# Damage Per Round



## loisel (Jul 6, 2008)

Damage Per Round

This thread is a comparison of the Damage Per Round of various character builds, in a one-on-one duel scenario. The only thing we're trying to do in this thread is to get the highest possible damage per round at various levels against a wide range of armor classes.

Related Threads

There's a few more statistical threads out there and they are very useful.


 The MM Statistics Thread
 Another DPR Thread: this one assumes an enemy with average defenses, and looks at your DPR as your level ranges from 1 to 30.

Notes about this thread


 I assume that all characters have all useful damage feats. This includes Lasting Frost and either Scimitar Dance or Hammer Rhythm. In order to get both at level 11, you must retrain a heroic feat.
 At Level 1, only basic nonmagical gear is allowed.
 At Level 11, All weapon-based attacks assume a +2 Frost Weapon, to help with Lasting Frost. This is upgraded to +4 at Level 20.
 At Level 11 and 20, All magical attacks assume a Wand of Icy Rays, and I assume that this is sufficient to give your power the [cold] keyword. I'm optimizing RAW, you may have to figure things out with your DM. Errata, er, I mean, "FAQ", says this doesn't work.
 For powers that proc when you are hit, I assume that your enemy hits you 50% of the time. This applies to the riposting Rogues, as well as to the Warlock's Hellish Rebuke.
 A power that targets Will is not directly comparable with a power that targets AC. As a heuristic, I am giving a bonus of +1 to hit if you target Reflex, and +3 to hit if you target Will or Fortitude; this is supposed to roughly match what monster defenses look like. *EDIT*: I know about this thread, I just haven't done anything about it yet.

The spreadsheet is here: v1.10.

At the time of this writing, I have looked at At-Will powers at level 10 and 20, and at Encounter powers at level 10.

I have looked at Fighters, Rangers, Rogues, Warlocks and Wizards. I have taken into account all the probabilities, critical hits, quarry, etc... very carefully. If you find an error in my spreadsheet, please let me know. I think my formulae are good, but I do find errors in my toons from time to time.

It's important to mention Fighter stances like *Rain of Steel* (see the Level 20 chart for an example of this). A particular awesome combination would be a Ranger who multiclasses into Fighter to pick up these stances.

If you can give me any suggestions for good builds that are going to score high on this contest, please let me know.

Without further ado, here are the graphs.

Level 1

At Level 1, unsurprisingly, characters are pretty well balanced, although already the Warlocks show their weakness. These are PHB-only characters and are not optimized to the max, but they are good characters. It's Level 1, we're still just playing games.

I've only looked at At-Will powers.

To read this table, look at the legend. Each line in the graph corresponds to a character using a specific power. I usually give the race, the class (and later the paragon path), as well as the level (in this chart, it's all 1), the weapon and the at-will power that's being used. The number(s) at the end (like 20 or 19/16) denote the ability scores. If it's just one number, that's the primary ability score (e.g., Str for a Fighter.) If it's two numbers, the first is the primary ability score, the second is the secondary ability score. The primary ability score is always the one that applies to the attack roll of the power being used. So, for instance, for a Wizard with Cloud of Daggers, the Primary is Intelligence, and the secondary is Wisdom. Sometimes, the Primary stat is lower than the Secondary!







Level 11

Level 11 is Serious Business. You get your Paragon Paths and, unless you've planned out carefully since Level 1 (or you cheat like in Dragon Magazine ), you won't be able to take those super important feats like Scimitar Dance. The very first graph I produced was for the Level 11 toons, and many of them are Bugbears and Minotaurs, because that lets you get slightly better weapons and get slightly better ability scores. However, I've also produced a second chart from PHB-only classes, adding some character types that people want to play, just to see what their "DPR cost" is (compared to the best possible characters).

You also now have many Encounter powers, so you can expect to be busting out lots of those during any given encounter. Therefore, I am including the Encounter Power chart as well.
















Level 20

At Level 20, your character is having his mid-life crisis, and is probably buying a corvette and cruising around the mall trying to impress the schoolgirls. Many of the game-changing powers (Blade Cascade?) make their appearance in the Paragon Levels, so I take another look at optimized characters. The big surprise here is the Fighter stance Unyielding Avalanche. Any melee character should multiclass to Fighter and substitute their daily for this stance, it is simply that good.

Important Remark: Although I have included "Unyielding Avalanche", which is a daily Fighter stance, it is *only as an example* of what happens if you throw in some dailies. There are many other DPR-enhancing abilities like Flaming Sphere, more stances, Armor of Agathys, etc... Because this one feature is causing so many comments, I will remove it from a future version of the spreadsheet.


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## blargney the second (Jul 6, 2008)

Neat stuff!  Thanks for posting these here. 
-blarg


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## Psychic Robot (Jul 6, 2008)

Ermm...shouldn't the warlock be a little higher up?  (Not in terms of math, but theory.)


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## loisel (Jul 6, 2008)

Psychic Robot said:


> Ermm...shouldn't the warlock be a little higher up?  (Not in terms of math, but theory.)




I wish. I wanted to play a lock, and I wanted to quantify the DPR cost of playing a Lock over a Ranger, so I did all this.

I still would like to play a lock but right now I'm finding it hard to swallow. It seems like the Wizard is a better choice...


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## MeMeMeMe (Jul 6, 2008)

There's more to class balance and power than DPR, though.


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## GnomeWorks (Jul 6, 2008)

Some rather nifty work, there. I'm not really sure I understand what's going on with those tables, but it looks like it took a long time...



MeMeMeMe said:


> There's more to class balance and power than DPR, though.




Not the point of the thread. It's an examination of potential damage output, not asking whether the classes are balanced or not.


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## Revinor (Jul 6, 2008)

I know it is a lot of work to prepare it, but what about actually sticking to PHB races? I don't really think that classes were balanced against MM races, so having same graph for PHB races would be great.

If I could request one more thing for checking... I know it is not possible with RAW, but assuming it would be allowed to multiclass into Stormwarden with Warrior of the Wild, how well Rogue->Stormwarden would manage here (synergy on dex giving probably like extra 20 guaranteed dmg at 16 lvl).

Are ranger archers completely out of competition ? I feel their damage is not best, but are they really worse that warlocks in this area?


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## MeMeMeMe (Jul 6, 2008)

GnomeWorks said:


> Not the point of the thread. It's an examination of potential damage output, not asking whether the classes are balanced or not.




I thought the OP's goal was to decide which class he wanted to play. Calculating DPR was just the way he chose to decide if it was worth it.


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## loisel (Jul 6, 2008)

Revinor said:


> I know it is a lot of work to prepare it, but what about actually sticking to PHB races?




Yeah, I'm wondering too. I'll probably do a level 10 matchup, but assuming the order doesn't change too much, I'll do just one chart.



> If I could request one more thing for checking... I know it is not possible with RAW, but assuming it would be allowed to multiclass into Stormwarden with Warrior of the Wild




That you'll have to try yourself (just download the spreadsheet). It will help the rogue for sure, although I'm guessing a Ranger Stormwarden will still be a little bit better.



> Are ranger archers completely out of competition ? I feel their damage is not best, but are they really worse that warlocks in this area?




I didn't do them, but Archers are probably comparable to Rogues. The reason why Stormwardens dominate is because of three reasons:

1) The damage on a miss, due do scimitar dance. That's 5-6 points of damage at the right end of the chart.

2) The automatic dex damage from the Stormwarden 11 ability. That's another 5-6 damage, everywhere on the chart.

3) At the left end of the charts, Power Attack plays an important role.

For these reasons, you can imagine the Archers as being maybe 10 DPR less than a Stormwarden across the board?

Archers do get access to Sly Hunter (+3 damage to isolated targets), but I personally think that's not a good feat, because it'll be too hard to find isolated targets.

Again, if you really want to know, just try the spreadsheet.


