One Stroke To Kill Them All - Half-Orc Avenger|Artificer/Ardent Champion/Lorekeeper, 227 DPR

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One Stroke To Kill Them All

Build Goal
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Most builds that go in for high DPR do so by trying to make as many attacks as possible; by stacking static modifiers this allows for beastly DPR.
This build aims to use all the tricks available to us in order to make a character with the most devastating MBA possible; he attempts to show Twin Strike (or other multi-attack abilities, including Hellish Rebuke) is not the only viable means of achieving high levels of DPR.  Not only does he achieve this goal using Overwhelming Strike, he also achieves the strongest BMA I have personally seen: 130 DPR assuming that his free attack limit has already been reached.


The Build @ lvl 30
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Half-Orc
Avenger|Artificer(Fighter)/Ardent Champion/Lorekeeper
Worshipper of Bane
Follower of 

Str 12->16, Con 12->14, Dex 12->22, Int 10->12, Wis 18->26, Cha 8->10

Feats (Order is roughly correct, although exact retraining not shown here; see lower level builds for more specifics)
Power of Skill
Gouge Proficiency
Painful Oath
Versatile Expertise (Weapon: Axe, Implement: Holy Symbol)
Axe Focus
Hybrid Talent: Censure of Pursuit
Impaling Spear 
Wintertouched 
Lasting Frost
Battle Awareness
Acolyte Power (Martial Supremacy)
Power Attack
Slashing Storm
Ferocious Critical
Deadly Axe
Devastating Critical
Leather Proficiency
Hide Proficiency

Pertinent Gear
+6 Frost Gouge w/ Siberys Shard of Frost (Epic)
Horned Helm (Epic)
Gloves of Ice (Epic)
Iron Armbands of Power (Epic)
Ring of Giants
War Ring
+6 Great Cat Elderhide

Pertinent Powers
Overwhelming Strike (Counts as MBA via Power of Skill)
Martial Supremacy (Allows re-roll of BA attacks; combines w/ Oath of Enmity for 4 attack rolls)
Vorpal Weapon (Encounter Power via Lorekeeper)
Battle Rapture (Encounter Power via Lorekeeper)


DPR Calculations
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Assumptions:
Oath of Enmity is on the target, 99.8775% of the time we have hit or crit the previous turn keeping Cold Vulnerability active, 52.39% of the time we have crit the previous turn, so Ferocious Critical adds +2 to hit and +2 to damage on our initial attack, Great Cat Armour permits us to shift+charge every round, Vorpal Weapon and Martial Supremacy and Battle Rapture are all active

Charge To Hit:
+15 lvl +8 wis +6 enh +3 feat +2 ferocious +2 CA (via Cold Vuln) +1 charge +2 prof -2 power attack
= +37 vs Ref 42 (via Impaling Spear)
miss: 0.1225% 
crit: 52.39% (4 rolls, 18-20 crit range, also crit if either the first 2 rolls are the same (and hit) or the last 2 rolls are the same (and hit))
hit: 47.4875%

Charge Damage:
4d5+4 base +8 wis +6 enh +3 feat +3d6 helm +1d10 +15 battle rapture +8 painful oath +8 slashing storm +9 power attack +6 item +5 vuln +5 shard +4 gloves +2 ferocious critical 
= 16 +10.5 +5.5 +79 
= 111 average damage

Charge Critical:
20 +18 +10 maxed rolls +83 normal bonus +12 giants +6d6 frost +6d5+6 high crit +2d5+2 war ring +1d10 devastating 
= 201.5 + MBA

MBA To hit:
No charge bonus -1, full Ferocious bonus +2 = +38 vs Ref 42
miss: 0.050625%
crit: 52.734375%
hit: 47.215%

MBA Damage:
No horned helm -3d6, no Slashing Storm/Painful Oath -16, full Ferocious bonus +2 = 86.5

MBA Critical:
No Horned Helm -18, no Slashing Storm/Painful Oath -16, full Ferocious bonus +2 = 169.5

MBA DPR:
86.5*0.47215 + 169.5*0.52734375 = 40.840975 +89.382565625 = 130.223540625

Final DPR:
111*0.474875 + (201.5+130.223540625)*0.5239 =  52.711125 + 173.7899472164375
=  226.5010722164375


General Comments
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The first thing to mention is that Hybriding to Artificer initially seems terrible.  I have to do it in order to guarantee an 18-20 crit range at level 30; but it might seem that levels 1-29 aren't really gaining that much, especially with the 10 intelligence we start with.
However there are 2 other highly useful benefits the Artificer hybrid gives us:
First, we get surgeless healing which is very important for keeping up the Fighter Stances.
Second, Sigils do not require any intelligence; as such, 2 of our 3 dailies will be Artificer Sigils.  Artificer utilities are also miles better than Avenger utilities, so (except for level 6) all our utilities will be Artificer.  Our only problem therefore is from our encounter power; by making sure we take an immediate weapon action, we at least ensure we can spam Overwhelming Strike (or some other Avenger/Ardent Champion power) every round, thus avoiding as much of the problem of low int as possible.

