Measuring Damage

Welcome to the Gibbering Mouth article for March 5th, 2014. Today’s article is a Theoretical Theurgy; the topic is damage calculation.

 I apologize in advance: this article is going to be a quick one because it is setting up for my Mythcleaving two-part series on rogues. But before we can get to that, we need to talk about how to measure a character’s damage because frankly, the Paizo community does it wrong. Often.

Why Measure Damage?

As I’ve mentioned, combat is the heart of the Pathfinder Roleplaying Game, so people often feel the need to compare the damage-dealing capacity of classes. It’s a logical thing to look at when comparing classes, especially martial types that often have very few alternatives in their tool kit. You’ll see some people take damage-dealing potential and use it to rank the classes; I personally don’t believe in this because most ranking systems I’ve seen only take theoretical potential into account and not practical potential. Example: paladins and cavaliers have a crazy-potent damaging ability in smite evil / challenge which drastically affects the amount of damage they can deal in a single round. The problem? The number of times the character can use of this ability is severely limited, so while the class has a theoretically high maximum damage potential, in practice the class’s damage dealing potential is much lower because most players will not be able to use smite evil in every combat they participate in. We won’t be discussing how to track damage over the course of an adventuring day in this article, but it is a factor to keep in mind when comparing damage outputs.

Ways to Measure Damage

It is important to know a class’s theoretical potential for damage as well as a class’s practical potential.  I’ll briefly outline how to calculate both theoretical damage and practical damage below:

Theoretical Damage

Theoretical damage is easy to calculate because you are assuming that every attack you make hits. Here are the steps to calculating theoretical damage.

  • Step One: Determine the average damage of all variable elements of your attack. For example, weapon damage is a variable element: if my dagger damage is 1d4, I can deal 1, 2, 3, or 4 points of damage with my dagger when I attack. The average is equal to the average of all results on the die: 1 + 2 + 3 + 4 = 10. 10 / 4 = 2.5 average damage. If your attack has multiple elements of the same type, multiply them together. For example, a greatsword’s average damage is 7 (2d6 = 3.5 average damage per d6 * 2). RULE: A die’s average result is equal to half the number of sides the die possesses + 0.5. For example, half of 8 is 4, plus .5 equals an average result of 4.5.
  • Step Two: Add all numerical bonuses to damage that your attack possesses to your average variable result. For example, Power Attack’s damage bonus is a numerical bonus; it is a static value that does not vary. (Increase over the course of the game, yes, but the number it provides is not random.)
  • Step Three: The sum of your attack’s variable damage and numeric damage is your theoretical damage. Huzzah!

Practical Damage

Practical damage, on the other hand, is more difficult to calculate because it requires more statistics. Here are the steps to calculating practical damage.

  • Step One: Determine the character’s attack bonus. This includes all bonuses and penalties that you can expect the character to possess. For example, I usually allow the paladin to have his smite evil bonus, but I also allow all characters to be flanking. Don’t forget to calculate penalties such as Power Attack and Two-Weapon Fighting.
  • Step Two: Determine the character’s average damage per attack; this is identical to determining the character’s theoretical damage (see above).
  • Step Three: Determine the character’s AC benchmark. This is the AC that the character(s) participating in the comparison must be able to hit. I use the AC associated with a monster whose Challenge Rating (CR) equals the character’s level, drawn from Table 1-1: Monster Statistics by CR in Pathfinder Roleplaying Game: Bestiary for my benchmark ACs.
  • Step Four: Determine the character’s total attack bonuses for each of the twenty results possible on the character’s attack roll. For example, a character with an attack bonus of +5 would have a +6 if she rolled a 1, a +7 if she rolled a 2, a +8 if she rolled a 3, and so on. Do this with every result from 1 to 20 and note which attacks successfully hit the target AC. Remember that a 1 is always a failure (barring mythic rules) and a 20 is always a hit.
  • Step Five: Determine the weapon’s critical threat range and any bonuses the character possesses when confirming critical hits. For each critical hit, use the following formula to determine the critical hit’s damage: ((F*DPA)+S*(DPA*M))/20. In this formula, DPA is the weapon’s average damage per attack (aka its Theoretical Damage), F equals the chance that the critical hit will not confirm, S equals the chance that the critical hit will confirm, and M equals the critical damage multiplier. Do not uses percentages for F and S; use the number of results out of 20 that will confirm the critical hit. For example, if I confirm a critical hit against my target on a 12 or better, that means 11 results out of 20 will not confirm the critical hit (F) while 9 results out of 20 will confirm it. As with attack rolls, a 1 always fails to confirm the critical hit while a 20 always succeeds.
  • Step Six: Average all 20 damage results together. The result is your build’s practical damage. Remember that a miss deals 0 damage. (Unless a miss does deal damage, such as with the grazing shot deed.)

Why Bother With Practical Damage?

