Damage Per Round

ac_noj · Jul 10, 2008

Thanks loisel, I found this very interesting. I did a quick analysis of striker damage when I first got the books, and while my approach was very different (it focused on the use of all 4 encounter powers over 4 rounds at level 30) the result was pretty similar: Rangers are the top damagers, then rogues, and then warlocks.

The reasons for it seem pretty clear too: The rogue beats out the warlock mostly on sneak attack damage, and the ranger beats both because their focus on multiple attacks lets them apply their Str/Dex and Enhancement bonuses multiple times per round.

I have a question about the way you've used Lasting Frost and Frost weapons. Does using a weapon that deals cold damage adds the Cold keyword to every attack?
If that's the case I can see it making an amazing combo with Wintertouched, Nimble Blade, and Sneak Attack.

Edit: Nevermind I just found the rule in the PHB page 226: "When you use a magic item as part of a racial power or a class power, the keywords of the item’s power and the other power all apply. For instance, if a paladin uses a flaming sword to attack with a power that deals radiant damage, the power deals both fire damage and radiant damage."

Danceofmasks · Jul 10, 2008

Weapon that deals cold damage isn't the reason the powers you use become cold powers.
It's due to keyword inheritance, PHB p226.
Seems if there's a keyword anywhere on the item you're using for your attack, the power you use gets all those keywords.

azarias · Jul 10, 2008

Interesting (and beautifully presented) analysis.

Are you planning to factor in the Cleric, Paladin and Warlord?

I might have missed the statement, but I suppose you've ruled these out as support rather than primary damage classes. Still, I'd be curious to see where they stand compared to the Wizard and Warlock.

loisel · Jul 10, 2008

Malicea said:
For the 'lock, if he's Infernal and using Hellish Rebuke, it's quite possibly worthwhile for him to intentionally take the OA for using it adjacent.

That's a good combo, and I guess the riposting rogues would benefit as well. I'm not sure what I'm going to do yet, we'll see.

I think allowing 1 encounter-duration daily might be relevant for the paragon and epic tiers

There are too many of those and I can't account for all of them. So I'm gonna leave the one that I put in for the Fighter, and mention the rest in the text or something.

loisel · Jul 10, 2008

azarias said:
Are you planning to factor in the Cleric, Paladin and Warlord?

I might have missed the statement, but I suppose you've ruled these out as support rather than primary damage classes. Still, I'd be curious to see where they stand compared to the Wizard and Warlock.

I'm not discriminating against clerics, paladins and warlords; I just don't know them very well. Maybe I'll add them later.

azarias · Jul 10, 2008

Clerics I know: since this is a damage comparison, the following might be useful bases:

(1) Melee Cleric: Dwarf Mauler (Dwarven weapon prof at 1st, etc)

(2) Ranged Cleric: Elf Cleric/Ranger (18/18 Wis/Dex, Ranger multiclass feats - essentially, Wis Cleric powers plus Dex Ranger powers instead of Cleric Str powers)

The latter is perhaps as close as 4E gets to a multiclass at Heroic, but it's probably also the highest-damage basic Cleric type.

My hunch is that some form of the latter, especially, comes higher on a damage chart than might be expected for a 'support' act.

Good thread anyway, thanks.

Natro · Jul 10, 2008

Your equation is incorrect. The equation that I have is more complicated, but I think it is correct. The basic idea is this. If you have 50% of missing on an attack, and if you have two attacks, then you have (50% x 50%) = 25% chance of missing on both attacks. Hence, you have a probability of 75% of hitting at least once. Therefore, you must add 75% of quarry damage. In general, if you hit with probability P, then (1-P) is the probability of missing, and (1-P)^2 is the probability of missing twice in a row, and 1-(1-P)^2 is the probability of hitting either once or twice.

I put a bit more thought into this and still think your calculation for quarry damage is incorrect.