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## generalhenry (Jul 6, 2008)

wooh

flash backs of 2E experience charts


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## Revinor (Jul 6, 2008)

One more thing - looking at http://www.enworld.org/forum/showthread.php?t=229092
it seems that attacking Reflex should be estimated more like 2.5-3 bonus compared to AC rather than just 1.

What is with critical for Warlock 11 Eldritch Blast 23 ? Seems that extras from magic rod/wand are not added in.


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## loisel (Jul 7, 2008)

Revinor said:


> One more thing - looking at http://www.enworld.org/forum/showthread.php?t=229092
> it seems that attacking Reflex should be estimated more like 2.5-3 bonus compared to AC rather than just 1.




I know, I saw it yesterday, but I haven't yet decided what changes to make. In the mean time, keep that in mind when you look at the graphs.



> What is with critical for Warlock 11 Eldritch Blast 23 ? Seems that extras from magic rod/wand are not added in.




Thanks for catching this error. I have fixed it and uploaded new versions, although I didn't bump the version number.


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## loisel (Jul 7, 2008)

Revinor said:


> I know it is a lot of work to prepare it, but what about actually sticking to PHB races? I don't really think that classes were balanced against MM races, so having same graph for PHB races would be great.




Done. The results are not very much different, just that everybody got shifted down a bit.


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## Roxlimn (Jul 7, 2008)

You want to replace Cloud of Daggers with Magic Missile backed by a Frost implement and Bracers of the Perfect Shot.  That ought to do a decent amount of damage on the left side of the chart, but the right side will suffer.  Also targeting Ref is worth at least a +3 to hit compared to AC.

Also, I don't understand the numbers besides each designation.  Is that estimated damage?  The damage for the Warlock seems a little low.


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## loisel (Jul 7, 2008)

Roxlimn said:


> You want to replace Cloud of Daggers with Magic Missile backed by a Frost implement and Bracers of the Perfect Shot.




I'll look into it, but at level 11, all I'll be using is the +2 to damage. So a magic missile is 2d4+2 + the rest, or average of 7 + the rest, whereas cloud of daggers is 1d6+the rest, and then later an automatic (wis bonus) damage. So that comes out to 1d6+6+the rest, which averages 9.5+ the rest. So my gut tells me that Cloud of Daggers is still better.

*EDIT: oh and I forgot. One of the reasons Cloud of Daggers is amazing is because it nets you 2x the Vulnerability 5 damage. That's because it's really two separate times that you damage your enemy, and both times are cold damage with the wand.*

In addition, Cloud of Daggers guarantees that every hit procs Lasting Frost, since the Wis Bonus damage comes from the Spell, which is Cold damage, which means that there is a 100% probability that your opponent is Cold vulnerable (which I take into account). On the other hand, Magic Missile does not always hit, which means that some rounds you will not have the Vulnerability...

Even if you gave the character a +4 Bracer, it would still be 9 vs 9.5...



> Also, I don't understand the numbers besides each designation.  Is that estimated damage?  The damage for the Warlock seems a little low.




That's my code for the ability scores of my characters. I forgot to describe that in the top post (will fix in a minute). When it's just one number, it's the primary stat (e.g., a Feylock with 23 would be 23 Charisma). When it's two numbers separated by a slash, it's primary/secondary. So a Stormwarden with 22/21 has Str 22, Dex 21. The primary is the stat you use to roll to hit. Even though I think a Stormwarden should have more Dex than Str, the primary stat is Str.

The damage from the warlocks is indeed low, but that's just the way it is.


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## Roxlimn (Jul 7, 2008)

I don't think that Lasting Frost combo works the way you think it does.


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## loisel (Jul 7, 2008)

Roxlimn said:


> I don't think that Lasting Frost combo works the way you think it does.




Why not?

The Wand of Frost or whatever, puts the [cold] keyword on Cloud of Daggers. This means that half of all damage dealt by Cloud of Dagger is cold. On your turn, you attack. Maybe you hit, maybe you don't, but half of that damage is cold. Then, on your opponent's turn (at the beginning), he takes another Wis damage, from your Cloud of Dagger power, so half of that is cold as well.

At this point, for sure, Lasting Frost has activated.

Now comes your turn again. Say you miss. Then comes your enemy's turn again. He's in the Cloud of Daggers, so he takes Wis damage, half of which is cold. So he also takes damage for his Vulnerability to cold, and Lasting Frost activates again.

Now comes your turn again. Say you hit. Then half the damage is cold, so he takes the damage for his vulnerability to cold. Then it's his turn again. He takes Wis damage, half of which is cold, so the vulnerability procs again.

I don't see where I went wrong...?


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## Klaumbaz (Jul 7, 2008)

DPR in isolation and "sterile" combat against the universal punching dummy isn't the be-all end-all of class ability.

many classes shine much better than your showing. 

This is only single target vs single target, not allowing for various conditions, multiple rounds of combat, and a host of other problems. 

How about you make 100 different scenario's ranging from one single target badass to a horde of a bajillion minions, and then multiply that by different environments (forest, cave, partial darkness, snow, fog, rain, etc). and log each action each round, and then post the statistical results?


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## Taldrin (Jul 7, 2008)

*Still not the point.*



Klaumbaz said:


> DPR in isolation and "sterile" combat against the universal punching dummy isn't the be-all end-all of class ability.
> 
> many classes shine much better than your showing.
> 
> ...




Wow, this is why I love forum threads.  Some people never read past the first post (if that) thus continuing to address non points that were brought up and dismissed several posts ago.  As stated by GnomeWorks: "Not the point of the thread. It's an examination of potential damage output, not asking whether the classes are balanced or not."


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## Archus (Jul 7, 2008)

loisel said:


> The damage from the warlocks is indeed low, but that's just the way it is.



My Warlock player has been wondering exactly how a Warlock is supposed to be a striker.  She feels somewhere between a rogue and a wizard without the damage of the rogue or control of a wizard.  And many at the table see how the cleric out controls the wizard (at least in AoE).  

Since it is about the effectiveness of the party and not a competition of how powerful characters are we are concerned about balance and role protection.  Thus far we see a need for some adjustments for role protection, but we have only played for a little while and expect to know better after a few more adventures are under our belts.


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## loisel (Jul 8, 2008)

Archus said:


> My Warlock player has been wondering exactly how a Warlock is supposed to be a striker.




Yeah, if you were expecting to "specialize in dealing high amounts of damage to a single target at a time" (PHB16), I don't think that's gonna happen...


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## peterparker18974 (Jul 8, 2008)

Show me where I can find this "wand of frost", since it doesn't appear in the players handbook, and none the wands grant any specific key words other than their dailies.  [FONT=Verdana, Arial, Helvetica, sans-serif][/FONT]


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## loisel (Jul 8, 2008)

peterparker18974 said:


> Show me where I can find this "wand of frost", since it doesn't appear in the players handbook, and none the wands grant any specific key words other than their dailies.  [FONT=Verdana, Arial, Helvetica, sans-serif][/FONT]




The wand in question is "Wand of Icy Rays", PHB243. However, for that debate, you're in the wrong thread. See http://www.enworld.org/forum/showthread.php?p=4346495


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## WOLead (Jul 8, 2008)

The data seems unfair, but when I can finally open that xlsx file I'll look over it and add in see.  Seems, not is as I have not actually opened that xlsx file.  Gotta update my OpenOffice in hopes of actually seeing it.

Just a few ideas of what I hope to work in, vs. Def average from that post the beginning post listed.  Also I'm hoping to look at the data and see if there was any optimization that was lacking in the Warlock's side.  Though that all depends on the equations I see.


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## loisel (Jul 8, 2008)

WOLead said:


> Though that all depends on the equations I see.




If you find a bug in my equations, please let me know.