Next on my list is the critfishing.  This build only has 50 DPR without crits.. but since it actually crits more often than it hits, critfishing is actually viable.

Which brings me to my next point:  Lorekeeper is most definitely not the best ED for a striker.  If you can swing it, get your leader with high Int to take Lorekeeper + Vorpal Weapon, so you don't have to.  Of course, you'll lose Battle Rapture as an encounter ability, so you'd better make sure your ED makes up for 20+ damage per hit, or Lorekeeper will still be better for you.

Battle Rapture itself is a bit of a sticky point.  If anyone else attacks your target.. you'll be hurting.  Which will cause you to spend a surge (unless your party leader is an Artificer.. yes please!) which will dismiss Martial Supremacy, which will drop your crit rate by 20%.  However, at level 30 you do enough damage that that shouldn't be a problem - especially if your Leader can grant out of turn attacks (like a Warlord).

So.. make sure your party leader is Killswitch!  And you'll do just fine.

Nova powers!
Nope, this build does not have a good nova potential.  It has no effective way to gain multi-attacks (unless there is a decent Avenger multi-attack power I've missed).  And you don't get Martial Supremacy with anything except Overwhelming Strike... and you can only get 1 free MBA per turn so AP Overwhelming Strike only adds 130 DPR.. so.. no Nova for you!
Bring along a different Half-Orc Avenger/Ardent Champion (specifically, an Eternal Seeker) in order to have nova.
Lower Level snap shots

Level 16 Feats 
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Feats:
Painful Oath
Power of Skill
Gouge Proficiency
Axe Expertise
Axe Focus
Power Attack
Hybrid: Pursuit
Impaling Spear 
Wintertouched
Lasting Frost


Level 16 DPR (57)
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To Hit: +8 lvl +6 wis +3 enh +2 prof +2 CA +1 charging +2 feat -2 power attack
= +22 vs Ref 28 (+21 vs Ref 28 for MBA)
miss: 6.25%
crit: 13.25%
hit: 80.5%

Damage:
2d5+2 base +6 wis +3 enh +2 feat +2d6 helm +6 painful oath +4 item +5 vuln +3 shard +2 gloves +6 power attack 
= 8 +7 +37
= 52 (39 for MBA)

Crit:
12 +12 maxed dice +39 bonus +6 giants +3d6 frost
= 79.5 (61.5 for MBA)

MBA DPR:
39*0.78 + 61.5*0.13 = 30.42 + 7.995
= 38.415

DPR: 
52*0.805 + (79.5 + 38.415)*0.1325 = 41.86 +15.6237375
= 57.4837375


General Comments
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This build on the surface is probably weakest in paragon.  No room for defensive feats, not enough room for all the multitudes of offensive feats, Martial Supremacy isn't around yet, etc.

However, one thing that isn't reflected in the At-Will DPR is the powers of the build.  Paragon is where this build likes it's powers the most: 3 sigils, vorpal weapon, battle rapture.  That's 5 encounters per day (6 if your avenger daily is something like Temple of Light) where all your attacks are getting big boosts.  Encounter powers don't have to compete with Martial Supremacy + Overwhelming Strike, and so are actually able to boost your DPR when used.

Not that any of that helps your defense.


Level 6 Feats + Gear changes
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Painful Oath
Power of Skill
Fullblade Proficiency (to be retrained to Gouge probably by level 7 to 9)
Mounted Combat (to be retrained as soon as the Dire Boar is no longer useful)

Pick up a +1 Vanguard Fullblade, Lion Claw Gauntlets, Bracers of Mighty Striking, a Horned Helm and a Dire Boar + any defensive items you can.


Level 6 DPR (34)
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Assumptions: Overwhelming Strike lets you shift away, or your leader shifts you, or you eat an OA; you charge every round.

To Hit:
+3 lvl +4 wis +3 prof +1 charge +1 enh +1 lion claw = +13 vs AC 20
miss: 9%
crit: 9.75%
hit: 81.25%

Damage:
1d12 +4 wis +1 enh +1d8 vanguard +2 item +1d6 helm  +4 painful oath = 6.5 +4.5 +3.5 +11
= 25.5 + Gore

Crit:
12 +8 +6 maxed rolls +11 bonus +1d12 high crit +1d8 vanguard = 37 +6.5 +4.5
= 48 + Gore

Gore:
+11 vs AC 20 = 5% crit, 50% hit
2d10+4 = 15 hit, 24 crit
DPR: 7.5 + 1.2 = 8.7

DPR:
0.8125*(25.5+8.7) + 0.0975*(48+8.7) =  28.35625 + 5.52825 
=  33.8845


General Comments
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In heroic, this build works very well.  34 DPR at level 6 is nothing to scoff at, when the build is also functional at higher levels.  Of course, the defenses are still somewhat low, but having that 1 artificer heal/encounter really helps out at this stage.  Even without the Boar, One Stroke still manages about 26 DPR, which is still very respectable.
I have to say that this is the most warlord friendly build I have ever seen.
DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
He doesn't have much nova potential for himself, but the warlord-friendliness certainly adds something to the party nova.

