Monday, July 5, 2010

How much damage is a basic attack worth?

A while ago, we discussed some common methods for calculating the damage dealt by a character on average. However, it is common, particularly for leader classes, to have powers that deal a certain amount of damage and allow one or more allies to make an extra attack. Estimating the exact value of these powers is usually difficult, since it varies with party composition and the specific allies chosen. In today’s article, I’d like to provide some basic guidelines about how much damage to expect from a player character’s basic attack, depending on level.

Although the most immediate application is the evaluation of ‘extra attack’ powers, as mentioned above, knowing about average PC attacks can be useful in other ways. We could, for example, use it to estimate how painful it is for certain monsters to provoke opportunity attacks, or to study encounter duration across levels. I’ll take a look at this kind of issues in future posts.

Character stats

The following stats were chosen for this study. They are intended to include all the options that almost every character, regardless of role, normally takes: good ability scores, expertise feats, and feats to increase critical range at epic. Keep in mind that there is much room for improvement here, through specialized feats, paragon paths, and gear, but this should provide a good baseline. If your character is minimally competent at making basic attacks, he should perform at least as well as the numbers below show - or significantly better, if he focuses on boosting accuracy and damage.

Starting main ability score: 18. The character is assumed to make basic attacks with the best (main) ability score. For some classes or builds, this may require taking melee training at level 1. The ability modifier will increase at levels 8, 14, 21 and 28, as usual.

  • Attack: Weapon attack vs AC, +2 proficiency bonus, 1d10 damage die, or Implement attack vs For/Ref/Wil, 1d10 damage die. Both are equivalent.

  • Expertise: The character gains an appropiate expertise feat at level 5.

  • Magic Weapon/Implement: The character gains a +1 weapon/Implement at level 2, and upgrades it at levels 6,11,16,21 and 26. No special enchantments are taken into account, but the crit damage is 1d8 per plus.

  • Epic Tier: At level 21, the basic attack deals an extra d10 damage. Also, the critical hit range rises from 5% to 10% - this assumes the character takes a weapon mastery feat or its equivalent for the chosen implement/class.

In addition to these almost mandatory stats, we have considered the extremely common scenario where a character has a magic item granting item bonuses to damage, such as Iron Armbands of Power, Bracers of Archery, Staff of Ruin. We’ll provide damage values for both cases.

  • Option - Item bonus to damage: The character gains a +1 item bonus to damage at level 2, and increases it by 1 at levels 6,11,16,21 and 26.

Hit Damage

With the stats described above, we have the following damage progressions. Only average damage on a hit is considered:

Since these tables are a bit cumbersome, and damage increases very linearly, we could approximate the values with simple formulas:

BA Damage (levels 1-20) = 9 + 0.6*Lvl
BA Damage (levels 21-30) = 14 + 0.6*Lvl

BA Damage (Item bonus, levels 1-20) = 9 + 0.6*Lvl
BA Damage (Item bonus, levels 21-30) = 14 + 0.6*Lvl

As we can see in the figures below, the formulas don’t deviate too much from the previous table. As a reference, we have also included monster damage progression, as calculated here.

Since our basic attack represents the lower bound of a PC’s damage, we can see that players will usually deal more damage than monsters of their level, even before taking at-will or encounter powers into account. However, this will not be necessarily true with monsters from Monster Manual 3 and later books, since their damage is higher - though we still haven’t figured out the exact numbers.

Hit Rate

The following figure shows the attack bonuses for our character’s basic attacks throughout levels, and the corresponding hit rates. These have been calculated as explained here. As usual, the character is assumed to be attacking a skirmisher monster of his level. Note that attack bonuses correspond with an implement attack; a weapon attack vs AC would have bonuses higher by 2 points. The chance to hit is the same for weapon and implement attacks, nevertheless.

As you can see, hit rates average 60%, never deviating more than 5% from that, and it tends to be slightly better at heroic levels, and slightly worse at epic.

Damage per Round

The next step, then, is to translate this data into actual damage dealt. We talked in depth about Damage-per-Round calculations in a previous article. The simplified formula that applies here would be:

Average Damage= (Hit rate * Average Hit Damage) + Crit Rate * Extra Crit Damage

We are still missing crit rates and damage. The rates are easy enough - the baseline 1/20 chance for heroic and paragon tiers, which increases to 10% with the appropiate feats at epic. As for the extra damage on a crit, it should amount to 1d8 per plus of the weapon, plus whatever damage you gain from maximizing each d10 (which is worth 4.5 average damage).

The table below shows DPR for characters with and without item bonuses to damage:

Adding striker damage, two-handed weapons

There are a LOT of ways to improve a character’s damage and accuracy beyond the minimum levels provided here. As we explained above, it’s not practical to go into every possible combination, so I chose to go for a straightforward build that can nevertheless be useful as a practical benchmark. That said, there are two hugely frequent character choices that affect attack performance and I wanted to comment: striker damage features, and two-handed weapons.

When talking about striker features, I refer specifically to those that directly add extra damage. Although there is a variety of these, the typical feature grants an extra d6 per tier to the damage roll, or some equivalent amount.

As for two-handed weapons, there is obviously a wide variety of them, including superior weapons, so it’s not easy to settle for a set of stats. Since our one-handed weapon attack assumed a +2 proficiency, 1d10 damage weapon, I’ve gone for the direct damage upgrade without feat investment: a +2 proficiency, 2d6 damage weapon. This would deal an extra 1.5 damage per [W].

The table below shows the increases in hit damage and average damage per attack from these options:

1 comment:

  1. When asking "how much damage is a basic attack worth" you really have to ask "under what context." A Warlord with Direct the Strike lets a Rangers make a basic attack, but since he presumably already triggered Hunter's Quarry the previous round, he doesn't actually add that +1/2/3d6 damage to his real DPR. However, compare a situation such as a Genasi Wizard paragon multiclassing as a sorcerer with Arcane Admixture-suddenly, you've got magic missile dealing Strength (your secondary stat with that builds) x2 for every basic attack, without the tiresome restriction of 1/round. That's sort of the severe case-an easier test case would be the Ruthless Punisher, wherein a ranger adds wisdom to damage not just once per round, but every hit.

    Ultimately, for factors that give allies additional attacks, you have the same issues at stake that tend to make Rangers overpowered in the first place. Except, you can't trigger a Monk's Flurry of Blows with Direct the Strike-well, not unless you make the loophole of readying an action for the monk's turn, and then giving him a melee basic attack (because he'll hit. And it's his turn. Ergo, he can trigger Flurry of Blows).