If you just want to ballpark it to see if my damage is right, the leftmost end of the graph is easy to estimate: it's basically the average damage if everything hits (for a rough estimate, ignore the probability of critical hits). The right end of the graph is also easy to estimate, it should be all the automatic damage, plus 1/20 of the average of the damage that requires a roll to hit. In between, it's close to a straight line (with a little bit of curve only for characters with multiple or secondary attacks).

Now if the numbers you get out of this rough estimate at the right and left end of the graph, is not the same as what I got, then there's an error in my calculations.


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## MeMeMeMe (Jul 8, 2008)

WOLead said:


> The data seems unfair, but when I can finally open that xlsx file I'll look over it and add in see.  Seems, not is as I have not actually opened that xlsx file.  Gotta update my OpenOffice in hopes of actually seeing it.



If you're using a version of excel earlier than 2007, you need the Microsoft Office Compatibility Pack


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## loisel (Jul 8, 2008)

Archus said:


> And many at the table see how the cleric out controls the wizard (at least in AoE).




I guess I should do the calculation, but that sounds weird to me. I guess it depends on your Wizard build. I really like the Wisdom wizard (e.g., Int 16, Wis 19), with Cloud of Daggers and Thunderwave (too much fire resistance for Scorching Burst). Orb specialist, sleep spell, that's very good control, no? Also, you can go to the front line with this guy just the same as a Ranger or Cleric; you've got essentially the same HP and defenses as a Ranger (if you wear, say, leather.)

Just make sure you keep the Sleep spell all the way to level 30.


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## NeoNick (Jul 8, 2008)

Great work, very interesting! 

As my original question regarding at-will, encounter and dailys already has been clarified I erase it.


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## loisel (Jul 8, 2008)

NeoNick said:


> Great work, very interesting!
> 
> As I couldn't get the spreadsheet to work, I don't know wether you have taken in just at-will attacks? Or did you include Encounters and Dailys? (What file should I click on after having downloaded it?)




What? The filename for version 1.6 is dnd4e-1.6.xlsx, or whatever you name it when you save it.



> The reason I'm asking is that if your analysis examines at-will-attacks, then there may be a chance that Wizard have tried to balance some classes by giving a weak at-will-class more powerful encounters/dailys?




If you look at the graphs in the top post (they are the same as in the Excel file), you will see that I've looked mostly at At-Wills, but I've also done an analysis for Level 11 Encounter Powers.

However, it doesn't make that much difference. For At-Wills, Rangers are on top, and Warlocks at the bottom. It's the same with Encounter Powers, but Warlocks are actually slightly worse.

I didn't do dailies, but I expect the same pattern to come up.


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## NeoNick (Jul 8, 2008)

loisel said:


> What? The filename for version 1.6 is dnd4e-1.6.xlsx, or whatever you name it when you save it.




I must be doing something seriously wrong. I've downloaded the link after your text "_The spreadsheet is here_" twice and to different locations just to check. I've unzipped it and checked all catalogues, but I cannot find the file ending with .xls nor .xlsx Buhuuu  Help please. 

edit: When I get prompted to save the file it suggest to name the file "dnd4e-1.6.zip". Is that the source to my problem? Should it end with .xlsx when downloaded? 



loisel said:


> If you look at the graphs in the top post (they are the same as in the Excel file), you will see that I've looked mostly at At-Wills, but I've also done an analysis for Level 11 Encounter Powers.




Thanks /blush/, I can see that from the graph now. Missed my perception first.


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## loisel (Jul 8, 2008)

NeoNick said:


> edit: When I get prompted to save the file it suggest to name the file "dnd4e-1.6.zip". Is that the source to my problem? Should it end with .xlsx when downloaded?




That's certainly a problem. You should save it as an .xlsx file, not as a .zip file.


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## Canine (Jul 8, 2008)

loisel said:


> That's certainly a problem. You should save it as an .xlsx file, not as a .zip file.




Running the .exe from Microsoft and renaming the file to .xlsx fixed the file to work with my older copy of Excel.

The sheet looks very interesting, but I am wondering how the "Best of" functionality is modeled. Theoretically, the Divine Oracle reroll power should push Eyebite up across the board, due to increased chance to crit, and of course the increased chance to hit, but when I change the "Best of" number, I am not seeing any change in any of the sheets. I looked through the formulas, and can't find any reference to the "Best of" cells. This could be an issue with converting the file to something Excel 2003 can run, but either way, I was hoping you could take a look. I'll be thinking about ways to model it using your current method, but I need to keep looking around some more to be sure I understand everything before I start with any edits.

Thanks for this excellent work!


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## KingCrab (Jul 8, 2008)

Looks like great work!


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## loisel (Jul 8, 2008)

Canine said:


> The sheet looks very interesting, but I am wondering how the "Best of" functionality is modeled. Theoretically, the Divine Oracle reroll power should push Eyebite up across the board, due to increased chance to crit, and of course the increased chance to hit, but when I change the "Best of" number, I am not seeing any change in any of the sheets.




That's because I never got around to implementing that. Sorry. Maybe in a later version. I should just delete that column...

Sorry about that.


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## slaughterj (Jul 8, 2008)

loisel said:


> Starting at level 15, something amazing happens. A Fighter using a Stance will out-damage everybody else, *by far.* As a result, even if you're a Ranger Stormwarden, it would be seriously worthwhile looking into taking the Fighter multiclass, just so you can take some of the Fighter stances.




I had actually considered that, thinking of swapping out the level 5 Ranger daily for Rain of Steel.



loisel said:


> At Level 20, your character is having his mid-life crisis, and is probably buying a corvette and cruising around the mall trying to impress the schoolgirls. Many of the game-changing powers (Blade Cascade?) make their appearance in the Paragon Levels, so I take another look at optimized characters. The big surprise here is the Fighter stance Unyielding Avalanche. Any melee character should multiclass to Fighter and substitute their daily for this stance, it is simply that good.




It is interesting that you mention Blade Cascade and Unyielding Avalanche together, and effective suggest Blade Cascade should be swapped for Unyielding Avalanche.  Per damage calculations though, presumably the level 5 Rain of Steel does just as good as the level 15 Unyielding Avalanche, right?  So one could just get the level 5 instead, and keep Blade Cascade.  Sure, Unyielding Avalanche has various other benefits, but CON will be low and not raised level-by-level for many other melee types (a couple though), so the regeneration won't be much for many.  Is Unyielding Avalanche worth trading down to (i.e., trading a higher level daily for it)?


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## loisel (Jul 8, 2008)

slaughterj said:


> Per damage calculations though, presumably the level 5 Rain of Steel does just as good as the level 15 Unyielding Avalanche, right?




Oh my word, I hadn't seen that. If I update the Maul Fighter at level 11 with Rain of Steel, no doubt in my mind that he'll be the leading DPR character.



> Is Unyielding Avalanche worth trading down to (i.e., trading a higher level daily for it)?




I think Rain of Steel is plenty sufficient, although the Reaper's Stance (L25) is of course better.


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## Machus (Jul 8, 2008)

Nice work.

Sorry if I missed it but what was your rogue sneak attack damage rate?
With a high rate, brutals should rate higher than artful because they can either use pierce for higher hit and same damage (add str to damage), or sly if they have a CHA modifier for combined dex+str+cha.


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## loisel (Jul 9, 2008)

Machus said:


> Nice work.
> 
> Sorry if I missed it but what was your rogue sneak attack damage rate?
> With a high rate, brutals should rate higher than artful because they can either use pierce for higher hit and same damage (add str to damage), or sly if they have a CHA modifier for combined dex+str+cha.




I assume that you have CA. Then, I count the probability of hitting, P. Then, I count the average expected damage of a sneak attack, D. The damage from Sneak Attack is P times D. I have counted Brutal Scoundrel and such in this damage.