I hadn't ever thought of lorekeeper before as the ED for a lazy or hybrid lazy, but there are certainly utilities that make that capstone worthwhile, if you're doing a lvl 30 game for some reason.

What changes would you make if you were building the guy to optimize on MBA damage across all 30 levels?  (or would you just scrap him and construct a new one from scratch?)
There is one good avenger multi-attack power: It is a 1[W]+stat+stat (with keywords) attack that, 1/round until the end of your next turn, you can repeat as a minor action.

In effect, it is a standard+minor two-attack that also gives you a second attack on the next round.

It is around level 13 or 17 if I remember rightly.
I'm not particularly sure.  I've never been all that good at optimizing level 16 because everything I do compare to my Half-Elf Radiant Twin Strike Mafia, and nothing really compares on the party level.

Aside from that; he's pulling pretty darn reasonable MBA's throughout his whole career.  As mentioned on the level 16 general notes, he 'only' has 57 DPR - but 5-6 encounters a day that increases by 6-25 DPR due to his daily encounter long buffs.

If I had to re-optimize for paragon, I would probably cry.  Most of the really nice feats are paragon, plus most of the gear comes in at paragon, and just having to choose what to take and what not to take is painful.  

The other big problem with optimizing over an entire career is that epic play (for this kind of character) is so different due to the increased crit range.  Heroic is simple (I'd stick with what I have although possibly dropping the mount if you only care about warlord friendliness); but paragon you have to choose whether to start getting ready for epic crit fests (which includes things like PP choice, and choosing avenger or something like a dragonborn sorc), or whether you're going to maximize your MBA potential and disregard crits.  You'd probably be able to push.. oh.. 52 DPR or so on an MBA attack at level 16 (assuming you don't get a free attack from a crit), but you'd hurt yourself rather badly in epic.

Actually.. ha!  I do have it.  My Dragonborn Fighter|Sorcerer hits 60.725 DPR using Dragonfrost (RBA instead of MBA, but still warlord friendly) at level 16, and doesn't have any free attack triggers.  But the same character only has 18 DPR at level 6, and 112 DPR at level 30 (and once epic is reached, we get the free-attack-on-crit trigger, which wouldn't be useable by the warlord).

Of course, my bias is towards epic; my group runs Paragon-Epic games, and virtually never touches Heroic. 
@The Yakk:  Thanks for pointing out that power.. I'm not a particular Avenger Power fan, so I'd forgotten it.  However, even though you'd be getting multi-attack, you'd lose Charging and you'd lose Martial Supremacy; so your actual DPR increase would probably be rather low for the initial round.  Really need a triple attack to make up for the losses (although I suppose you could argue that power as being a triple attack -  the minor attack the second round would is quite nice)
There is one good avenger multi-attack power: It is a 1[W]+stat+stat (with keywords) attack that, 1/round until the end of your next turn, you can repeat as a minor action.

In effect, it is a standard+minor two-attack that also gives you a second attack on the next round.

It is around level 13 or 17 if I remember rightly.


Soulforge Hammering(17th enc) deals 1[w] fire and radiant.  Repeat attack as a minor action it's used and again your next turn.  During these 2 turns your attacks damage get +max(dex,int)
DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
If you were to play this would you reallocate stats to prioritize Con instead of Dex to take advantage of your sigils, focus on Wisdom based artificer powers, or Leave Dex and prioritize avenger riders?
DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
What about having starting stats be 13 Str, 10 Con, 13 Dex, 10 Int, 18 Wis, 8 Cha.  Boost Wis and alternate Str/Dex every other bump.  This gives you 19 str, 19 Dex at level 21 thus you can take spear mastery.  Not the 18-20 crit range, but quite close.  If you're willing to give up Battle Rapture (ouch I know, but less ouchy in real play) and take Sage of Ages for a floating d20/round you could get close.
DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
I've ran a simulation of a sage of ages floating d20 + martial supremacy + OoE + 19-20 crit range for 1000000 itterations and found that the expected number of crits / MBA comes out to 0.57938.
The advantage that Sage of Ages has is that you can match the floating d20 to the double rolls of pre-martial supremacy and post.  And it works at level 24.
DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
In your 6th level snapshot, painful oath is paragon
You can't take impaling spear w/o MC fighter at 16. 
DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
Instead of spear mastery you can take hand of divine guidance(epic) to get the 19-20 crit range coupled with sage of ages to obtain an expcted number of crits/round of 
    0.5821
DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
myversion

