Single/Dual Wielding

[Faceman]

There is a third, the Scarlet Ninja-To (Scimitar +3, poison dmg) which is sold by one of the Bonus Merchants (see the forum FAQ for details), but it can only be used by Monks.

And monks can't dual-wield
I'd really like to do the math but I gotta go. Maybe later [img]smile.gif[/img]

[Dundee Slaytern]

Originally posted by Klutz: ~~ The scary thing is that Impaler is SO nasty with its +10 piercing damage that it actually comes close in raw damage to Celestial Fury dual-wielded with Belm, but is still edged out by the dual-wield combo. ~~

CFury: 1d10+3, + 5% 20 electrical damage

Belm: 1d8+2

The Impaler: 1d6+3, +10 piercing damage

Grandmastery Patch: +5 damage
No Grandmastery Patch: +3 damage
19 STR: +7 damage
GoWE: +2 damage
.
Damage Bonuses: 3 + 7 + 2 = 12
With GM Patch : 5 + 7 + 2 = 14
.
Two-Handed Weapon Style: +1

Base ApR: 1
Warrior Bonuses at clvl 13: +1
Dualwield: +1
Belm: +1
Specialisation: +0.5
Grandmastery Patch: +1.5

---

The Impaler (Without GM Patch):
--------

Total ApR: Base(1) + clvl 13(1) + 2*(0.5) = 2.5

Average Damage Per Normal Hit: (( 1 + 6 ) / 2 ) + 3 + 1 + 12 + 10 = 29.5
Average Damage Per Critical Hit: = ( 19.5 * 2) + 10 = 49

Total Average Damage For 20 Rounds: (29.5*2.5*17)+(49*2.5*2) = 1498.75
Average Damage Per Round: 1498.75/20 = 74.9375
Average Damage Per Hit: 74.9375/2.5 = 29.975

The Impaler (With GM Patch):
--------

Total ApR: 1+1+1.5 = 3.5

Average Damage Per Normal Hit: (( 1 + 6 ) / 2 ) + 3 + 1 + 14 + 10 = 31.5
Average Damage Per Critical Hit: ( 21.5 * 2 ) + 10 = 53

Total Average Damage For 20 Rounds: (31.5*3.5*17)+(53*3.5*2) = 2245.25
Average Damage Per Round: 2245.25/20 = 112.2625
Average Damage Per Hit: 112.2625/3.5 = 32.075

---

Celestial Fury + Belm (Without GM Patch):
--------

Total ApR: 1+1+1+1+0.5 = 4.5

CFury:
----

Average Damage Per Normal Hit: ((1+10)/2)+3+3+7+2 = 20.5
Average Damage Per Critical Hit: (5.5+3+3+7+2)*2 = 41

CFury takes up 3.5 ApR, while Belm takes up 1 ApR.

Total Average Damage For 20 Rounds: (20.5*3.5*18)+(41*3.5) = 1435
Average Damage Per Round: 1435/20 = 71.75
Average Damage Per Hit: 71.75/3.5 = 20.5

Belm:
----

Average Damage Per Normal Hit: ((1+8)/2)+2+3+7+2 = 18.5
Average Damage Per Critical Hit: (4.5+3+3+7+2)*2 = 37

CFury takes up 3.5 ApR, while Belm takes up 1 ApR.

Total Average Damage For 20 Rounds: (18.5*18)+37 = 370
Average Damage Per Round: 370/20 = 18.5
Average Damage Per Hit: 18.5/1 = 18.5

Together:
----

Total Average Damage For 20 Rounds: 1435+370+(20*2.5) = 1855
Average Damage Per Round: 1855/20 = 92.75
Average Damage Per Hit: 92.75/4.5 = 20.611

Celestial Fury + Belm (With GM Patch):
--------

Total ApR: 1+1+1.5+1+1 = 5 (due to ApR cap)

CFury:
----

Average Damage Per Normal Hit: ((1+10)/2)+3+5+7+2 = 22.5
Average Damage Per Critical Hit: (5.5+3+5+7+2)*2 = 45

CFury takes up 4 ApR, while Belm takes up 1 ApR.

Total Average Damage For 20 Rounds: (22.5*4*18)+(45*4) = 1800
Average Damage Per Round: 1800/20 = 90
Average Damage Per Hit: 90/4 = 22.5

Belm:
----

Average Damage Per Normal Hit: ((1+8)/2)+2+5+7+2 = 20.5
Average Damage Per Critical Hit: (4.5+3+5+7+2)*2 = 41

CFury takes up 4 ApR, while Belm takes up 1 ApR.