Some of you might be wondering why you should bother calculating practical damage instead of doing things the good, old fashioned way with theoretical damage. The major reason is that practical damage accounts for the benefits associated with a successful hit. So many theorycrafters calculate their build’s damage with the assumption that they hit, but as we’ll see with the rogue next week a poor attack bonus really hurts a character’s practical damage in-play because a character who does not hit deals no damage. This is a credence that any MMO player is familiar with, and it’s high time that this concept was applied to the Pathfinder Roleplaying Game.

And that about wraps up my thoughts on calculating average damage for this installment of Theoretical Theurgy. What do you think? How do you calculate your character’s average damage? Does the difference between theoretical and practical damage matter to you? Do you care about the concept of Damage Per Round at all? Leave your answers and comments below, and I’ll see you next week with the the debut of Gibbering Mouth’s Mythcleaving article with a two-week special on rogues! Don’t miss it!

Alexander “Alex” Augunas has been playing roleplaying games since 2007, which isn’t nearly as long over 90% of his colleagues. Affectionately called a “budding game designer” by his partner at Radiance House, Alexander is the author of the Pact Magic Unbound series (Radiance House) and a handful of other Third-Party Products. Before founding the Everyman Gaming blog, Alexander gained notoriety for writing the GM’s Guide to Challenging Encounters, which remains accessible to this day. His favorite color is blue, his favorite Pathfinder Race/Class combination is kitsune ranger, and his favorite pastime is wearing the label “Mathematics Hipster” with pride!  

Advertisements

9 thoughts on “Measuring Damage

  1. I’m unsure as to what your Mythcleaving article on Rogues will cover. Is it that you will clarify Rogues are good, or that Rogues are bad or that Rogues are DPR machines or something?

    DPR is important to me, because dealing bad damage means fights lasts longer and enemies have more chances to kill or injure party members. However, it isn’t the end-all-be-all mechanic for determining a characters quality. Someone who can easily, and regularly, render an opponent harmless (for example, always able to Daze or Stun a target) is just as, or better than a high DPR opponent. If you can nullify or negate an opponent, and keep them that way, then they are as good as dead in a combat frame. The exception comes from a time-sensitive combat.

    For example the Dirty Trick Master by chaoseffect on Paizo (http://paizo.com/threads/rzs2qqod?Making-a-Dirty-Trick-specialist-Lore-Warden) may not have a high DPR, but by judicious applications of Dirty Trick, he can lock enemies down to being useless and denying them their actions entirely, letting the party take their time in dealing with them. A high DPR opponent can only do the same if he can kill the enemy in a single round, because an opponent still standing, is an opponent who is dangerous. The Dirty Trick Master could keep dazing an enemy, and keep them dazed, to such an extent, even a Str 7 Wizard could eventually club the enemy to death with a rock from the ground.

    Plus, being able to do more than just DPR (like Spell Sunder or Lay on Hands) is an important consideration for characters. If all your character can do is swing a Greatsword, then he’ll have a hard time functioning in anything that isn’t combat or doesn’t directly involve killing an enemy.

    If consistent (practical) DPR were the only consideration, then the Fighter would be the superior martial class beause he’s the only one who’s abilities aren’t limited use in some fashion, be in uses per day, like Smite, rounds per day, like Rage, or dependent on enemies, like Favored Enemy.

  2. @Darrel If you like that version of a Dirty Tricks character, you’ll want to stay tuned for my version on March 14th. I think you’ll REALLY like that one! 😉

    Believe it or not, but DPR is actually the last thing that I consider when I make my builds, more often the not. For martial characters, achieving good DPR is as easy as taking the Power Attack feat most of the time. (Which is one of the fundamental design problems with the feat, but that’s a topic for a different Gibbering Mouth!) I would rather make a character who is fun for me to play than a character who is mathematically superior to all other options I could use. Sometimes those ideas are one and the same (like my blaster sorcerer build) but other times they don’t (like my current kitsune PC, who has pretty terrible DPR, actually).

    As for my approach to the Rogue, you’ll just have to wait until next week (and the week after, because its a two-part series) to see my take on it! Know that regardless of what I say about the rogue, I’m going to be fair and I’ll be using the contents of this article to justify my opinions.

  3. Great article! personally i have never really looked at theorycrafting and its associated parts however this has me kind of interested in looking at practical damage and trying to contribute that to the theory craft threads over at paizo.

    • If it makes you feel better, I almost never test the Practical Damage of my builds unless I’m trying to either prove a point or test the effectiveness of an archetype; you’ll see me do both in various articles in the coming weeks. 😉

  4. That’s a lot of math (lol) to figure out how good a melee character is at combat, just look at them when they play as a DM do you just know that character is going to kick ass or just takes up space, that being said another great all though short article.
    Keep up the great work

    • You don’t need to do this much math to tell if a character is going to be any good; if you can consistently hit the average damage for a creature of your CR, you’re fine.

      This article is really for the nitpickers and optimizers. Not everything I publish is going to be strictly for GMs. 😉

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s