3.02.2006

+2% Chance for an Extra Attack Has No Material Benefit Over +2% Hit

Known Facts:
HoJ procs off both special attacks and normal attacks.
HoJ can proc on another HoJ proc.
HoJ proc triggers an extra Main Hand attack.

Now assume a normal 5% hit 30% crit rogue (20% miss rate on normal attacks, 0% miss rate on special attacks) SS spamming over the course of 100 seconds using two 2.4 speed weapons. Further assume 250 non-crit white attacks and 318 non-crit SS for simplicity.

Default:
Total # of white attacks = (2*100/2.4)*(100%-20%) = 66.7
Damage from white attacks = 66.7 * (250+250*0.5) /2 * 1.3 = 16,258
Total # of SS = 25
Damage from SS = 25 * 318 * (0.7+0.3*2.3) =11,051
Total # of attacks = 91.7
Damage Total = 27,309

2% Hit:
Total # of white attacks = (2*100/2.4)*(100%-20%+2%) = 68.3
Damage from white attacks = 68.3 * (250+250*0.5)/2 * 1.3 = 16,648
Total # of SS = 25
Damage from SS = 25 * 318 * (0.7+0.3*2.3) =11,051
Total # of attacks = 93.3, or 1.74% more attacks than the original.
Damage Total = 27,699, or 1.43% improvement over the original.

2% Chance for an Extra Attack:
Total # of white attacks = (2*100/2.4)*(100%-20%) *1.02 + 25 * 0.02 = 68.5
Damage from white attacks = 16,258 + (68-66.7+25*0.02)*250*1.3 + = 16,843
Total # of SS = 25
Damage from SS = 25 * 318 * (0.7+0.3*2.3) =11,051
Total # of attacks = 93.5, or 1.96% more than the original, or 0.2% over +2% Hit.
Damage Total = 27,894, or 2.14% improvement over the original, or 0.7% over +2% Hit.

I have ignored proc on proc since those have very marginal benefit (2% for proc, 2.04% for proc on proc, 2.0408% for proc on proc on proc, etc).

Conclusion:

  • Is +2% chance for an extra attack better than +2% hit? Yes.
  • Is the difference significant? No, unless you consider 0.2%/0.7% more swings/damage material.
  • For modeling purposes, it's easier to proximate +2% chance for an extra attack to +2%

16 comments:

Anonymous said...

Would this math then say that HoJ is equal to or worse than Blackhands Breadth for rogues? Once you get 5% to hit, generally you'd say 2% to hit is 1% to crit, and then 22 AP is about 1% to crit as well. Thus, BB = HoJ?

VitaminC said...

You forgot the +20 AP part of HoJ.

So the effective stats for HoJ (for my lazy ass) is +2%Hit, +20AP.

That is about 50% better than Blackhand Breath.

pf said...

You show that 2% to gain an extra attack is 50% better than 2% to hit, yet its only a marginal difference? On top of the fact that you have several wrong assumptions with your math.

1) sword rogues use same speed offhand
2) sword rogues dont have agression
3) sword rogues dont use slice n dice
4) sword rogues dont have dual wield spec.

These are not minor things you overlook.

-pf

VitaminC said...

pf:

First of all, I've shown a 0.5% increase in DPS from 2% hit to 2% for an extra attack. That's far from 50% that you read.

1) I assumed 2.4 speed for both MH and OH. Most MH sword speed ranges from 2.6 to 2.9. There are only 4 epic sword that has speed less than 2.4: 1 craftable, 1 from AQ Gate quest, 2 drops. 2.4 speed for both hands is a fairly reasonable assumption. Mind you that Sword Spec or HoJ procs will slightly decrease your # of MH attacks as they cancel out attack-in-motion.
2) Aggression won't change the results. Extra 6% damage on SS does not have anything to do with extra MH attacks gained through +Hit or +Chance to attack.
3) Same as above. SnD won't change the results either as it benefit both the same way. Neither will Blade Flurry skew the results.
4) Duel wield spec will only reinforce my argument further. OH DPS weights 75% instead of 50% of the white DPS, thus the damage from MH extra procs will be reduced as a % of overall damage.

Extremely minor details I should say.

Anonymous said...

+585 dmg with extra attack
+390 dmg with extra hit

585/390 = 1.5

50% better using your own math.
weighing 1% hit being about 8AEP,
the difference between 2% to hit and 2% to gain extra attack would be 8AEP.

