A Walk in the Dark A look in to the mind of an RPG designer



4th Edition Attack Math

NOTE #1: Steve Winter has already addressed most of this on his blog, Howling Tower... With charts, no less! Since I couldn't get it out of my mind today, I'm writing this anyway. 🙂

NOTE #2: I have not checked *all* the math, and I'm sure many of you out there who do this kind of thing in your sleep will correct me. I'm bracing myself for criticism, so have at it.

Today was the first day of DDXP, where everyone except me some very special people had the opportunity to be exposed to the first round of playtesting Dungeons and Dragons 5th Edition. Needless to say, because of the all-powerful Non-Disclosure Agreement they all had to sign in blood, there isn't a whole lot of information coming from them.

But the first D&D 5th Edition seminar hosted by Monte and Mike wasn't under such threat of legal violence, and many that were in attendance were able to relay some of the questions we were allowed to ask (it seems like *all* the questions I wanted to ask were classified as "off limits" before the seminar even started) and live tweet the responses.

For now it's all one big gray area and there's a lot of speculation as to how this modular system of play is going to work. I have my questions and I have my doubts, but I'm not one to speculate on a whim and try to guess what they have in mind. And I certainly am not one to impose on to them what I think their game should be like.

But one concept stuck in my mind: during the discussion, they brought up something which I am calling "level-less monsters". Basically, they seemed to hint at having monsters that were not level-specific, and could be a threat at any level. An orc is always an orc, and you better be damn well concerned about said orc regardless of whether you were level 1 or level 10.

I got to thinking about how they would be able to do such a thing... And on the way home I realized it: they kind of already did. It's just wrapped amongst so many rules and technical details that you just don't realize it.

So I created the following tables in Excel to see for myself. These tables detail what a player's ability to attack is relative to a monster of similar level. I also decided to do the math in reverse, calculating what it takes for a monster to hit (on average).

The results are somewhat surprising... or perhaps not.

D&D 4th Edition Attack Analysis (PDF)

The first two tables in the attached PDF define the attack bonuses and defenses when a player attacks a monster, analyzing attacks vs AC and vs non-AC defenses.

The above tables makes the following assumptions:

  • Attacks being made against a monster's AC use a weapon with which the wielder is proficient. To maintain consistency, I'm assuming the +3 proficiency of your average longsword.
  • The attacker starts with an 18 as their attack attribute (Strength for fighters, Dexterity for rogues, etc...).
  • The attacker is human and that the +2 racial bonus will be applied to the attack attribute.
  • Every other time they get to manually increase their attributes - at levels 4, 14 and 24 - they manually increase their attack attribute one point. I assume every other time just to keep the attributes even; if a player wants to pile all 6 in to the attribute, they'll gain an additional  +1 or +2 by the time they're epic.
  • The table does not take in to consideration any increases due to epic destinies. For example, a fighter that becomes an Eternal Defender gets +2 to Strength at level 21. Adjustments of that nature are not factored in because they could be considered optimizations; I'm trying to be as close to average as possible.
  • I'm assuming inherent bonuses (Dungeon Master's Guide 2, page 138). Magic item math is hard enough as it is.
  • I'm assuming the attacker takes an Essentials-style weapon/implement expertise feat at level 1, which gives them a +1 at level 1, +2 at level 11 and +3 at level 21.

The table for attacking a monster's non-AC defense is similar but the weapon proficiency column is removed and the monster's defense is adjusted (level +13).

For the next two tables, I decided to look at it from the monster's point of view... What does it take for a monster to hit a PC?

The AC table makes the following assumptions:

  • The attribute that determines AC will be based on an initial value of 14. This may be considerably higher for some classes, but I'm using the typical value for a fighter. As the player levels, the attribute is increased in the same manner as above.
  • Assuming the three types of chainmail armor listed in the PHB, the enhanced ones being chosen as soon as the inherent bonus matches the armor requirement: basic chainmail (+6 to AC), Forgemail (+9 to AC, minimum +4 enhancement required) and Spiritmail (+12 to AC, minimum +6 enhancement required).

For the monster vs. player non-AC tables, I assume:

  • Defense attribute is based on 14, as above.
  • The player is human, so I factor in the +1 racial bonus to all non-AC defenses.
  • The player takes the Essentials feat Improved Defenses at level 1, which gives him a +1 defense bonus per tier.

Even though I'm sure to be missing a lot of possible bonuses (things get really cloudy in epic tier, I imagine), the results were quite enlightening.