====== Created Using Wizards of the Coast D&D Character Builder ======
MBA master, level 30
Longtooth Shifter, Avenger|Artificer, Ardent Champion, Sage of Ages
Hybrid Avenger: Hybrid Avenger Reflex
Hybrid Artificer: Hybrid Artificer Fortitude
Hybrid Talent: Avenger's Censure (Hybrid)
Avenger's Censure: Censure of Pursuit
Versatile Expertise: Versatile Expertise (Axe)
Versatile Expertise: Versatile Expertise (Heavy Blade)

FINAL ABILITY SCORES
Str 17, Con 13, Dex 12, Int 24, Wis 26, Cha 10.

STARTING ABILITY SCORES
Str 13, Con 11, Dex 10, Int 16, Wis 16, Cha 8.


AC: 42 Fort: 35 Reflex: 39 Will: 39
HP: 171 Surges: 7 Surge Value: 42

TRAINED SKILLS
History +34, Perception +29, Dungeoneering +35

UNTRAINED SKILLS
Acrobatics +16, Arcana +28, Bluff +15, Diplomacy +15, Endurance +18, Heal +23, Insight +23, Intimidate +15, Nature +29, Religion +28, Stealth +16, Streetwise +15, Thievery +16, Athletics +20

FEATS
Level 1: Power of Skill
Level 2: Gorebrute Charge (retrained to Impaling Spear at Level 13)
Level 4: Mounted Combat (retrained to Battle Awareness at Level 12)
Level 6: Weapon Proficiency (Fullblade)(retrained to Weapon Proficiency (Gouge)
at Level 11)
Level 8: Versatile Expertise
Level 10: Hybrid Talent
Level 11: Painful Oath
Level 12: Power Attack
Level 14: Armor Proficiency (Leather)
Level 16: Gorebrute Charge
Level 18: Devastating Critical (retrained to Hand of Divine Guidance at Level 22)
Level 20: Beasthide Shifting (retrained to Deadly Axe at Level 21)
Level 21: Slashing Storm
Level 22: Acolyte Power
Level 24: Devastating Critical
Level 26: Weapon Focus (Axe)
Level 28: Mighty Enmity
Level 30: Punishing Radiance

POWERS
Hybrid at-will 1: Thundering Armor
Hybrid at-will 1: Overwhelming Strike
Hybrid encounter 1: Angelic Alacrity
Hybrid daily 1: Temple of Light
Hybrid utility 2: Avenger's Resolve
Hybrid encounter 3: Shocking Feedback
Hybrid daily 5: Corrosive Sigil
Hybrid utility 6: Animate Helper
Hybrid encounter 7: Chains of Censure
Hybrid daily 9: Radiant Sigil
Hybrid utility 10: Eye of Justice
Hybrid encounter 13: Avenger's Demand (replaces Angelic Alacrity)
Hybrid daily 15: Lightning Sigil (replaces Corrosive Sigil)
Hybrid utility 16: Vorpal Edge
Hybrid encounter 17: Soulforge Hammering (replaces Angelic Alacrity)
Hybrid daily 19: Hellfire Sigil (replaces Lightning Sigil)
Hybrid utility 22: Bag of the Four Winds (retrained to Martial Supremacy at Acolyte Power)
Hybrid encounter 23: Mental Beacon (replaces Avenger's Demand)
Hybrid daily 25: Life-Shock Sigil (replaces Radiant Sigil)
Hybrid encounter 27: Grave-Dust Cloud (replaces Chains of Censure)
Hybrid daily 29: Haste Sigil (replaces Hellfire Sigil)

ITEMS
Horned Helm (epic tier), Boots of Adept Charging (heroic tier), Ring of Giants (paragon tier), War Ring (paragon tier), Bloodiron Fullblade +6, Siberys Shard of Radiance (epic tier), Strikebacks (heroic tier), Bracers of Mighty Striking (epic tier), Marauder's Starleather Armor +6, Backlash Tattoo (heroic tier), Symbol of Victory +2 (5), Rending Khopesh +6, Blood Fury Handaxe +1, Waistband of the Grappler (paragon tier), Badge of the Berserker +6
====== Copy to Clipboard and Press the Import Button on the Summary Tab ======

 

DPR

to hit

8 wis
15 (1/2 level)
2 prof
6 enh
3 feat
1 charge
-2 PA
--------
+32 vs 42 Ref.