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## small pumpkin man (Jul 9, 2008)

loisel said:


> Oh my word, I hadn't seen that. If I update the Maul Fighter at level 11 with Rain of Steel, no doubt in my mind that he'll be the leading DPR character.
> 
> I think Rain of Steel is plenty sufficient, although the Reaper's Stance (L25) is of course better.



May I ask why you're inlcuding these dailys anyway? Since they only show up one encounter a day, they aren't really part of the characters "normal" damage potential.


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## loisel (Jul 9, 2008)

small pumpkin man said:


> May I ask why you're inlcuding these dailys anyway? Since they only show up one encounter a day, they aren't really part of the characters "normal" damage potential.




That's why I include both cases: using the stance, and not using it. If you don't like the comparison, just ignore that particular line.


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## small pumpkin man (Jul 9, 2008)

loisel said:


> That's why I include both cases: using the stance, and not using it. If you don't like the comparison, just ignore that particular line.



Blah, silly me, of course, continue.


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## DLichen (Jul 9, 2008)

Are you accounting for warlock's prime shot somewhere I'm not seeing for level 1s?


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## loisel (Jul 9, 2008)

DLichen said:


> Are you accounting for warlock's prime shot somewhere I'm not seeing for level 1s?




Wow, I totally missed it. For some reason, I had forgotten that Locks got this -- in fact, I misremembered the opposite, i.e., that Locks didn't get this bonus!

I am uploading fixed graphs and XLS files as I write this.


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## userbob (Jul 9, 2008)

Hi,

Just a quick one, unless i am missing something i am not sure that the comparisons are fair. Eyebite and Cloud of Daggers for example hit Will and Reflex not AC.

Unless like i say i missed something?

Also please bear in mind that in a lot of cases for example Eyebite the secondary effect is the main reason for casting, as is the fact that it targets Will.

In fact i would say that one of the main benefits i have found with Locks so far is there ability to hit lots of different defences.

Anyways just my 2 cents.


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## loisel (Jul 9, 2008)

userbob said:


> Hi,
> 
> Just a quick one, unless i am missing something i am not sure that the comparisons are fair. Eyebite and Cloud of Daggers for example hit Will and Reflex not AC.




Thanks for your comment. If you read the top post, you will see that I've given a +3 to hit for attacks that target Will, so that these attacks are more directly comparable to attacks that target AC.


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## userbob (Jul 9, 2008)

gah, sorry i did read all the posts just seem to have missed that one...

apologies

however i think a straight DPS is sometimes not the whole picture. for me being invisible to the enemy i just hit is sometimes much nicer than extra damage.


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## Andur (Jul 9, 2008)

Though I am sure you put plenty of work into this, it falls into the same line as other "single analysis" items, i.e. it is worthless when applied to actual gameplay.  The old saying "The sum is greater than its parts" applies tenfold to 4e.  

Net Damage mitigation needs to be figured out as well to give a "truer" approximation of power, in other words you would need to figure out for any given encounter how much damage a character both gives and receives and give a net figure.  If character 1 can dish out 20 DPR but takes 30 DPR and has 60 hp he will do less damage per encounter than Charater 2 who does 10 DPR only takes 5 DPR and has 70 hp.

DPR in itself means very little, Net Damage per day (4 encounters let's say) would be a more accurate model, but even then it needs to be done in a party environment.


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## small pumpkin man (Jul 9, 2008)

Andur said:


> Though I am sure you put plenty of work into this, it falls into the same line as other "single analysis" items, i.e. it is worthless when applied to actual gameplay.  The old saying "The sum is greater than its parts" applies tenfold to 4e.
> 
> Net Damage mitigation needs to be figured out as well to give a "truer" approximation of power, in other words you would need to figure out for any given encounter how much damage a character both gives and receives and give a net figure.  If character 1 can dish out 20 DPR but takes 30 DPR and has 60 hp he will do less damage per encounter than Charater 2 who does 10 DPR only takes 5 DPR and has 70 hp.
> 
> DPR in itself means very little, Net Damage per day (4 encounters let's say) would be a more accurate model, but even then it needs to be done in a party environment.



Nobody said anything about "power" except for you. Nobodies looking at this except as what it is, a limited look at at-will DPR. Interesting and only really helpful to say that if you want to build a pure dpr character, don't make a Warlock. 4e Tactics _are_ multileveled and tend to involve multiple characters, yes, but you have to walk before you can run, simple graphs like these help people understand what exacty the different classes are good at.

If you want more well rounded examinations of classes and powers, look for the threads discussing first level at-will/encounter/daily powers in their entirety.


----------



## Omen of Peace (Jul 9, 2008)

Interesting.
From calculations made in a "Dagger vs Rapier" thread over at WotC, I seem to remember Rogue Daggermaster was better than Shadow Assassin. The Wraithblade from Dragon 364 can be nice for multiple SAs per round.

I'm not too surprised about the Warlock. To me, it's the secondary effects (debuffs) they cause that make them interesting in the first place.


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## loisel (Jul 9, 2008)

Omen of Peace said:


> Interesting.
> From calculations made in a "Dagger vs Rapier" thread over at WotC, I seem to remember Rogue Daggermaster was better than Shadow Assassin. The Wraithblade from Dragon 364 can be nice for multiple SAs per round.




You can't have a frost weapon that's also a wraithblade, and a frost weapon is better than a wraithblade if you have Lasting Frost, which all these characters have.

So, in the scenario that I give, and for the levels that I consider, the Daggermaster seems to have slightly less DPR than the Rapier Shadow Assassins.


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## Andur (Jul 9, 2008)

spm, I have and have posted pretty much the exact same thing in those threads as well.  Looking at anything in 4e in a bottle is a pointless endeavour.  For any given round in an encounter one has to lok at all the resources available to the PARTY in that round and what combination is the best for the situation.  Anything less is lots of theory little practical...


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## Old Gumphrey (Jul 9, 2008)

Gotta love that we're comparing a _bugbear _ranger with a level 7 fighter power and the scimitar dance feat to a generic warlock with a level 3 area power using it on a single target.


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## loisel (Jul 9, 2008)

Old Gumphrey said:


> Gotta love that we're comparing a _bugbear _ranger with a level 7 fighter power and the scimitar dance feat to a generic warlock with a level 3 area power using it on a single target.




I tried to compare the bugbear ranger to a non-infernal warlock, and that's the best I could come up with. On the other hand, I did find a good combo with the Life-Stealer, but I guess you were too busy prejudging my calculations to notice.


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## Malicea (Jul 9, 2008)

I can't tell if you're figuring encounter-duration dailies into this. You mentioned Rain of Steel though. Is this comparison only for the first round in an encounter?

Apart from powers like Rain of Steel there's Armor of Agathys (warlock level 1 daily), and a bunch of wizard dailies that apply automatic damage over an entire encounter.

Did you consider multiclass combos? Fighter picking up Armor of Agathys, or Warlock picking up Rain of Steel, etc.?

The absence of all this would of course skew the DPR results against the classes that feature more of these powers.

Also: Why Spellstorm Mage for Wizard? No Blood Mage with Bolstering Blood on Cloud-of-Daggers?


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## loisel (Jul 9, 2008)

Malicea said:


> Apart from powers like Rain of Steel there's Armor of Agathys (warlock level 1 daily), and a bunch of wizard dailies that apply automatic damage over an entire encounter.




Good point, although I'm starting to regret having added that option for Rain of Steel, because I'm sensing a combinatorial explosion. You are right about Armor of Agathys, it's an awesome spell for DPR, better than Rain of Steel. I'm not 100% sure how it plays out in the duel for a Warlock, for the following reason.

Right now, I'm assuming that it's a "reasonable" duel, and that if you're a Warlock, each turn you start by sliding 1 square, then zapping him. The result is that the opponent doesn't start his turn adjacent to you. You could omit the slide, but then you would draw an OA...

