Rheebus

03-12-2009, 07:01 PM

I am playing with some formulas to calculate Average Damage per Hit for multiple weapon types. I started with Bastard Swords vs. Khopeshes, because I was trying to work through which I should pick up for my battle cleric.

Assumptions:

Please let me know any comments you have about these assumptions.

Average damage for a weapon was based on randomly rolling the dice for damage, example: 1d6 would average 3.5 damage per hit because each number 1, 2, 3, 4, 5, 6 should be rolled an equal number of times. (1+2+3+4+5+6) / 6 = 3.5

I am assuming a hit on a 5+ on average. Monster AC is variable. Also, this is very difficult to predict because as you progress in your attack sequence you get huge bonuses to hit. As they get to their 3rd and 4th attacks the bonus to hit goes up by 5 each time. This dramatically improves the chance to hit on those last two (and any subsequent attacks).

All critical hits are confirmed. For most melee toons, this is a 95% chance.

Definitions

WD = Weapon's Average Base Damage

BONUS = Any Damage Bonus applied BEFORE critical multiplier on a critical hit.

FDB = Average first damage bonus from alignment burst (always 7 - Holy Burst, Anarchic Burst, Axiomatic Burst)

SDB = Average second damage bonus from a secondary source (always 3.5 - pure good, lesser X bane)

%H = Percent chance any swing will do normal damage

CM = Critical Multiplier (x2, x3, x4)

BDB = Average burst damage bonus (5.5 for x2 critical multiplier weapons, 11 for x3s, and 16.5 for x4s)

%CH = percent chance of a critical hit (assumes they are confirmed)

Formula

Average Damage per Hit = (((WD + BONUS) + FDA + SDA) * %H) + ((((WD + BONUS) * CM) +FDB + SDB +BDB) * %CH)

Now, let's see it in action.

Khopesh

Damage: 1d8

Critical Threat Range: 19-20

Critical Multiplier: x3

Bastard Sword

Damage: 1d10

Critical Threat Range: 19-20

Critical Multiplier: x2

These two weapons have the same threat range. The bastard sword has a higher base damage and the khopesh has a higher critical multiplier. My hypothesis is that they will have similar Average Damage per Hit at low damage bonuses and that the khopesh's average damage per hit will increase faster than the bastard sword's because of its higher Critical Multiplier.

">http://spreadsheets.google.com/pub?key=pWFlHYWf8o0mYtNnnRaaKYg&oid=7&output=image (http://forums.ddo.com/%3Cimg%20src=)

This hypothesis seems to be correct. On average, the Khopesh will outperform the bastard sword at higher damage bonuses. At +15 to damage, the Khopesh will do 11% more damage per swing on average (38.5 and 34.65 respectively).

Tell me what you think. I am currently working to make this simpler and include every weapon in my analysis. If you have any questions. Please do not hesitate to ask.

I will not answer flame replies.

The Rheeb

Assumptions:

Please let me know any comments you have about these assumptions.

Average damage for a weapon was based on randomly rolling the dice for damage, example: 1d6 would average 3.5 damage per hit because each number 1, 2, 3, 4, 5, 6 should be rolled an equal number of times. (1+2+3+4+5+6) / 6 = 3.5

I am assuming a hit on a 5+ on average. Monster AC is variable. Also, this is very difficult to predict because as you progress in your attack sequence you get huge bonuses to hit. As they get to their 3rd and 4th attacks the bonus to hit goes up by 5 each time. This dramatically improves the chance to hit on those last two (and any subsequent attacks).

All critical hits are confirmed. For most melee toons, this is a 95% chance.

Definitions

WD = Weapon's Average Base Damage

BONUS = Any Damage Bonus applied BEFORE critical multiplier on a critical hit.

FDB = Average first damage bonus from alignment burst (always 7 - Holy Burst, Anarchic Burst, Axiomatic Burst)

SDB = Average second damage bonus from a secondary source (always 3.5 - pure good, lesser X bane)

%H = Percent chance any swing will do normal damage

CM = Critical Multiplier (x2, x3, x4)

BDB = Average burst damage bonus (5.5 for x2 critical multiplier weapons, 11 for x3s, and 16.5 for x4s)

%CH = percent chance of a critical hit (assumes they are confirmed)

Formula

Average Damage per Hit = (((WD + BONUS) + FDA + SDA) * %H) + ((((WD + BONUS) * CM) +FDB + SDB +BDB) * %CH)

Now, let's see it in action.

Khopesh

Damage: 1d8

Critical Threat Range: 19-20

Critical Multiplier: x3

Bastard Sword

Damage: 1d10

Critical Threat Range: 19-20

Critical Multiplier: x2

These two weapons have the same threat range. The bastard sword has a higher base damage and the khopesh has a higher critical multiplier. My hypothesis is that they will have similar Average Damage per Hit at low damage bonuses and that the khopesh's average damage per hit will increase faster than the bastard sword's because of its higher Critical Multiplier.

">http://spreadsheets.google.com/pub?key=pWFlHYWf8o0mYtNnnRaaKYg&oid=7&output=image (http://forums.ddo.com/%3Cimg%20src=)

This hypothesis seems to be correct. On average, the Khopesh will outperform the bastard sword at higher damage bonuses. At +15 to damage, the Khopesh will do 11% more damage per swing on average (38.5 and 34.65 respectively).

Tell me what you think. I am currently working to make this simpler and include every weapon in my analysis. If you have any questions. Please do not hesitate to ask.

I will not answer flame replies.

The Rheeb