My proof:

Code:

 [/FONT]
[FONT=Times New Roman]Original Equation for Quarry Damage:[/FONT]
[FONT=Times New Roman](1-(1-PCrit!RC)^Toons!RC3)*(Toons!RC34)+(1-PCrit!RC)^Toons!RC3*(1-(1-PHit!RC)^Toons!RC3)*((Toons!RC32+Toons!RC34)/2)[/FONT]
[FONT=Times New Roman] [/FONT]
[FONT=Times New Roman]http://en.wikipedia.org/wiki/Probability[/FONT]
[FONT=Times New Roman] [/FONT]
[FONT=Times New Roman]Probability of inflicting damage:[/FONT]
[FONT=Times New Roman]Mutually Exclusive Events P(A or B) = P(A)+P(B)[/FONT]
[FONT=Times New Roman] [/FONT]
[FONT=Times New Roman]Chance to inflict non-critical Quarry Damage(on any primary attack):[/FONT]
[FONT=Times New Roman]P(First Primary Attack) = PHit!RC[/FONT]
[FONT=Times New Roman]P(Second Primary Attack) = PHit!RC[/FONT]
[FONT=Times New Roman]P(First Primary Attack or Second Primary Attack) = (PHit!RC)+(PHit!RC)[/FONT]
[FONT=Times New Roman]Applying the mathematical distributive property…[/FONT]
[FONT=Times New Roman]P(Any Primary Attack) =  (PHit!RC)*Toons!RC3[/FONT]
[FONT=Times New Roman] [/FONT]
[FONT=Times New Roman]Chance to inflict non-critical Quarry Damage(on any secondary attack):[/FONT]
[FONT=Times New Roman]P(Any Secondary Attack) = (PHit2!RC)*Toons!RC16[/FONT]
[FONT=Times New Roman] [/FONT]
[FONT=Times New Roman]Chance to inflict non-critical Quarry damage on ANY attack:[/FONT]
[FONT=Times New Roman]P(Any Primary Attack) + P(Any Secondary Attack) = [/FONT]
[FONT=Times New Roman]((PHit!RC)*Toons!RC3)+((PHit2!RC)*Toons!RC16)[/FONT]
[FONT=Times New Roman] [/FONT]
[FONT=Times New Roman]Probable ‘scaled’ non-critical quarry damage:[/FONT]
[FONT=Times New Roman](Probability of inflicting the damage)*(Damage inflicted) =[/FONT]
[FONT=Times New Roman](((PHit!RC)*Toons!RC3)+((PHit2!RC)*Toons!RC16))*((Toons!RC32+Toons!RC34)/2)[/FONT]
[FONT=Times New Roman] [/FONT]
[FONT=Times New Roman]Apply the same principles as above to critical damage…[/FONT]
[FONT=Times New Roman]Probable ‘scaled’ critical quarry damage:[/FONT]
[FONT=Times New Roman](((PCrit!RC)*Toons!RC3)+((PCrit2!RC)*Toons!RC16))*(Toons!RC34)[/FONT]
[FONT=Times New Roman] [/FONT]
[FONT=Times New Roman]Corrected Equation for Quarry Damage:[/FONT]
[FONT=Times New Roman]Probable non-critical damage + probable critical damage =[/FONT]
[FONT=Times New Roman](((PHit!RC)*Toons!RC3)+((PHit2!RC)*Toons!RC16))*((Toons!RC32+Toons!RC34)/2)[/FONT]
[FONT=Times New Roman][SIZE=2]+ (((PCrit!RC)*Toons!RC3)+((PCrit2!RC)*Toons!RC16))*(Toons!RC34)[/SIZE][/FONT]
[FONT=Times New Roman]

Quote:
In your assumptions you state that secondary effects will trigger 50% of the time. I think this should extend also include the extra attack a fighter would get for an adjacent marked opponent moving or shifting.
No, what I assume is, that your foe attacks you every turn and hits you 50% of the time. If you have a power that depends on being attacked or hit, that's where this 50% comes in. There are no OA in this duel, because it's just a duel without any complications.