But a Fighter who multiclasses into Warlock and picks up this daily, that would make an awesome combo. You can even layer it on top of Rain of Steel (holy crap!)

I'm going to think how to handle this. Maybe what I'll do is, I'll mention that there are lots of dailies that last for the whole encounter, but that I only give one example in the text at level 20? Whaddayathink?



> Also: Why Spellstorm Mage for Wizard? No Blood Mage with Bolstering Blood on Cloud-of-Daggers?




That's a good idea, I'll try to add it.


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## Natro (Jul 9, 2008)

Overall, I think this is a wonderful analysis!

I took a closer look at your DPR formulas and think I found some mistakes in your calculations...

1) For the 'Quarry' part of the equation (which covers warlock curse damage, ranger quarry, and rogue sneak attack damage) you are accounting for multiple attacks in both your probability and damage.  Per the rules, this damage can only be applied once per round.  This should greatly simplify this section of your calculation down to PHit(Dam) + PCrit(Dam).

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?

Additionally, it appears that some of your 'Toon' data is incorrectly entered in some cases (I only looked at the level 1 data).  It appears some min/max damages in accordance to the attribute values you provided are incorrect.  Perhaps this was due to an assumed feat?  Also the warrior and mage had some automatic damage being added to the equation.

Other Comments:
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.

It might be useful to indicate which feats are included in your analysis cases.

The general analysis should only include At-Will powers since this is the bread-and-butter of each class.  A comparison of daily, encounter, or any combination of these is only really valid for a single round of combat.


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## blargney the second (Jul 9, 2008)

Hi Natro, welcome to ENWorld!



Natro said:


> 'Toon' data



WTH does that mean?  Toon is a separate game has no relevance to any edition of D&D.
-blarg


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## Natro (Jul 9, 2008)

'Toons' is the name of one of the sheets in the excel workbook used to generate this analysis.  This is where all of the character data is summarized to be used in the analysis.


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## loisel (Jul 9, 2008)

Dear Natro,

Thanks for your comments.



Natro said:


> 1) For the 'Quarry' part of the equation (which covers warlock curse damage, ranger quarry, and rogue sneak attack damage) you are accounting for multiple attacks in both your probability and damage.  Per the rules, this damage can only be applied once per round.  This should greatly simplify this section of your calculation down to PHit(Dam) + PCrit(Dam).




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.

The equation you propose is only correct if you have a single attack.



> 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.



> Additionally, it appears that some of your 'Toon' data is incorrectly entered in some cases (I only looked at the level 1 data).  It appears some min/max damages in accordance to the attribute values you provided are incorrect.  Perhaps this was due to an assumed feat?




Yes, as detailed in the first post of this thread, I assume that the toons have all the pertinent feats. Mostly, this means Weapon Focus, or the equivalent feats for spells. In addition, as detailed in the first post in this thread, I am giving a flat +1 bonus to hit if you target Reflex, and +3 bonus to hit if you target Fort or Will. Although a Reflex attack is not directly comparable to an AC attack, the intent is to make them more comparable in this fashion.



> 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.



> It might be useful to indicate which feats are included in your analysis cases.




I think I listed them in the top post: weapon focus, scimitar dance or hammer rhythm and lasting frost are the main ones.



> The general analysis should only include At-Will powers since this is the bread-and-butter of each class.  A comparison of daily, encounter, or any combination of these is only really valid for a single round of combat.




There is one chart with encounter powers. Feel free to ignore it. The level 20 chart has a couple of toons using a daily stance power. Feel free to ignore those lines as well.


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## Malicea (Jul 10, 2008)

loisel said:


> Good point, although I'm starting to regret having added that option for Rain of Steel, because I'm sensing a combinatorial explosion. You are right about Armor of Agathys, it's an awesome spell for DPR, better than Rain of Steel. I'm not 100% sure how it plays out in the duel for a Warlock, for the following reason.
> 
> Right now, I'm assuming that it's a "reasonable" duel, and that if you're a Warlock, each turn you start by sliding 1 square, then zapping him. The result is that the opponent doesn't start his turn adjacent to you. You could omit the slide, but then you would draw an OA...
> 
> I'm going to think how to handle this. Maybe what I'll do is, I'll mention that there are lots of dailies that last for the whole encounter, but that I only give one example in the text at level 20? Whaddayathink?




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. With say a 20 starting Con on a Dwarf, with a minor action Second Wind to help with his damage taken as well, it's a viable tactic. Note that the OA on Hellish Rebuke will not trigger in the same turn, because OAs are interrupts and will resolve before Hellish Rebuke does, but it will trigger damage from last turn's HR. The combo yields up to 3 hits/round, triggering Cold vulnerability up to 3 times in the process.

The Fighter/Warlock with a Frost weapon, Wintertouched/Lasting Frost, Armor of Agathys, along with the rest of the fighter goodies should go pretty high yea.

I think allowing 1 encounter-duration daily might be relevant for the paragon and epic tiers, where character have 3-4 dailies. The above Fighter/Warlock for example, could have all three of Armor of Agathys, Rain of Steel and Unyielding Avalanche, and use them separately in three encounters.


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## 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."


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## 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.


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## 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.


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## 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.


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## 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.


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## 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.