VitaminC said...

Math 101.
Q: Dagger A does 3 dps. Dagger B does 4 dps. Dagger C does 5 dps. So dagger C does how many % more dps than dagger B?

A:
(your logic)
(5-3)/(4-3) - 1 = 2/1 - 1 = 100% (e.g. holy fuck, 5dps dagger is 100% better than 4dps dagger if i currently have a 3dps dagger)

(my logic)
5/4 - 1 = 25% (e.g. hmm, 5dps dagger is 25% better than 4dps dagger if i currently have a 3dps dagger)

Now for the real one.
Q: Originally you do 27309 damage. Your damage improve to 27699 damage with +2% hit. Your damage improve to 27894 with +2% chance to extra attack. So +2% chance to do extra attack does how many % more damage than +2% hit.

A: Your logic:
(27894-27309)/(27699-27309) - 1 = 589/390 - 1 = 50%.

My logic:
27894/27699 - 1 = 0.7%

- - - - - - - - - - - - - - - - - -

You are calculating "the % increase in damage from the IMPROVEMENT from +2% hit to the IMPROVEMENT from +2% chance for extra attack." Deadly wrong.

In other words, you are calculating the marginal benefit gained from the marginal benefit gained from +2% hit to the marginal benefit gained from +2% chance for extra attacks. (similar to the concept of 2nd derivative, 2nd moment of inertia, etc)

Another serious mistake is the use of AEP. Agility can be break down into AP and Crit thus is not suitable as a basic unit of comparison.

EDIT, removed the first post because i used the wrong html tags. :S

pf said...

Yes, when comparing stats, you have to use marginal benefit. When comparing % of your entire DPS, a .7% dps gain is a substantial gain... according to your own math, thats approximately 1% to hit. So if you say .7% dps increase is of no material benefit, then 1% to hit "has no material benefit."

Your math:
3% to hit = 2% to gain extra attack.

Now, if you use brogetta's dps calculator on a combat sword spec, youll notice that it usually values 3% crit at about 2% hit.

Note: Brogetta's DPS calculator is not perfect, but is fairly close.

-pf

VitaminC said...

Good point Pf.

I might overlooked the benefit of 0.7% increase in DPS. ><

So 3% to hit ~ 2% to chance for extra attack.

However, I should run some more numbers on this using my Excel calculator to better proximate.


Brogetta's DPS calculator is not far from exact I am afraid, and 3% crit values way more than 2% hit. The white damage and special attack damage part is fairly accurate. However the finishers and other DPS components are extremely primitive.

Rogue DPS = White DPS + Special Attack DPS + Finisher DPS + Trinket DPS + Perm Enchant DPS + Temp Enchant DPS.

Most DPS calculators only have 2 out of the 6 components, and the missing 4 components usually accounts for 25-35% of my total damage output. Pretty significant difference.

pf said...

wow, i meant brogetta usually shows:
3% hit = 2% crit, which would put extra attack about the same level as crit.

Also, I have my own spreadsheet which I use for gear/stat comparison. It does not take into account active trinkets, but everything else can easily be accounted for.

-pf

VitaminC said...

Do you mind sending me your spreadsheets?

I am in the process of revamping my spreadsheet and add some damn pivot tables for scenario analysis.

VitaminC said...

Pf,

I am not going to publish your last comment so your bandwidth won't get wtfpwnt. :p

I hate pivot tables and INTC throwing curveballs on a fucking Friday. ><

I am going to fix up something on my DPS Calculator so I can proximate better. I can send you mine if you are interested. My email is in my details.

guy from the first post said...

So in other words, while HoJ is > Blackhands, or Royal Seal, its not worth the countless hours of farming.


Thank goodness we learned this now when I have never gotten it. Good old epic trinkets, you do me no wrong.

VitaminC said...

Try to read me and pf's discussion. HoJ ist stil the best passive trinket besides DFT.

Need to run more numbers using DPS calculator though. I am still in the process of revamping it and Data Table is not cooperating :S

Anonymous said...

Get a life nerd.

Eminence #1 PvE guild.

Anonymous said...

lol PVE

Anonymous said...

paxil
ultram abuse - tramadol -
ee.net/url/2859.html>generic fioricet
- carisoprodol online