  • Average die roll required for Player vs Monster's AC defense: 8.7
  • Average die roll required for Player vs Monster's non-AC defense: 9.7
  • Average die roll required for Monster vs Player's AC defense: 8.1
  • Average die roll required for Monster vs Player's non-AC defense: 8.3

In the epic tier things get complicated; by the numbers, players need a higher number to hit and monsters can hit much more easily (especially non-AC defenses). But I assume epic characters have a whole slew of powers, feats and god-knows-what that adjust these values a lot. Things like combat advantage, concealment, cover, etc. probably happen much more often in epic tier, but they are not considered here.

So, looking at the data... Wouldn't this be much more simple when the DM is told "it takes a 9 or higher to hit", regardless of the monster's level? One could argue that this is THAC0 - the math does work out in a similar fashion - but it's here, in D&D 4E, masked behind a barrage of modifiers.

Another potential advantage of using something of this nature is hit points do not need to vary so dramatically and require adjustments to the damage rolls. A longsword always does 1d8 damage and an orc always has 30 hit points; it doesn't matter if it's level 1 or level 20. The "toughness" of a monster isn't compared to a party of equal level since that party is also tough; two heavyweight champions fighting each other are as evenly matched as two amateurs fighting. It's all relative regardless.

Let the record show that I have no idea if a similar method is being considered for D&D 5E, or if the above has any bearing on anything. I just felt the need to do all the math to see things for myself. And, now that I know how things end up, I'm tempted to not even look at the defense scores or attempt to do the attack bonus math myself... whether you're bashing a decrepit skeleton's skull or raining hellfire in the middle of the Elemental Chaos, I'll just look for the "9 or higher" and be done with it. If you're nice, maybe I'll even accept an 8...

Filed under: 4e, 5E, DnD, Mechanics, RPG Comments Off
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  1. I’ve been thinking about this too and, at a glance, your numbers seem to fall in line with what I’ve seen in the D&D Adventure games such as Wrath of Ashardalon.

    What I hope to see is a shift where levels are de-emphasized as a measure of player achievement to become a tool for DMs to use when comparing monsters to PCs. If PC levels persist (as I expect them to), a monster’s attack could be expressed as 1/2 target’s level +X, where X is determined by the monster’s role and perhaps the tier of play.

  2. The ‘red queen’ effect is only as good as it’s positive effect on the game, and preserving it hidden behind all those values strikes me as a bit pointles these days. Imagine a game where you hit anything on a 10, with around 1-5 points of sicuational attack bonus from combat, positioning, ect.

    Such a game could put more emphasis on the really fun bits of combats- powers, maneuvers, and even more system support for various non-combat goals in combat (like picking a lock in mid battle, for instance).

  3. This is very cool to see. I’ve been simplifying my 4e experience as far as it’ll go toward influences of lighter more narrativist games. I’ve done away with tracking monster HPs (using Haze’s hitbox idea that basically introduces level-less monsters with regard to HP: http://atminn.wordpress.com/2011/07/08/games-without-hit-points-damage-without-math-part-1/)

    Plus I’ve been using Mike Shea’s Master DM Cheat Sheet to run most of the game without needing statblocks.

    Now you’ve got me musing how to cut it down even further on the attack roll side of things. I know the players still like to have variable defenses, from each other and from the other types of defenses, but I think they’d be open to shifting to a flat attack bonus system like you’re describing here.

    Heck, the way catastrophe puts it, it sounds like they could even use a d6 instead with 4-6 being hits, or something like in Apocalypse World, where it’s success, success with fallout, or just fallout. That or, the 1-5 points of situational bonus/penalty could make use of fudge dice or d6-d6 systems.

  4. To clarify a point: are you saying 18 from point buy, or 18 after modifier? (I interpret what you wrote to mean the former, in which case I think all your die rolls for players should go up 1 point, but wanted to check.)

  5. Nicely done. WotC R&D has all of this expressed as equations, of course. Those aren’t shared with the public, but they’re pretty readily deduced with this type of analysis.


  6. I had a look at this in an analysis that I did of the attack bonus progression in the various editions of D&D.


    The problem with a system that always allows a 50% chance of a hit is that you have the same chance of hitting a dragon as you have of hitting a kobold. And your Mage has the same chance of hitting as your Fighter.

    One way of addressing this is to include a relative level modifier, which would adjust that target number by the difference between the attacker and the defender’s level. This is pretty much what all of the attack modifier progression is ultimately achieving, but with a lot more factors.

    Again though, this doesn’t take into account any differences between a dragon trying to hit a Fighter or a Mage of the same level (you’d assume the Mage would be squishier because he can’t wear armor), which doesn’t make a lot of sense.

    Ultimately, the whole system is finely tuned, and unless people are willing to forgo all sorts of underlying sub-systems (armor, proficiencies, feats, etc), then it’s not practical to simplify the system.