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## 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:


```
[/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.


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## 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.


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## loisel (Jul 10, 2008)

double post


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## 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.


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## bardolph (Jul 21, 2008)

loisel said:


> The Wand of Frost or whatever, puts the [cold] keyword on Cloud of Daggers.



Can you please direct me to the reference that says you can use a wand to transfer the [cold] keyword to other powers?


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## yu gnomi (Jul 21, 2008)

The reference is to a customer service ruling that has since been reversed. At the time that this spreadsheet was made, the ruling was in effect. 

If you want to search for it, on gleemax it was known as "Doomsayer and the wand of Howling Doom" (or something very similar to that) question.


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## bardolph (Jul 21, 2008)

An interesting combo for the Warlock is to combine Armor of Agathys with Hellish Rebuke spammed from point blank range, deliberately provoking OAs in order to get the bonus damage from HR.  It gets even better if the enemy is marked by a Paladin or Fighter.


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## frankthedm (Jul 21, 2008)

generalhenry said:


> wooh
> 
> flash backs of 2E experience charts



Specifically, the charts out of the 2e _DM's Option: Hight level Campaigns_ IIRC.


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## bardolph (Jul 21, 2008)

yu gnomi said:


> The reference is to a customer service ruling that has since been reversed. At the time that this spreadsheet was made, the ruling was in effect.
> 
> If you want to search for it, on gleemax it was known as "Doomsayer and the wand of Howling Doom" (or something very similar to that) question.




So, does that mean that the OP (and associated spreadsheets) are no longer valid?

Another error I found is assuming that Lasting Frost can be inflicted by a melee attack with a Frost weapon.  I don't believe this is the case, since a martial _power_ does not have the cold keyword, even when the _weapon_ deals cold damage.

Is there any way for the Warlock to reliably inflict 1 hit point of damage to himself every round?  If so, then Hellish Rebuke becomes the highest damage At-Will power available, doing 3d6+(CON x2) per round without feats or enhancement bonuses.  If not, then the Warlock has to wait until 11th level and the Blood Mage Paragon Path, in which case Bolstering Blood + Hellish Rebuke every round becomes a very high damage combo.  In the meantime, there's always Armor of Agathys plus Hellish Rebuke spam at point-blank range, triggering OAs from the opponent (which would trigger Defender punishment as well).

Hmm, how about if the Warlock suits up in some Black Iron Plate (accepting the -2 penalty to attack rolls) and parks next to a Flaming Sphere or Wall of Fire?


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## small pumpkin man (Jul 21, 2008)

bardolph said:


> So, does that mean that the OP (and associated spreadsheets) are no longer valid?



It means the Warlock does even less damage, and possibly the Wizard too. The ranger, Rogue and Fighter are not affected.


bardolph said:


> Another error I found is assuming that Lasting Frost can be inflicted by a melee attack with a Frost weapon.  I don't believe this is the case, since a martial _power_ does not have the cold keyword, even when the _weapon_ deals cold damage.





			
				FAQ said:
			
		

> *When do a Magic Item's keywords apply?*
> 
> If you use a magic item's power in conjunction with a power granted to you by your race or class, that item's keywords are added to the regular keywords of the power you are using. For example, if you are have a Flaming Weapon, and you use an at-will power to attack an enemy along with the at-will power of the Flaming Weapon, your attack will have the Fire keyword in addition to the normal keywords of your attack. You have to be using the powers of the weapon for those keywords to be added; simply using the magic item does not necessarily mean every keyword attached to a power of that item will be added.





bardolph said:


> Is there any way for the Warlock to reliably inflict 1 hit point of damage to himself every round?  If so, then Hellish Rebuke becomes the highest damage At-Will power available, doing 3d6+(CON x2) per round without feats or enhancement bonuses.  If not, then the Warlock has to wait until 11th level and the Blood Mage Paragon Path, in which case Bolstering Blood + Hellish Rebuke every round becomes a very high damage combo.  In the meantime, there's always Armor of Agathys plus Hellish Rebuke spam at point-blank range, triggering OAs from the opponent (which would trigger Defender punishment as well).



Bolstering Blood only works with Wizard Encounter powers.


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## bardolph (Jul 21, 2008)

FAQ said:
			
		

> When do a Magic Item's keywords apply?
> 
> If you use a magic item's power in conjunction with a power granted to you by your race or class, that item's keywords are added to the regular keywords of the power you are using. For example, if you are have a Flaming Weapon, and you use an at-will power to attack an enemy along with the at-will power of the Flaming Weapon, your attack will have the Fire keyword in addition to the normal keywords of your attack. You have to be using the powers of the weapon for those keywords to be added; simply using the magic item does not necessarily mean every keyword attached to a power of that item will be added.



Wow, interesting.  I'm surprised that WotC supports combining Lasting Frost with Martial Powers.  Seems overpowered to me, and counter to the intention of the feat (just an assumption of mine, but it seems like Lasting Frost was designed with Arcane powers in mind).  I wonder if they'll reverse this decision.  In the meantime, I think I'm houseruling this one away, since it contradicts the RAW anyway.


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## Splart (Jul 21, 2008)

Most excellent work.  I was thinking of making a similar chart, but plotting PC level on the X axis instead of AC.  AC would be assumed to be 14 + PC level.  This would give clear answers on how much damage a certain class does over another one at a particular level, and should show how PCs damage output changes as they level.  Ah well.  Work for another day.

Can you help me understand the critical damages?  For starters, what gives the level 1 rogue on line 144 a bonus on crits?

Next, let's look at line 129, the Elf Ranger 11 Stormwarden  Twin Strike Scimitar 19/22.  For his base damage, the damage range is +2 weapon, +1 weapon spec and +1 TWF, and 1d8 weapon damage to give 5 to 12 range.  For his crit range, first we give the max 12 damage for crit, then add 2 W since this is a scimitar, a high crit weapon.  This is the same as hit base attack, so this adds 2 X ( 5 to 12 ) = 10 to 24.  Adding 12 for the crit, we have 22 to 36.  Now we also add 2d6 for the frost weapon crit, giving 24 to 48.

However, your spreadsheet gives the crit range as 16 to 40.  My first guess is that you did not add in the +2 weapon, +2 feats into the 2 W for scimitar.  Is that correct?  If so, can you let me know why you thought the damage from 2 W would exclude enchantment and feat bonuses?

Can you let me know how you did your calculation, or what I missed?

--Splart

P.S.  One high damage combination I didn't see is a rogue who forgoes his paragon path to steal the Ranger At-will of Twin Strike.


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## Cirex (Jul 21, 2008)

bardolph said:


> Wow, interesting.  I'm surprised that WotC supports combining Lasting Frost with Martial Powers.  Seems overpowered to me, and counter to the intention of the feat (just an assumption of mine, but it seems like Lasting Frost was designed with Arcane powers in mind).  I wonder if they'll reverse this decision.  In the meantime, I think I'm houseruling this one away, since it contradicts the RAW anyway.




But just remember that : 



> You have to be using the powers of the weapon for those keywords to be added; simply using the magic item does not necessarily mean every keyword attached to a power of that item will be added.




So, if you are wielding a frost weapon, the [cold] keyword doesn't get added. Now, if you turn the damage into cold damage (with the power) then you do. 

It's just a minor point, but it's important to keep in mind for other weapons.


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## HeinorNY (Jul 21, 2008)

Welcome to the new era of Table Top Role Playing Games.


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## loisel (Jul 22, 2008)

Splart said:


> Next, let's look at line 129, the Elf Ranger 11 Stormwarden  Twin Strike Scimitar 19/22.  For his base damage, the damage range is +2 weapon, +1 weapon spec and +1 TWF, and 1d8 weapon damage to give 5 to 12 range.  For his crit range, first we give the max 12 damage for crit, then add 2 W since this is a scimitar, a high crit weapon.  This is the same as hit base attack, so this adds 2 X ( 5 to 12 ) = 10 to 24.  Adding 12 for the crit, we have 22 to 36.  Now we also add 2d6 for the frost weapon crit, giving 24 to 48.




You're counting the +4 to damage three times or something. The damage on a crit is 1d8 (base, maximized), +2d8 (high crit), +2d6 (frost), +2 (weapon focus), +2 (enhancement bonus). TWF is not counted (as noted in the first post), because it was complicating my calculations and is a minor bonus.

So the end result is 8 (base) + 2-16 (high crit) + 2-12 (frost) + 2 (weapon focuse) +2 (enhancement bonus), which is 16-40, as in the spreadsheet.



