +20% ranged damage bonus. You get:
(1.49 + 1.49) * 1.20 = 3.576, which is rounded to 4 in the tooltip.

Although I must admit, if the constant +1 from the tooltip should get added before the 120% multiplier, then the tooltip is misleading (should say "Ranged damage +1, +20%"). Of course this could also be a bug. Or a hidden bonus at low levels. Nice catch anyway! +rep
I thought the bow values are fixed damages, so I didn't round the 1 of "1-3" to 1.499. But thanks for pointing that out

PS:
I logged my hunter to try figuring those skill damages. There are most certainly hidden values that get added. I tried to find relationships to explain them, but couldn't. Sometimes the same amount is added to the min and max of the skill, sometimes (if you switch bows) it's a different amount. Each skill gets added a different amount. So that seems to be a mystery. Or a bug, hopefully only in the skill tooltips with no bow equipped.
That's interesting. Maybe I missunderstood the formula, but in my opinion it's
120% ( min + bonus ) ≈ 4
and
120% ( max + bonus ) ≈ 5

That means that the displayed value is actually "120% * bonus ≈ 1". Maybe that explains the different values you get?

36. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

i've just realised a major limitation to the formulae in the OP. at least for tactical skills offence bonuses for individual skills are calculated additively (see the formula here). I can only speak for lore-masters, but we have a bunch of things which increase the damage output of our individual skills beyond the TDR rank on our weapon, including trait line bonuses and a number of general and individual skill legacies. The net effect of all this is that increased tactical offence only increases skill damage by about half of the tooltip % for most LMs. That obviously makes a big difference in the calculations.

Also I've heard from others that critical multiplier (or perhaps just tac crit multiplier?) is somehow linked to fate. is anyone aware of this?

37. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Originally Posted by PsychobabbleJJ
i've just realised a major limitation to the formulae in the OP. at least for tactical skills offence bonuses for individual skills are calculated additively (see the formula here). I can only speak for lore-masters, but we have a bunch of things which increase the damage output of our individual skills beyond the TDR rank on our weapon, including trait line bonuses and a number of general and individual skill legacies. The net effect of all this is that increased tactical offence only increases skill damage by about half of the tooltip % for most LMs. That obviously makes a big difference in the calculations.

Also I've heard from others that critical multiplier (or perhaps just tac crit multiplier?) is somehow linked to fate. is anyone aware of this?
You can easily incorporate additional bonuses to those formulas, whether they be additive to Offence or multiplicative with Offence.

Extra % bonus (B) additive with Offence%:

Formulas (Crit Multiplier applied to Average Damage). f is an increase in Offence%:
dc = dn*(1+F) * (1 + C*M + V*N)
R = f/(1+F)

Adjusted formulas. f is an increase in Offence% or B%:
dc = dn*(1+F+B) * (1 + C*M + V*N)
R = f/(1+F+B)
The remaining R formulas are not affected.

Formulas (Crit Multiplier applied to Maximum Damage). f is an increase in Offence%:
Dc = Dn*(1+F) * [1 + C*(g*Mx-1) + V*(g*Nx-1)]
R = f/(1+F)

Adjusted formulas. f is an increase in Offence% or B%:
Dc = Dn*(1+F+B) * [1 + C*(g*Mx-1) + V*(g*Nx-1)]
R = f/(1+F+B)
The remaining R formulas are not affected.

Extra % bonus (B) multiplicative with Offence%:

Formulas (Crit Multiplier applied to Average Damage):
dc = dn*(1+F) * (1 + C*M + V*N)
Adjusted formulas. b is an increase in B%:
dc = dn*(1+F)*(1+B) * (1 + C*M + V*N)
R = b/(1+B) (additional, new formula)
The remaining R formulas are not affected.

Formulas (Crit Multiplier applied to Maximum Damage):
Dc = Dn*(1+F) * [1 + C*(g*Mx-1) + V*(g*Nx-1)]
Adjusted formulas. b is an increase in B%:
Dc = Dn*(1+F)*(1+B) * [1 + C*(g*Mx-1) + V*(g*Nx-1)]
R = b/(1+B) (additional, new formula)
The remaining R formulas are not affected.

The case you're mentioning is where: R = f/(1+F+B)
If you can evaluate B (all the other bonuses, other than F, the offence%), you will find out exactly how much an increase (f %) in offence% will end up increasing the skill's damage (R is the net % increase in the skill's damage compared to what it was before you added the extra f% of Offence.)
Example: Offence (F) is 35%, other bonuses (B) add 25% to offence (additive as you say). You increase offence by 3%. The net increase in damage is: R = 0.03 / (1+0.35+0.25) = 0.188 or 1.88%.
Even if you didn't have the 25% additional bonus, adding +3% to 35% obviously doesn't represent a net increase (R) of 3%, but only 0.03/(1.35) = 2.2%. This is normal.
Also, in this additive case, adding 1% to F is exactly the same as adding 1% to B. So if your purpose is to see where it is more efficient to increase damage, by increasing F or B, you can just compare the % increases themselves, without having to calculate the net increase, R.

Regarding Tactical Critical Multiplier:
Pre-Isengard, the Fate tooltip indicated it increased the Tactical Critical Multiplier. Now the Fate tooltip doesn't mention this any more. I did some tests on very low level Minstrel where I doubled Fate and saw no increase in crits at all. This may not apply to high level characters, though, so further testing is needed.

Last edited by Alad.; Nov 09 2011 at 01:08 PM.

38. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

I love this thread. It occurred before my own work on RoI and corroborates the equations and most conclusions very nicely.

If you would like to review/critique it, it can be found in the link below. It's hunter-centric and takes into account all the various buffs from LIs etc.

39. ## Re: How to Evaluate/Compare Different Damage Bonuses Reliably

Looks like you spent some dummy time there as well I wish more people did that and discovered all the bugs and features. I can't comment though; I'm sure others would have caught any glitches.

What would be nice is if each skill tooltip showed all the data about that skill:
Base, before any bonuses:
- Min-Max damage
- Crit and Dev Crit chance and Multipliers
After all bonuses:
- Min-Max damage
- Crit and Dev Crit chance and Multipliers

At least then we'd be able to tell how the bonuses interact with the base damage, what the skill's crit chances and multipliers are, etc... It would also allow us to determine mob mitigations more easily.