non-crit-Damage

10 horned helm
2 longtooth shifting
8 wis
9 PA
6 bracers
3 gorebrute charing
5 shard of radiance
3 focus
16 gouge(4d6 brutal 1)
-------
54 + crit%*(10 punishing) + 8(painful oath)+8(slashing storm) = 75.6

crit

100 expected from rending MBA
1d10 devestating
1d10 war ring
12 ring of giants
6d6 high crit(brutal 1)
12 maxed horned helm
24 max gouge
2 shifting
3 focus
8 wis
9 PA
6 bracers
3 gorebrute charging
8 painful oath
5 shard
8 slashing storm
--------
147

hit/crit chance breakdown

We have a floating d20 from sage of ages
Oath of emnity double roll and
(1a)see if any are 19-20(hand of divine guidance)
(1b)if not we check if any are equal and hitting(9+)
(2)If we didn't crit we will reroll(martial supremacy)
Check to see if we crit(2a), hit(2b) or miss(2c).
The chance of critting on (1a,b) is found through simulation and is 33.6%
Thus our chance of going to (2) is 66.4%.
Assumming (2) the chance of critting is the same as original(33.6%), the chance of missing is all 3 must miss(.4*.4*.4 = 6.4%)
chance of hitting = 1-.336-.064 = 60%
multiply (2) by 66.4% to get our totals

Crit: 55.9%
Hit: 39.8%
Miss: 4.25%

.559*147 + .39*75.6 = 162
I'm going to do some other variations like no PA, adding in belt of the brawler.
DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
If youre going for Bane as as a deity, why not pick up power of war (scaling bonus damage to OS).
If youre going for Bane as as a deity, why not pick up power of war (scaling bonus damage to OS).


You can only apply one power of X at a time.
DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
Yeeks!  I totally mucked my miss chance, thanks Borg.

And... I forgot Impaling spear was Martial.  Not sure how I managed that.  Painful Oath is obviously paragon... I knew there was a reason it seemed overpowered at level 6.

Didn't think of Sage of Ages... I'll switch things around a bit and see what I can come up with (although it probably won't be until.. oh.. next week, as I'm working like a fiend right now.)


Thanks for all the constructive criticism! 
I ran my own numbers for 19-20 crit + sage of ages re-roll, and I ended up with a 58.275577% crit change (higher than yours - if you know it, I'd like to know exactly what calculations you were using to get yours, since I'm not 100% sure mine are the right ones).
 However, the loss of Battle Rapture means I lose about 34 DPR, while the increased crit only adds about 12 DPR.  Still a net loss of 20 DPR, which for a DPR king canditate isn't really worth it.  (I don't think any epic destiny will actually be better than Lorekeeper at level 30.  Also note, as a Lorekeeper, most creatures I fight will be in one of my knowledge skills, as I have 4 of them, and that will get me an extra +3 DPR per round, approximately.  Of course, before level 30, Sage of Ages is certainly better, although you have to drop a feat in order to get the 19-20 crit range, which means your DPR will go down yet again.)
Hmm... I am only getting 53.4% (or there abouts) as the chance to crit. borg, do you want to look over my code?

[spoiler Boring code]
int roll()
{
    return (rand()/(int)(((unsigned)RAND_MAX + 1) / 20))+1;
}

int critcheck(int roll1, int roll2, int soa)
{
    if (roll1 > 18 || roll2 > 18 || soa > 18)
        return 1;
    if (roll1 == roll2 || roll1 == soa && roll1 > 8)
        return 1;
    if (roll2 == soa && roll2 > 8)
        return 1;
    return 0;
}


int main(int argc, char *argv[])
{
    int noruns = atoi(argv[1]);    
    int soa;
    int crits = 0;
    int misses = 0;
    int hits = 0;
    int roll1;
    int roll2;
    int i;

    for (i = 0; i    {
        // Determine SOA result
        soa = roll();
        // First Roll
        roll1 = roll();
        roll2 = roll();
        // Look for crits
        if (critcheck(roll1, roll2, soa))
            crits++;
        else //reroll
        {
            roll1 = roll();
            roll2 = roll();
            if (critcheck(roll1, roll2, soa))
                crits++;
            else
            {
                //Check if any of the rolls hit
                if (roll1 > 8 || roll2 > 8 || soa > 8)
                    hits++;
                else
                    misses++;
            }
        }
    }
    printf("Hits: %d Misses: %d Crits: %d \n", hits, misses, crits);
    printf("Crit: %f Hit: %f Miss: %f \n", ((float)crits * 100)/(float)noruns, ((float)hits * 100)/(float)noruns, ((float)misses * 100)/(float)noruns);
}
[/spoiler]

Hmm... for some reason the first line of the crit check code is showing up oddly. Should read: if (roll1 > 18 || roll2 > 18 || soa > 18)
Hmm... I am only getting 53.4% (or there abouts) as the chance to crit. borg, do you want to look over my code?

