Today I'm starting yet another article series, this time devoted to the calculation of a player character's statistics. The idea is to provide ways to measure and compare different aspects of a PC's performance, much like the post on attack and defense normalization, a while ago. I have a few cool formulas lying around to quantify stuff that hasn't really been explored in depth... but I should start from the beginning. So this post will focus on damage dealing, which is pretty much all that is looked at, nowadays. You will find some basic definitions and formulas, as well as guidelines for calculating damage in some common special scenarios.
Most message boards have adopted the term "Damage Per Round" (DPR) as a measure of the amount of damage that can be dealt during a game turn. Although I can't tell for sure where this expression originated, it does look awfully similar to the "Damage Per Second" (DPS) commonly used in MMORPGS.
- Damage per round (DPR): Average damage inflicted by a character to a single enemy in a round. It takes into account hit rates and extra damage from critical hits. DPR typically measures the abilities of a single character, so bonuses from other party members are ignored.
We usually clasify DPR in two types, depending on whether it involves a character using spendable resources or not: At-will DPR, and Nova DPR.
- At-Will DPR: Damage per round that can be achieved by using exclusively at-will powers. Bonuses from daily or encounter effects do not apply, and spending of action points or other consumable resurces is not considered. Exceptionally, an encounter power granting encounter-lengh effects can be considered a valid modifier because of being permanently active.
At-will DPR is the most commonly used metric in optimization boards. It isn't the most realistic estimation of actual PC damage, since the contribution of encounter and Daily powers is usually very significant. On the other hand, it's relatively straightforward to calculate, and a reliable indicator of damage in the worst case scenario for a damage dealing PC.
- Nova DPR: Damage that can be dealt in a round with all the tools that a single character has at his disposal, including action points and daily powers. Used to measure a character's maximum offensive potential.
- Area DPR: When attacking multiple enemies, damage that can be dealt to each of these enemies in a round. Area DPR measurements should specify what kind of area or how many enemies can be covered: "Area DPR (area burst 1)" or "Area DPR (2 targets)".
The DPR of a character making a single attack each round is equal to the average damage of that attack. For scenarios with more than one attack per round, see below.
Average Damage of an attack.
The following calculations assume that a character is attacking a standard skirmisher monster of his own level. If you want to find out DPR values against different types of enemies, you will need to adjust Hit Rates accordingly.
Average Damage= (Hit rate * Average Hit Damage) + (1 - Hit Rate) * Average Miss Damage) + Crit Rate * Extra Crit Damage
AD= HR*Dh + (1-HR)*Dm + CR * Dc
- Hit rate (HR), chance to hit a Skirmisher Monster of the same level. Can be calculated from here. If an attack has an intrinsic bonus to the attack roll, add it to the HR (+0,05 per extra point).
- Crit Rate (CR), chance to score a critical hit.
Roll to crit - Crit rate
Crit on a 20 - 0.05
Crit on 19-20 - 0.1
Crit on 18-20 - 0.15
- Average Hit Damage (Dh). To calculate, add the average value of all rolled dice, and any damage modifiers that apply.
Die - Average value
d4 - 2.5
d6 - 3.5
d8 - 4.5
The Brutal property adds 0.5 to the average value of a die per point of brutal.
- Average Miss Damage (Dm). Usually 0, but can be half the hit damage (Dh/2) for certain Daily attacks, or a fixed falue in certain cases.
- Extra Crit Damage (Dc), or how much more damage is dealt by a critical hit, on average, in excess of the average damage of a normal hit.
Dc = Dh - Average Crit Damage.
(Average Crit Damage is the sum of all maximized damage dice, plus damage modifiers, plus extra crit dice).
When your character can make several attacks during a single round, calculate separately the average damage of each one and add them together.
When you have an attack that only triggers after hitting with a previous power, multiply that attack's Average Damage by the Hit Rate of the previous attack.
Attacks that trigger on conditions not completely under your control, such as a Fighter's Combat Challenge should not be considered on DPR calculations.
If an attack deals automatic damage in addition to, or instead of a conventional attack roll, that damage is directly added to the total Average Damage.
If an attack allows you to roll twice and use the highest value, the effective Hit Rate and Crit Rate are increased. You can calculate these new values, HR' and CR' from the original HR and CR as follows:
HR' = HR * (1-HR)
CR' = CR * (1-CR)
Once-per-turn damage bonuses
Most striker classes have features that deal extra damage once per round. When calculating DPR, you can add this extra damage to Average Hit Damage only if you are making a single attack per round. When making multiple attacks, calculate this extra damage separately, as follows.
Striker damage contribution = Chance to hit once * average extra damage
The chance to hit once (H1) depends on the number of attacks and the Hit Rate HR:
2 attacks: H1= HR * (1-HR)
3 attacks: H1= 1 - (1-HR)*(1-HR)*(1-HR)
N attacks: H1 = 1 - ((1-HR) ^ N)