Total Average Damage For 20 Rounds: (20.5*18)+41 = 410
Average Damage Per Round: 410/20 = 20.5
Average Damage Per Hit: 20.5/1 = 20.5

Together:
----

Total Average Damage For 20 Rounds: 1855+410+(20*4) = 2345
Average Damage Per Round: 2345/20 = 117.25
Average Damage Per Hit: 117.25/5 = 23.45

[ 11-04-2003, 02:18 AM: Message edited by: Dundee Slaytern ]

[Leslie]

Wohoo !
Dundee does it again ! [img]smile.gif[/img]

I like numbers ...

(and after many many games I actually have a game where I use Impaler)

[Feral]

Impressive work - thanks!

[Jim]

Great work Dundee. You grace us with your number crunching skills once again. An observation from my point of view:

Taking the Impailer (Non GM Patch, but still applies to the GM patched calculations):

Total Average Damage For 20 Rounds: (29.5*2.5*18)+(48*2.5) = 1447.5

I assume you are multiplying by 18 since there are 20 rounds in total, and 5% of hits are critical misses and 5% are critical hits (i.e. 2.5 attacks of each or 1 round), correct? Then the 48*2.5 represents the single round of critical hits, and therefore the round of critical misses is ignored gives us 19 damaging rounds?

However[/list]Since we are assuming specialisation in Two Handed Weapon style, we will in fact have 10% of our total hits as criticals, therefore the values need asjusting slightly to (29.5*2.5*17)+(48*5). This does not alter your conclusion however, as it tips the scale even further in favour of the Impailer.

Also worth noting, your calculations assume a 19 STR. It is in fact very feasible to aquire a 21 STR in SoA, and since the dual wielding combination is more scalable due to the higher APR, a 21 STR might just even things up a little.

[Klutz]

Dundee's post quoted but abbreviated for brevity:

Originally posted by Dundee Slaytern: quote: Originally posted by Klutz: ~~ The scary thing is that Impaler is SO nasty with its +10 piercing damage that it actually comes close in raw damage to Celestial Fury dual-wielded with Belm, but is still edged out by the dual-wield combo. ~~

Actually...

The Impaler (Without GM Patch):
--------

Average Damage Per Round: 1447.5/20 = 72.375

Celestial Fury + Belm (Without GM Patch):
--------

Average Damage Per Round: 1445/20 = 72.25

With or without the GM Patch, the Impaler can outdamage CFury+Belm. Something to keep in mind. [/QUOTE]I humbly accept my correction, but seeing as the difference came down to 1/8 of a hit point of damage per round for the case I had in mind, and I did go far enough down the math to identify that it would just be "edged out" the other way, I'll consider myself only slightly chastised. I may have to eyeball this further at home, given Jim's response, but thanks to both of you regardless.

EDIT: Wait a minute... for vanilla SOA, CF primary hand + Belm offhand, 13th level warrior specialized in Katana, that's 4.5 attacks per round... 3.5 from CF in primary hand and 1 from Belm in off hand! The numbers above (for vanilla SOA) were based off 2.5 attacks for CF and 1 for Belm. I'm definitely going to give this another look...

[ 11-03-2003, 05:10 PM: Message edited by: Klutz ]

[Dundee Slaytern]

Oops! Forgot about the +1 ApR from Dualwielding.

Eh-hehehehe... *insert sheepish grin*

CFury+Belm win this time round. Calculations edited above. Thanks to Jim and Klutz for pointing out the errors.

Although one might want to note that Impaler is good for those one-hit kills. CFury+Belm excel at tough singular opponents while Impaler is good for hordes (since it may take 2 hits to kill one target with CFury+Belm (note: this is just an example. In reality, it might take 3-4 hits), negating its' ApR advantage).

[ 11-04-2003, 12:58 AM: Message edited by: Dundee Slaytern ]

[Dundee Slaytern]

Oh, and I used 19 STR because let's face it... that is the most realistic STR figure we can have with most players at any one time in the game. Maximum (or close thereof) STR possible is fine and dandy when we want to calculate the maximum possible damage, but in this case, we are trying to figure out which combination works better between two choices, and so we have to choose more... "realistic" figures for the players who have not learn how to tweak or choose not to bother with tweaking.

[Klutz]

*SIGH* Now I have to re-edit... tried to post earlier but forum was down and by the time I got back in Dundee had beaten me to the punch. Most of what I wrote is still relevant, so here goes.