[spoiler Boring code]
int roll()
{
    return (rand()/(int)(((unsigned)RAND_MAX + 1) / 20))+1;
}

int critcheck(int roll1, int roll2, int soa)
{
    if (roll1 > 18 || roll2 > 18 || soa > 18)
        return 1;
    if (roll1 == roll2 || roll1 == soa && roll1 > 8)
        return 1;
    if (roll2 == soa && roll2 > 8)
        return 1;
    return 0;
}


int main(int argc, char *argv[])
{
    int noruns = atoi(argv[1]);    
    int soa;
    int crits = 0;
    int misses = 0;
    int hits = 0;
    int roll1;
    int roll2;
    int i;

    for (i = 0; i    {
        // Determine SOA result
        soa = roll();
        // First Roll
        roll1 = roll();
        roll2 = roll();
        // Look for crits
        if (critcheck(roll1, roll2, soa))
            crits++;
        else //reroll
        {
            roll1 = roll();
            roll2 = roll();
            if (critcheck(roll1, roll2, soa))
                crits++;
            else
            {
                //Check if any of the rolls hit
                if (roll1 > 8 || roll2 > 8 || soa > 8)
                    hits++;
                else
                    misses++;
            }
        }
    }
    printf("Hits: %d Misses: %d Crits: %d \n", hits, misses, crits);
    printf("Crit: %f Hit: %f Miss: %f \n", ((float)crits * 100)/(float)noruns, ((float)hits * 100)/(float)noruns, ((float)misses * 100)/(float)noruns);
}
[/spoiler]

Hmm... for some reason the first line of the crit check code is showing up oddly. Should read: if (roll1 > 18 || roll2 > 18 || soa > 18)


Everything looks good except this line
if (roll1 == roll2 || roll1 == soa && roll1 > 8)
I feel you either need more parenthesis to make sure it's getting compiled to do what you want or seperate it into 2 checks.

The way I did it is to simply have a function that tells me if an attack crit.  I then calculate the rest analytically.
If(crit)
   return 1;
else
reroll()
if(crit)
   return 1;
end 
return 0;


Here is my revised code and the results I got
<br />function crit = roll(critrange,missOn)<br />    floating = ceil(20*rand(1,1));<br />    d1 = ceil(20*rand(1,1));<br />    d2 = ceil(20*rand(1,1));<br />    crit = 0;<br />    if(d1 &gt; critrange || d2 &gt; critrange || floating &gt; critrange)<br />        crit = 1;<br />        return<br />    end<br />    if(d1 == d2 &amp;&amp; d1 &gt; missOn)<br />        crit = 1;<br />        return;<br />    end<br />    if(d1 == floating &amp;&amp; d1 &gt; missOn)<br />        crit = 1;<br />        return;<br />    end<br />    if(d2 == floating &amp;&amp; d2 &gt; missOn)<br />        crit = 1;<br />        return;<br />    end<br />end<br /><br /><br />The code that calls this function is<br />rounds = zeros(1,100000);<br />clc<br />miss = 8;<br />for critrange = 17:19<br />    for i=1:100000<br />        rounds(i) = roll(critrange, miss);<br />    end<br />    mymean = mean(rounds);<br />    criton = mymean + (1-mymean)*mymean;<br />    misson = (1-mymean)*(miss/20)^3;<br />    hiton = (1-mymean)*(1-(miss/20)^3-mymean);<br />    disp(['Crit on ' num2str(critrange+1) '-20']);<br />    disp(['Crit: ' num2str(criton)]);<br />    disp(['hit: ' num2str(hiton)]);<br />    disp(['Miss: ' num2str(misson)]);<br />end<br /><br /><br />And my results<br />Crit on 18-20<br />Crit: 0.68764<br />hit: 0.27659<br />Miss: 0.035769<br /><br />Crit on 19-20<br />Crit: 0.56263<br />hit: 0.39504<br />Miss: 0.042326<br /><br />Crit on 20-20<br />Crit: 0.38791<br />hit: 0.56202<br />Miss: 0.050071<br />

DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
and if it matters at all if you only miss on a 1 then here are my results
Crit on 18-20
Crit: 0.73181
hit: 0.26812
Miss: 6.4734e-005

Crit on 19-20
Crit: 0.61387
hit: 0.38605
Miss: 7.7674e-005

Crit on 20-20
Crit: 0.46434
hit: 0.53557
Miss: 9.1486e-005
DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
er..
82% crit for a 19-20 crit range?  That seems high.

My calculations:

Chance to crit, assuming +37 vs Ref 42 (hit on 5+)
Crit on 19-20.  Crit if both OoE rolls are same, and hit.
Roll Twice (OoE), Re-Roll both if that's not a crit; floating d20 that can replace any of the 4 rolls.