Any ranged or casting class is almost guaranteed to draw an extra attack from a fighter. You can assume the fighers opponent is always marked. Assuming a smart duel, a ranged or casting class on their turn can either 1) move away thus drawing an attack of opportunity, 2) shift away thus drawing a basic melee attack from being marked (is not an attack of opportunity), or 3) attack/cast while adjacent to the fighter thus drawing an attack of opportunity. The only way to not have an extra attack would be to make a melee based attack against the fighter which is not likely a good option for these class types. For these reasons, I do not think it is unreasonable to assume that a fighter will make a secondary attack 50% of the time in this general analysis.

Quote:
2) I am confused about your addition of the 'Auto' damage in the extra damage section. It looks like you have already accounted for attribute modifier damage in the basic attack damages. This portion should be omitted from the calculation if it is already accounted for in the basic attack damages. What would grant this automatic damage anyway?
This is not the attribute damage. The auto damage is damage that occurs regardless whether you hit or miss. For instance, a Stormwarden gets to apply Dex Bonus damage to one adjacent for at the end of each turn. Since this is a duel, I assume that every round, the stormwarden bases the enemy and hits, so at the end of each round, that one enemy gets dex bonus damage.

There are other ways of delivering automatic damage. For instance, a mage with "cloud of dagger" will automatically deal Wisdom Bonus damage to a foe that begins its turn in the square of the spell. Therefore, hit or miss, you get Wisdom Bonus damage once per turn.

I have been focused on the level 1 analysis. Since we are assuming a smart duel, I have got to believe an opponent would not stay in the square that has the "cloud of dagger" effect maintained in it. Additionally, I could not figure out what the fighter was gaining the automatic damage from. The damage on miss is handled in different columns.

loisel · Jul 10, 2008

Natro said:
I put a bit more thought into this and still think your calculation for quarry damage is incorrect.
Mutually Exclusive Events P(A or B) = P(A)+P(B)
P(First Primary Attack or Second Primary Attack) = (PHit!RC)+(PHit!RC)

I didn't look at the rest, but hitting the first time does not exclude hitting the second time (they are not mutually exclusive events...)

If it makes a difference to you, I'm a math professor at Temple University.

Any ranged or casting class is almost guaranteed to draw an extra attack from a fighter.

Yeah, there are many interesting special cases for the foe. For instance, a foe could have a fear aura that stuns you. However, for simplicity in this duel, I'm just assuming that your opponent is some miscellaneous monster with no special abilities, no special resiatances, etc...

I have got to believe an opponent would not stay in the square that has the "cloud of dagger"

Certainly, nobody would voluntarily stay in that square. However, you take damage from being in that square at the start of your turn, before you've had a chance to move, so the enemy doesn't have a choice.

But, for instance, being an orb specialist and prolonging the cloud of daggers until the next turn, that would be entirely useless in this little experiment, because I would assume that after the first turn of damage, your opponent moves out of that square.

loisel · Jul 10, 2008

double post

Natro · Jul 10, 2008

This analysis is very interesting to me and I am just trying to make sure it is yielding meaningful and represtative results within its scope.

I didn't look at the rest, but hitting the first time does not exclude hitting the second time (they are not mutually exclusive events...)

In general, if you hit with probability P, then (1-P) is the probability of missing, and (1-P)^2 is the probability of missing twice in a row, and 1-(1-P)^2 is the probability of hitting either once or twice.

You are correct; my mistake! I incorrectly applied the appropriate probability equation for this case. We are talking about quarry damage which gets applied only once in a round and the attacker gets to choose which attack to apply the damage to after all the attacks are rolled. It does not matter which attack hits or which attack the damage gets applied to. Essentially this a logical 'OR' where the success of either event will grant the opportunity to apply the quarry damage. P(A or B) = P(A)+P(B)-P(A and B) = P(A)+P(B)-P(A)P(B). Since in this case P(A)=P(B) we get 2*P(A)-P(A)^2 which is equal to your formula.

The only additional thing I tried to account for is the secondary attack. Since this attack is only possible if the primary attack is successful, it should not be included in the chances to apply quarry damage.

Damage Per Round

ac_noj

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Danceofmasks

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azarias

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loisel

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loisel

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azarias

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Natro

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loisel

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loisel

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Natro

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