How Do You Calculate the Average Damage for Twin Strike?

Question

I'm looking for a formula that can calculate the average damage of a power. Specifically, the Ranger at-will power Twin Strike. This is a bit more complicated, since it's two attacks. Furthermore, Hunter's Quarry damage will be used once if either of the two attacks hit, or both hit, but not if both miss... how I make a formula that includes two attacks, two chances to crit, and the use of Hunter's Quarry is beyond my Statistics skills. lol

Things the formula needs: 1. Basic value for what I need to roll to hit; 2. A value for the damage die; 3. Take into account crits; 4. take into account Hunter's Quarry (used only once on 1 or 2 hits); 5. Take into account miscellaneous bonuses (such as weapon enchantment bonus and weapon focus feats adding to the damage; even though Ability Mods do not)

If the formula is easily modified for the Epic Tier feat increasing the crit range to 19-20, that'd be awesome, since this will be used specifically for Twin Strike's damage during Epic Tier.

Answer 1

• To Hit : H (Your to-hit as given by charbuilder)
• Level : L (Your Level)
• Bow Dice: B
• Quarry: U
• CritChance: C
• CritDamage: D
• Static Modifier: S

HitChance (T) = 1-((L+14-H-1)/20)-C

Odds of Quarry (Q) = 1-( (1-T)^2 ) * U + 1-( (1-C)^2)*max(U)

Average Damage = ( T*(B+S) + C*(max(B)+S+D) )*2 + Q

In english: Calculating twin-strike without quarry is trivial, you simply apply the average damage calculation as presented here and then calculate the odds of hitting at least once and multiply that through the quarry. I will assume that you are competent to add misc bonuses into your hit modifier and your static modifier.

In terms of optimization, for double-attackers, getting accuracy and the staticMod as high as possible is key. Hunter's quarry is "meh" in comparison.

Edit Running the numbers provided from your comment with the following:

If it's not to much to ask... what would the average damage for Twin Strike be for: Ranger, Level 26, To-hit +32, Weapon Ench +5, Weapon Focus Feat giving +3 damage, hit chance 10% (epic tier feat making crits 19-20), Quarry 3d8, and +2 to damage (due to Bracers giving +2 item bonus to melee attacks). He's using 2 bastard swords (d10 damage). –

We start by listing assumptions and requirements.

Requirement: Does a twin-bastard sword ranger do excessive damage?

Assumption: Excessive damage will be defined as being able to drop a standard monster in less than two rounds, as per the DPR king thread.

Assumption: PP and ED play a significant role in this calculation. Therefore we must calculate damage with and without an optimal PP and ED.

Assumption: An optimal PP is one that is sky blue here as is ED

Assumption: Weapon choice has a significant impact, therefore we must also perform these calculations with and without magical weapon.

Assumption: Stated +32 to hit resolves into an 18 strength at level 1 pre-racial or ED. Therefore, I will assume a +2 due to ED, and not apply racial cheese.

Assumption: Feat choice has a significant impact, therefore I will assess the damage with and without the paragon-tier prime * feats. I will not perform further calculations as to frostcheese or other damage strategies.

Therefore:

Build 1, semi-competent damage: Half-orc, two-blade ranger, Heavy weapon expertise, bastard sword prof, Stormwarden PP, Indominable Champion ED (Boring as *, but whatever), Lethal Hunter, Heavy Blade Mastery, Called Shot, Prime Punisher, Slashing Storm, Weapon Focus (Heavy Blade), Iron Armbands of Power (Heroic Tier?)

There are so many more optimizations possible, but this is a good "Not too glassy" option leaving many feat, items, and so-forth.

Character builder produces the following attack: +32 v. AC // 2d19+10 damage,+3d8 quarry, +5 to damage rolls due to called shot, prime punisher, +1 to accuracy due to prime shot.

The complete expression to be evaluated is, therefore:

(32 accuracy, AC of 26+14, extra -1 due to prime shot)

Base damage, before quarry. (1-(26+14-32-1-1)/20-.1)*(5.5*2+10+5)*2+.1*(10*2+10+5+3.5*5)*2 = 41.700 Rounds to drop 1 enemy, before quarry = 5.5 = absolutely pathetic for a striker. Minimum recommended striker rounds = 4

Quarry damage, calculated correct follows the following pattern: Odds of hitting the first time * quarry + odds of critting the first time * quarry + (odds of hitting the second time * odds of missing first time) * quarry + (odds of critting the second time - odds of missing the first time) * quarry.

Odds of hitting: (1-(26+14-32-1-1)/20-.1) 60% Odds of critting: 10% Odds of missing: (26+14-32-1-1)/20)=30% Total odds =1

.6*4.5*3+.1*8*3+.6*.3*4.5*3+.1*.3*8*3=13.65 expected quarry damage from one twin strike

Total DPR:

13.65+41.700=55.130 (8*26+24)/55.130=4.208

Not quite in minimum striker level damage.

Extra DPR 2*Dex (stormwarden, assuming both 11 and 16 come into play) + Wis (slashing storm)= +8+8+2 = +18

55.130+18=73.130 (8*26+24)/73.130=3.172

Just about right for a semi-optimized ranger at-will.

Dropping prime punisher and called shot gets twin-strike DPR to: 32.6, 13.257 quarry damage

32.6+13.257+18 = 63.857, 3.633 rounds, just right.

Dropping stormwarden:

32.6+13.257+2 = 47.857, 4.847 rounds, unacceptable.

Therefore, based on the parameters you described, the ranger's damage probably fits into the low end of the "striker damage" window or below and should be allowed into your game.

Answer 2

Here is the great thing about Twin Strike. They are not dependent. Because they are not dependent, without Hunter's quarry you can just add them. With Hunter's quarry, you just add it once.

Here is the formula I would use:

=(1-(N+A)/20)(C+F) +(A/20(D+H+I))

Where: A - Crit Chance/.5 (1 or 2) N - Roll Needed C - Average of 2[W] + (Feat bonus + item bonus) F - Average of Hunter's quarry dice (10.5 or 13.5 if you have Lethal Hunter at epic) D - Max 2[W] + modifiers H - Average of Crit Dice I - Max Hunter's quarry (at epic its 18 or 24 with Lethal Hunter)

To calculate average damage for a weapon die you take the min and the max of the die and divide by 2. (Normally this is 1+max, but if its brutal its 2 or 3 + max).

Roll Need can be calculated by the following formula:

(14 + your level) - (1/2 level + Weapon Prof + Ability Mod + Magic Item Bonus + Feat Bonus)

If you need further clarification, or to see a google doc with all of this calculated leave a comment.