> P.S.  One high damage combination I didn't see is a rogue who forgoes his paragon path to steal the Ranger At-will of Twin Strike.




That's an interesting suggestion, and like all the rogues it will probably do well against low armor foes, but poorly against high armor foes. The reason is that, although you can get something like 3d8+str bonus backstab, vs 2d8 for quarry, you lose the scimitar dance (since backstab only works on light blades...)


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## Splart (Jul 24, 2008)

loisel said:


> You're counting the +4 to damage three times or something.




Thanks, you're right.  I had confused the definition of 2 [W].  PHB 278 set me straight.  

On the flip side, for line 85, the Bugbear Rogue Shadow Ass. 11 Torturous Rapier 22/21, it looks like his feat damage is simply 2 X his normal damage, as in line 55 for the Bugbear Rogue Shadow Ass. 11 Riposte Rapier 22/21.  The 2 [W] for Torturous Strike should only double the weapon damage, and not the Dex bonus and Weapon Spec bonus, etc, so the Torturous Strike Primary Damage should be equal to the Riposte damage plus a d4.



loisel said:


> That's an interesting suggestion, and like all the rogues it will probably do well against low armor foes, but poorly against high armor foes. The reason is that, although you can get something like 3d8+str bonus backstab, vs 2d8 for quarry, you lose the scimitar dance (since backstab only works on light blades...)




High armor doesn't come into play that much.  Even dealing with an Elite Soldier like a Red Dragon, the AC is usually level + 18, compared with level + 14 for the average monster.  Sliding over 4 AC slots on the charts doesn't hit the areas where the minimum damage for Scimitar Dance or Hammer Rhythm are critical.

--Splart


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## loisel (Jul 25, 2008)

Splart said:


> the Bugbear Rogue Shadow Ass. 11 Torturous Rapier 22/21, it looks like his feat damage is simply 2 X his normal damage, as in line 55 for the Bugbear Rogue Shadow Ass.




For the encounter block, I've assumed that you wait until you've got the frost vulnerability on to strike your opponent. That adds a flat 5 damage to all damage rolls.

This character (row 85) is a Brutal Scoundrel hitting with Torturous Strike with a Large Rapier. His damage is 2d10 (Large Rapier) +6 (Dex) +5 (Str) +2 (Enhancement) +2 (Weapon Focus) +5 (Cold Vulnerability).

So the range is [2-20]+6+5+2+2+5, which is 22-40, as in the spreadsheet.

Did I get something wrong?


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## grailhawk (Jul 26, 2008)

On line 107,108 and I would assume other reaping maul using fighters you are stacking the damage on miss form reaping and hammer rhythm (7+6=13). My understanding of the hammer rhythm feat is that it will add you constitution damage if "you wouldn't otherwise still deal damage" (p203). Perhaps the added 6 is coming form some other feat or power?

Further more the reason I noticed this is that I'm trying to understand how you are adding damage form Unyielding Avalanche. My assumption is that you are adding the average damage of the attack in the Extra field but I have yet to come up with the combination of feat bonuses, and enchantments that results in 30 any insight you could provide would be greatly appreciated. 

P.S. Very nice spreadsheet thank you for sharing.


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## loisel (Jul 27, 2008)

grailhawk said:


> On line 107,108 and I would assume other reaping maul using fighters you are stacking the damage on miss form reaping and hammer rhythm (7+6=13). My understanding of the hammer rhythm feat is that it will add you constitution damage if "you wouldn't otherwise still deal damage" (p203). Perhaps the added 6 is coming form some other feat or power?




Thanks for catching that error, I will make corrections and upload new versions.



> Further more the reason I noticed this is that I'm trying to understand how you are adding damage form Unyielding Avalanche. My assumption is that you are adding the average damage of the attack in the Extra field but I have yet to come up with the combination of feat bonuses, and enchantments that results in 30 any insight you could provide would be greatly appreciated.




I recall I had a hard time with that one, and I think there's another error here (thanks for catching it.)

First off, I figured that Unyielding Avalanche would proc the Lasting Cold (it has the [weapon] tag, so your frost maul tacks on the [cold] tag...) So basically you have 100% chance of having the benefit of cold vulnerability each strike. This means that instead of putting 5 in the "Lasting Frost" column, I should have put 0 and added 5 to all the other damages. I see that I kind of screwed that up.

The Unyielding avalanche damage is 2d8 (Large Maul), +2 (Weapon Focus), +4 (Enhancement), +4 (Kensei), +5 (cold vulnerability), which is 24 on average. I think I mistakenly added the Str bonus. I will fix it.

Another thing is, there's a FAQ which makes it so that you can't deal the extra cleave damage to your main target, so the Cleave lines are wrong...


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## Splart (Jul 27, 2008)

Loisel,

Thanks, I understand the Bugbear damage now.  I noticed that the first level rogue is using a rapier, and also has the weapon specialization feat, which is not possible for a halfling.

Why does the level 1 longbow ranger have +9 to hit?  All I can find is +5 Dex, +2 prof, +1 prime shot.  Is there something else?

By the way, I finished the spreadsheet I mentioned to show the amount of damage given and taken over the lifespan of the PC.  Here's the post on it: http://www.enworld.org/forum/showthread.php?p=4399004

I checked the damage against your sheet, and our results match.  I didn't do the check to see if the Lasting Frost had landed or not, since I figure more than one PC in the party will be taking care of that, so it's safe to assume the monster will always be vulnerable.

Let me know what you think.

--Splart


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## loisel (Jul 27, 2008)

Splart said:


> Loisel,
> 
> Thanks, I understand the Bugbear damage now.  I noticed that the first level rogue is using a rapier, and also has the weapon specialization feat, which is not possible for a halfling.




What? Damage is 1d8 (W) + 4 (Dex) +4 (Cha), which is 9-16. He's got Weapon Prof (Rapier), and that's it... Did I make an error?



> Why does the level 1 longbow ranger have +9 to hit?  All I can find is +5 Dex, +2 prof, +1 prime shot.  Is there something else?




My mistake. I was convinced Longbow was +3 prof.



> By the way, I finished the spreadsheet I mentioned to show the amount of damage given and taken over the lifespan of the PC.




Good job. I'm looking at it now.


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## Splart (Jul 28, 2008)

Thanks, I'm clear on the halfling rogue with sly flourish.  My mistake.

Your answer above about the Rain of Steel damage kicked up something I've been struggling with.  For high crit weapons, it says add an extra 1 W to the attack, which I thought meant you get to add feats, magic, etc, but on PHB 276, it clearly explains that this is not the case for 2 W or more attacks.  Yet, for Rain of Steel, it says you do only 1 W.  My guess is that the designers meant for this to be only the weapon damage, without any additional modifiers.  I've got no FAQs to back that up, but it makes more sense to me than the interpretation that it is normal auto-hit minus dex against all adjacent monsters.  Maybe designer clarification will be coming later.

--Splart


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## loisel (Jul 28, 2008)

Splart said:


> Your answer above about the Rain of Steel damage kicked up something I've been struggling with.  For high crit weapons, it says add an extra 1 W to the attack, which I thought meant you get to add feats, magic, etc, but on PHB 276, it clearly explains that this is not the case for 2 W or more attacks.




Keep reading a bit further on PHB276 to dispel your doubt. On a 2[W], you get to add your bonuses as usual. On a crit, you maximize that damage, then add any random dice to the damage (again, example on PHB276). You don't get to add your bonuses twice.


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## Splart (Aug 1, 2008)

You miss my point.  I'm clear about the scimitar damage.  My guess is that WotC meant for Rain of Steel to do only weapon damage, not weapon damage plus WF, plus weapon enhancement, plus etc.  Again, this is just a theory, since the power seems so over powered, and I don't know of any FAQs or errata that back it up.


By the way, I was comparing our damage formulas and think you should take a look at your quarry probability again.  You've divided the quarry damage into the situation where one of two attacks is a critical, and where neither attack is a critical but one attack hits.  Unfortunately, the PC doesn't get to choose to apply his quarry when the crit lands.  If he rolls a normal hit on the first attack and crits on the second attack, he will only do normal quarry damage, not crit quarry.

Also, the chance of hitting with a normal attack is not a dependent probability on not hitting with a critical attack, so it should not be multiplied against the chance of not having a critical hit.  The chance of having a normal hit without a critical isn't (chance of no crit) * (chance of a normal hit), but rather (chance of having a normal hit) - 2 * (chance of a crit and normal hit combo).  Fortunately, this isn't necessary to calculate due to the first point above.

In math,

 (1-(1-PCrit)^PCattacks)*crit quarry dmg + (1-PCrit)^PCattacks*(1-(1-PHit)^PCattacks) * average quarry dmg)

Should be:

(1-(1-Pmiss)^PCattacks)*(crit quarry dmg * Pcrit + average quarry dmg * PHit)/(PCrit + PHit)