Roll 1: 10% crit + Roll 2: 10% crit - Roll 1 and Roll 2: 1% 
=19% base.
+ Roll 1 = Roll 2, between 5 and 18 = 14/20*1/20 = 3.5% 
=22.5%
+ Roll 1 not crit and Roll 2 not crit and Roll 1 not equal Roll 2 and Floating crit (3 possibilities: roll 1 hit and roll 2 missed/hit, roll 1 missed and roll 2 hit, neither roll 1 or 2 hit; note that they are distinct possibilities because 1 could equal 2 as long as they both miss): 14/20*17/20*1/10 (5.95%) + 4/20*14/20*1/10  (1.4%) + 4/20*4/20*1/10 (0.4%)
= 30.25%
+ Roll 1 hit and Roll 2 not crit and Roll 1 not equal Roll 2 and Roll 1 equal Floating: 14/20*17/20*1/20 = 2.975%
= 33.325 
+ Roll 1 not crit and Roll 2 hit and Roll 1 not equal Roll 2 and Roll 2 equal Floating: 17/20*14/20*1/20 = 2.975%
= 36.3% (Final Chance of Crit without Martial Supremacy)

Chance of not critting: 63.7%
Re-Roll on oath has all same chances, except for the one where the floating crit, since we already checked that.  (I forgot that on my previous number)
So Re-Roll has 36.3-5.95-1.4-0.4 = 28.55

Final Crit:
 0.363 + 0.637*0.2855 = 54.48635%
er..
82% crit for a 19-20 crit range?  That seems high.


You must have read my post between my posting and catching and fixing a bug. sorry
DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
So floating d20, and 2d20 attack, with a bonus attack from a crit.

You hit on an 8+.  You crit on a 19+.

You shouldn't be simulating this on a computer -- you should be examining all 8000 possible dice combinations.  It is easier and perfecty accurate. 

But because I like math, I'm going to do it manually.

.55 hit, .1 crit, .35 miss per die.
11 pips hit, 2 pips crit, 7 pips miss.


Legend:
*: Hit or Miss
H: hit
C: crit
M: miss

Pip counts:
HHH: 11^3
HHM: 3*11^2*7
HMM: 3*11*7^2
MMM: 7^3
C**: 3*2*18^2
CC*: 3*2^2*18
CCC: 3*2^3

Now, the "hits" can contain doubles.
With HHH, we have 3 numbers from 1-11.  How many of them have exactly two 1s?
11* - 10
1*1 - 10
*11 - 10
111 - 1
31 of them have exactly 2 1s, plus the triple 1.  The same is true of each number from 1 to 11, and we aren't double counting, so we have 341 doubles.

With each of HHM, HMH and MHH, there are 2 numbers from 1-11 that matter.  There are 11 pairs each, times 3 for 33.  Each of them have 7 misses each, so 231 pips of doubles.

So our hit chance (in pips) is:
11^3 -341  + 3*11^2*7 - 231 + 3*11*7^2
= 11*11*11 -341  + 3*11*11*7 - 231 + 3*11*7*7
= 4917 pips

Our crit chance (in pips) is:
341 + 231 + 3*2*18^2 + 3*2^2*18 + 3*2^3
= 341 + 231 + 3*2*18*18 + 3*2*2*18 + 3*2*2*2
= 2756 pips

With 8000 possibilities, that is 0.343125 crit and 0.614625 hit chance.

Now for supremacy.  The ones that have already crit we ignore, because we are keeping that ****.

That leaves 5244/8000 pips we do a reroll on.  (Note: we could also choose to not-reroll if our sage of ages die is the suck, but I doubt we'll make that choice).

We have to break this into sage of ages misses and sage of ages hits.  So lets rewind!  (at this point, I'm throwing out all of the work above.  It doesn't preserve the needed information about how many of the "try supremacy" that have a miss or a hit sage of ages die, which makes a huge difference.)

Sage:
H 11/20
M 7/20
C 2/20

If Sage crit, we are done.

Sage Hit branch (pass 1) 400 pips:
2*18*2+2*2: one or both dice got a crit.  Done.
1: we got a triple matching our sage die.
1*19*2: one of the other two dice matched our sage die.
11: the other dice rolled a double.
Crit total: 126/400 (not bad!)

So at this point, .1 from sage crit, plus .17325 from sage hit that turns into a crit.

Sage Hit branch (supremacy reroll): 400 pips:
126/400 crits
Total chance: 11/20*(400-126)/400*126/400

This adds 0.11867625 crits.

We are at 0.39192625 crits per MBA.

Sage Miss branch (pass 1) 400 pips:
2*18*2+2*2: one or both dice roll 19+.  Done.
11: the other dice roll a double.
87/400 pips are a crit.