Two out of three mistakes taken care of (+1 APR and extra critical from two-handed weapon style). One mistake left:

Although you noted in the description Celestial Fury's 5% chance of doing 20 points of electrical damage, you didn't figure that into the calculations. Since 5% of 20 is exactly 1, I simply added 1 to the damage for CF (not doubling it for the critical).

Also, one "hidden" assumption we are making is that every roll that isn't a critical miss is a hit... meaning we're not considering the effect of THACO. This helps the dual-wielding combo a tad, since considering THACO would slightly weaken the contribution of the off-hand weapon. But taken to the extreme it also helps the two-handed weapon, since the tougher your opponent is to hit the more likely it is that you're only hitting on criticals... which is where the extra critical on a 19 will shine for the two-handed weapon user. So I'll leave that out myself also.

One minor question, not a correction (though it could be). What is "GoWE"? I left it in my calculations as +2 damage per attack, but if that's a TOB item we should probably remove it for this forum... and if it's the TOB item I think it is, it affects more than just damage per attack in the calculations.

As you'll see below, it's no longer even close:


13th level fighter
Grandmastery: +3 dmg
19 str: +7 dmg
GoWE: +2 dmg
NO Grandmastery patch

Total bonus damage per attack: 12

And, for Impaler only:
Two-weapon style: +1 dmg, crit hit on 19 & 20

Impaler D6+3, +10 piercing damage

Average damage per normal hit: =3.5+3+10+12+1 =29.5
Average damage per critical hit: =2*(3.5+3+12+1)+10 =49
Attacks per round: 2.5
Damage over 20 rnds (17 hits, 2 criticals, 1 miss)*APR: =(17*29.5+2*49)*2.5 = 1498.75
Average dmg per round: =1498.75/20 = 74.9375

Celestial Fury D10+3, +5% chance of 20 electrical damage

Average damage per normal hit (+1 for avg electrical damage): =5.5+3+12+1 =21.5
Average damage per critical hit: =2*(5.5+3+12)+1 =42
Attacks per round (including Belm's bonus attack): 3.5
Damage over 20 rnds (18 hits, 1 critical, 1 miss)*APR: =(18*21.5+42)*3.5 =1501.5
Average dmg per round: =1501.5/20 = 75.075

Belm D8+2, +1 APR (APR bonus applied to Celestial Fury)

Average damage per normal hit: =4.5+2+12 =18.5
Average damage per critical hit: =2*(4.5+2+12) =37
Attacks per round: 1
Damage over 20 rnds (18 hits, 1 critical, 1 miss)*APR: =(18*18.5+37)*1 =370
Average dmg per round: =370/20 =18.5

Summary
Average damage per round, Impaler only: 74.9375
Average damage per round, CF + Belm: 93.575

That's about 25% more damage using CF + Belm over Impaler.

Although I'm not going to revise based on just this, with my own calculations my only remaining nitpick is that I'm assuming grandmastery in both Katanas and Scimitars... which is kinda unlikely. However, the damage bonus for strength, proficiency, and items, doesn't matter as much as I thought. Just to give you a taste, here's what the summary looks like when you change that value from 12 to 3 (15 str or below, or 16-17 str and specialization only, no +dmg items) you get:

Average damage per round, Impaler only: 51.3125
Average damage per round, CF + Belm: 53.075

So even for your wimpy fighter, dual-wielding is better... though not by too much. Crank it up the other way to say 19 (21 str from Girdle of Frost Giant Str + grandmastery patch) and you get:

Average damage per round, Impaler only: 93.3125
Average damage per round, CF + Belm: 125.075

Now that's 34% more damage for the dual-wielder. And finally, back to 19str (+7 dmg) and specialization (+2 dmg) with no mods, but no GoWE, for a total of +9 damage per attack (which is the most realistic set of assumptions for an SOA warrior type I'd be likely to create/use), and you get:

Average damage per round, Impaler only: 67.0625
Average damage per round, CF + Belm: 80.075

Corrections, clarifications, or questions welcome.

[ 11-04-2003, 01:21 AM: Message edited by: Klutz ]

[Dundee Slaytern]

I did factor in the electrical damage.

Together: ---- Total Average Damage For 20 Rounds: 1435 (this is CFury)+370 (this is Belm)+(20*2.5) (tada!) = 1855 Average Damage Per Round: 1855/20 = 92.75 Average Damage Per Hit: 92.75/4.5 = 20.611

Same goes for the one with GM Patch.

GoWE are the Gauntlets of Weapon Expertise. They are a SoA item. The ToB item you are thinking about is the GoES.

[ 11-04-2003, 02:00 AM: Message edited by: Dundee Slaytern ]