If it makes a difference to you, I'm not a math professor anywhere.


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## loisel (Aug 1, 2008)

Dear Splart,

Thanks for your reply.



Splart said:


> My guess is that WotC meant for Rain of Steel to do only weapon damage, not weapon damage plus WF, plus weapon enhancement, plus etc.




Well, I can't take that into account here, I'm doing RAW.



> Unfortunately, the PC doesn't get to choose to apply his quarry when the crit lands.  If he rolls a normal hit on the first attack and crits on the second attack, he will only do normal quarry damage, not crit quarry.




PHB104: under "Hunter's Quarry": "If you can make multiple attacks in a round, you decide which attack to apply the extra damage to after all the attacks are rolled."



> Also, the chance of hitting with a normal attack is not a dependent probability on not hitting with a critical attack, so it should not be multiplied against the chance of not having a critical hit.




I'll double check the formula in a minute, but the reasoning is this. If you crit on either attack, you get crit damage. However, if you hit on either attack, you don't necessarily get normal damage, because if you crit, then hit, you get crit damage already. So the probability of crit damage is simply the probability of at least one crit. However, the probability of normal damage is the probability of hitting at least once, but also not critting on the other attack.

The probability of critting thus has an effect on the regular damage component, but I may have got the wrong formula. I'll check it.

EDIT: I'll check the formula when I get home, I don't have my stuff at work.


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## Splart (Aug 2, 2008)

loisel said:


> PHB104: under "Hunter's Quarry": "If you can make multiple attacks in a round, you decide which attack to apply the extra damage to after all the attacks are rolled."




Huh.  I'm impressed with your deep knowledge of the books.  So, this would apply even if the ranger used an action point to get 4 attacks in a round.  Funky.  So, is that a feature of the ranger only, or is that a feature of all "quarry-like" attacks?  I.e. does the rogue/ranger get the same benefit from this, or does he have to name which dice is the "first" sneak attack, and only gets crit damage if rolled on that one?

According to RAW, I would say no, so the quarry probability formulas have to be made separate for the ranger versus the rogue/ranger.

In any case, for the ranger at least, the formula then becomes:

(1-(1-PCrit)^PCattacks)*crit quarry dmg + (1-(1-PHit)^PCattacks - 2 * PCrit * PHit) * average quarry dmg 



loisel said:


> I'll double check the formula in a minute, but the reasoning is this.  If you crit on either attack, you get crit damage. However, if you hit on either attack, you don't necessarily get normal damage, because if you crit, then hit, you get crit damage already. So the probability of crit damage is simply the probability of at least one crit. However, the probability of normal damage is the probability of hitting at least once, but also not critting on the other attack.




The problem with your reasoning is that the chance not getting a crit attack includes the chance of missing totally, which is not accurate when the rest of the calculation assumes at least one hit.  It's like the old math problem -- I have two children and at least one boy:  what is the chance I have two boys?  According to the reasoning you used, the answer is 50% * 50% = 25%, but the correct answer is 33%, because there are three equal probability combinations that meet the 1 boy condition, boy-boy, boy-girl, and girl-boy.  In this calculation, when you have already included the condition that one attack hits (1-(1-PHit)^PCAttacks), multiplying this by the chance that no crits hit (1-(1-PCrit)^PCAttacks) doesn't work because the no crit chance includes the chance that both attacks miss.

--Splart


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## brehobit (Aug 2, 2008)

I've not read all this carefully, but it looks like you assume things like fighter daily stances are being used for extra damage.  How about flaming sphere for the wizard?


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## loisel (Aug 2, 2008)

brehobit said:


> I've not read all this carefully, but it looks like you assume things like fighter daily stances are being used for extra damage.  How about flaming sphere for the wizard?




It's only included as an example on the Level 20 chart. I will put a clearer warning.


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## loisel (Aug 2, 2008)

Dear Splart,

Thanks for your reply.



Splart said:


> deep knowledge of the books




Well, I can't take credit. I originally had it that you used quarry on the first hit, but someone on the WotC forums pointed out that rule.



> According to RAW, I would say no, so the quarry probability formulas have to be made separate for the ranger versus the rogue/ranger.




Right, which doesn't affect me because my rogues only attack once per round, but you've got a twin strike rogue in there you might want to fix.

EDIT: actually, I do have a TS rogue I forgot about...



> (1-(1-PCrit)^PCattacks)*crit quarry dmg + (1-(1-PHit)^PCattacks - 2 * PCrit * PHit) * average quarry dmg




I think it's something like that, but I'm not 100% on the second part. I think the way I'm going to handle it is:

P(crit quarry) = (1-(1-PCrit)^n), like you suggest
P(*no* quarry) = PMiss^n
P(normal quarry) = 1 - P(crit quarry) - P(no quarry).

I think probably the P(normal quarry) in my spreadsheet is incorrect.

EDIT: which is, uh, P(normal quarry) = (1-PCrit)^n - PMiss^n

Sounds good to you?


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## Splart (Aug 2, 2008)

loisel said:


> Dear Splart,



No need for formalities, especially with someone with a silly board name like "Splart."

Now, let's get down to brass tacks, shall we?



loisel said:


> Right, which doesn't affect me because my rogues only attack once per round, but you've got a twin strike rogue in there you might want to fix.



Yup.  Sigh.  I'll have to compare the probability matrices and add in the extra ranger quarry crits.

PCritQuarry=PCritSneakAttack + PCrit * (PHit + PMiss)



loisel said:


> P(crit quarry) = (1-(1-PCrit)^n), like you suggest
> P(*no* quarry) = PMiss^n
> P(normal quarry) = 1 - P(crit quarry) - P(no quarry).



Yes, that's all good, and more eloquent than what I had.  Nice.



loisel said:


> I think probably the P(normal quarry) in my spreadsheet is incorrect.
> 
> EDIT: which is, uh, P(normal quarry) = (1-PCrit)^n - PMiss^n



Actually, this is fine too.  In fact, it's mathematically equivalent to P(normal quarry) above, since (1-PCrit)^n - PMiss^n = 1 - P(crit quarry) - P(no quarry)

However, that's not what your spreadsheet uses.  From cell DPR!B4, for normal quarry you have: (1-Pcrit!B4)^Toons!$C4*(1-(1-PHit!B4)^Toons!$C4), which simplifies down to (1-PCrit)^n * (1-(1-PHit)^n), which is neither here nor there.


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## loisel (Aug 2, 2008)

Splart said:


> However, that's not what your spreadsheet uses.




I think you're looking at a previous version. I updated to 1.10 when I posted the formulae.


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## Splart (Aug 2, 2008)

Right-o.  I was looking at 1.8.  I didn't realize you'd already fixed it while we were talking.


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## DracoSuave (Aug 3, 2008)

Splart said:


> Huh.  I'm impressed with your deep knowledge of the books.  So, this would apply even if the ranger used an action point to get 4 attacks in a round.  Funky.  So, is that a feature of the ranger only, or is that a feature of all "quarry-like" attacks?  (rest cut)




It's a feature of the ranger only.

Rogues and Warlocks decide their extra damage after the -DAMAGE- is rolled, which is even later than the ranger.


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## loisel (Aug 3, 2008)

DracoSuave said:


> It's a feature of the ranger only.
> 
> Rogues and Warlocks decide their extra damage after the -DAMAGE- is rolled, which is even later than the ranger.




Not clear that it's necessarily later than the ranger (does it say anywhere that you roll all attack rolls first, then all damage rolls?)

However, I think it's a reasonable reading that you can apply your sneak attack damage to any 1 attack you performed, so the effect for this thread is the same as the ranger's.


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## Splart (Aug 4, 2008)

Ok.  Cool.  I'll give both the rangers and TS rogues the same crit benefit.


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## Splart (Sep 21, 2008)

Loisel,

I went ahead and made the other spreadsheet I mentioned.  While the focus of both your spreadsheet and mine was to compare between classes, the new spreadsheet focuses closely on maximizing the defense and damage of a single PC, within a given class.  Take a look:  http://www.enworld.org/forum/d-d-4th-edition-rules/241384-feat-optimizer-excel-spreadsheet.html

--Splart


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## Dausuul (Sep 21, 2008)

(deleted)


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## Dausuul (Sep 21, 2008)

loisel said:


> If you look at the graphs in the top post (they are the same as in the Excel file), you will see that I've looked mostly at At-Wills, but I've also done an analysis for Level 11 Encounter Powers.
> 
> However, it doesn't make that much difference. For At-Wills, Rangers are on top, and Warlocks at the bottom. It's the same with Encounter Powers, but Warlocks are actually slightly worse.
> 
> I didn't do dailies, but I expect the same pattern to come up.




IMO, the balancing factor is supposed to be all the status effects and conditionals that warlocks pile on their enemies.


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