If we fail to get a crit, we repeat (maybe?).
0.17019375 (reroll) + 0.2175 (first roll) = 0.38769375 that we get a crit.
Times 7/20 = 0.1356928125 from the start

Summing up: 0.527619012 chance to crit once.

So what did I miss?

Aha -- I see that people missed the fact you cannot crit from a matched die on your float on the second pass if they got the crit on the first pass.  I probaby also made mistakes, but I don't see anyone accounting for that.

You'll note that having a sage die in the hit range is a huge boost to your crit chance, because either of the other two dice can match it.  But if you have it in your first round, you are less likely to have it in your second, because it is more likely to be consumed.

Note that there are 20^5 = 3200000 different sets of "float, die, die, martial die, martial die".

Walking that entire matrix, and counting the possible results, should take a fraction of a second in a reasonable language.

The possibilities are:
1: Crit with a crit sage die leftover.
2: Crit with a hit sage die leftover.
3: Crit with a miss sage die.
4: Hit with a hit sage die leftover.
5: Hit with a miss sage die.
6: Miss!

Simply use an int, increment the count for each possibility (note that you don't short-circuit the "martial die not rolled" -- you pretend you rolled them "for fun".  This makes the math easier, as each count is 1/3,200,000 chance).

Once that is done, you run a second simulation on each of the above 6 cases, and you'll be able to work out the average number of hits you get from your MBA.

It is also interesting that you can use this second simulation to model an action point round. 

Nice build!  My Rain Lord would love to play with this guy =)
Reborn champion has a level 30 feature that lets you take an extra standard action whenever you score a critical hit.  Sadly Ardent champion states that you must still hit with both dice, but gaining an extra action as a free action.  Because you're gaining a standard action as a free action you're not making an attack as a free action, so you can do this as many times as you like.

The formula that we will use with this is base DPR/(1-r) where r is the chance of critting with an attack.

The chance of critting with 19-20 crit range, OoE and Martial Supremacy are as follows
5Crit on 19-20
Crit: 0.40058
hit: 0.59322
Miss: 0.0061938

Thus our DPR is multiplied by 1.6683  
 
DPR King Candidates 3.0
How much damage should I shoot for?
You're fired : 1 Kills Per 5 Rounds = .2 KPR Fair Striker : 2 Kills Per 5 Rounds = .4 KPR Highly Optimized : 3 Kills Per 5 Rounds = .6 KPR Nerfbat please : 4 Kills Per 5 Rounds = .8 KPR It's OVER 9000!!!!!: 5 Kills Per 5 Rounds = 1+ KPR
DPR? KPR? KP4R? Bless you
DPR = Damage Per round ~= Chance to hit * damage on a hit KPR = Kills Per Round. 1 Kill = 8*Level+24 damage = DPR/(8*level+24) KPNR = Kills Per N Rounds. How many standards can you kill in N rounds?
I considered that; but Sage of Ages is useable earlier, and Lorekeeper + Vorpal/Battle Rapture is (I think) still higher DPR at level 30.  

Of course, if you have alternative ways of getting better than 19-20 crit rates, then Reborn Champion would be better than Lorekeeper.


Incidentally, looking into 'high BMA over entire career', I have found a build with level 6: 19 DPR, level 16: 48 DPR, level 30: 92 DPR.  But I don't really think that's quite high enough.  So if anyone can find anything better for a BMA let me know (especially the level 6 one...). 
Very interesting build, I knew there was a way to abuse the Ardent Champions dice matching = crit ability and this certainly takes it far, but a couple of things stand out: It looks like you're using the SoA version's crit chance alongside the assumption of Lorekeeper's Vorpal/Rapture as encounter powers.  And how do you get around both Supremacy and Rapture being stances, and thus not active at the same time?  I assume the Gouge is Dark Sun, is there a place where all the new stuff is listed, since it's not in Compendium yet?
"Invokers are probably better round after round but Wizard dailies are devastating. Actually, devastating is too light a word. Wizard daily powers are soul crushing, encounter ending, havoc causing pieces of awesome." -AirPower25 Sear the Flesh, Purify the Soul; Harden the Heart, and Improve the Mind; Born of Blood, but Forged by Fire; The MECH warrior reaches perfection.
My original build doesn't use SoA at all.

I actually missed that Battle Rapture is a stance; for some reason I thought it was just an 'until end of encounter' ability.  If that's not true, then SoA + 19-20 crit is actually better than Lorekeeper, even at 30.  Probably. 

Additionally:  I'm working on a build that gets 8 attack rolls per attack (and doesn't use SoA at all, since it has no arcane compenent.)

The only problem is that I can't figure out ANY way for the build to get a decent crit, so... it's DPR simply isn't that high.