Wednesday, January 25, 2012

"To Hit" vs. Armor Class

Enough theory! How do attack bonuses really compare in use?

In 4th Edition, that's easy to answer. Monster defenses scale smoothly by +1 per level. Character attacks scale by approximately +1 per level, though not as smoothly as monster defenses. Still, the relationship is tight and balanced.

In AD&D, the relationship is complex. Character attacks (for fighters) scale at approximately +1 per level or a fraction more. But monster defenses are all over the board. Here's a plot of AC for all monsters from the AD&D Monster Manual that have 20 or fewer hit dice.

Scatter Plot of AD&D Monster AC by Hit Dice
The first thing you'll notice is that it's a scatter plot. AD&D has no smooth correspondence between a monster's hit dice (level) and it's armor class. The line is the closest approximation Excel can draw to this mess of data points.

What's important about the plot is the slope of the approximated line when compared to the slope of the attack bonuses. At 1 hit die, the average monster AC is between 6 and 7. At 20 hit dice, the average monster AC is 0. That's a spread of only 7 points. Yet the AD&D fighter's* attack bonus increases by 20 or more points between level 1 and 20. That's a huge discrepancy.

AD&D Fighter Attack Bonuses
* (By comparison, the cleric's attack bonus increased by 11-15, the thief's by 10-14, and the magic-user's by 9-13. The range depends on how much of a bonus the character gets from a magic weapon, which could vary from 0 to +4. I assume any +5 weapon was given to the fighter.)

So in AD&D, as characters advance up the level scale, they constantly gain ground against the monsters' defenses. A 15th-level fighter doesn't just hit lower-level monsters more often; he hits all monsters, even those of his own level, more reliably than before.

Before anyone gets too excited, I need to point out another big facet of AD&D: the damage that characters do with their weapons doesn't scale at all across levels, aside from magical bonuses. Heroes' attacks need to get more accurate because hitting more often is the main way the characters do more damage to the monsters, whose hit points increase in direct proportion to their hit dice. 

The last conclusion I want anyone to draw from this analysis is that edition Y got it right and edition Z got it wrong. My goal is to establish some facts so we can talk about these subjects from a factual basis instead of from the vague and emotional impressions we form during the heat of play and across the haze of years. Early editions of D&D handled math very differently from later editions. I'm not about to pick a winner--not yet, anyway. That's a subject for Friday.



  1. Thanks for this!! It's all needed work!

  2. I'm curious, why does it matter "To Hit" versus AC? Or even why AC related to HD?

    I would expect some critters to be more adept at combat (ogres) and some would have better defenses (giant turtle). I don't see the corollary between AC and To Hit or HD and AC. Because of one they should have the other?

    1. It goes directly to the game's balance, which is a hot-button issue if there's ever been one. (Getting D&D players to even agree on what "balance" is would be a step forward.) Some of this analysis was done just to satisfy my curiosity--I like numbers--but the results have implications that intrude all over D&D.

  3. Hey Steve, long time no talk! I hope you are doing well!

    This phrase is troubling:
    "Heroes' attacks need …"

    AD&D has almost no built-in expectation that PCs ought to (be able to) succeed in any given endeavor, nor does it necessarily expect success to come through fair fighting. Assuming you're interested in level advancement, the real goal is the gold, not the kill. Why fight if you can get the gold some other way? And even if you're not interested in level advancement, the risk of loss from fighting is so comparatively large, that the PCs are encouraged to stage unfair fights whenever they think fighting might be necessary to achieve their goals. And simply run away from potentially-deadly fights that happen unexpectedly. Or find a way to measure-up the potential opposition, then choose fights carefully.

    There's also the fact that AD&D promotes antiheroic behavior just as much, if not more than, heroic behavior.

    By framing the analysis around what PCs "need" to be able to achieve in combat, you're sort of missing the AD&D forest for the trees. Sure, AD&D's "to hit" system might happen to be a best fit for some other rpg that has different sensibilities. But AD&D's "to hit" tables actually play a comparatively minor role in determining whether PCs can be successful in AD&D combat. Or successful in their overall goal.

    (All of the above is from the 1e perspective.)

    (And I also agree with what Celestian said above. Overthinking some of these mechanics feels distasteful to me. I like to design in a naturalistic way.)

  4. While driving home from work, a more concise explanation percolated up:

    The reason AD&D's "to hit" system slopes upward isn't in order to counteract the upward hit point slope. The primary reason is so the champion lands more telling blows against the dragon than the warrior lands. (Using level titles for a more pleasant sounding point.)

    That AD&D's "to hit" slope happens to fractionally counteract the hit point slope is a pleasant side-effect. But by no means must both slopes necessarily be present in the face of the other. It's all about genre approximation. The swords & sorcery genre benefits from having both slopes. (An essay in itself.) But the wild west genre - the quick and the dead - wants the "to hit" slope without a hit point slope. And the Rocky film genre probably wants the reverse. (Taking some liberties with genre distinctions here, but hopefully the point is clear.)

    It gets weird when D&D design becomes self-referential. The first wave of D&D combat system design was emulating certain aspects of swords & sorcery combat, thus producing a set of mechanics. Those mechanics had certain emergent properties. Some later waves of design tried to emulate the emergent properties, and it makes the result feel "engineered" (for lack of a better word), and not in a good way.

    Without a clear idea of the genre-to-be-emulated, it feels odd to be studying the hit ratios in order to find the "winning" one. It's almost like we're looking for a mechanic based on its own aesthetic, instead of based on how well it achieves a particular naturalistic result.

    1. Guy; Great to hear from you again! Thanks for dropping in and for offering that thought-provoking reply.

      I don't disagree with your viewpoint at all. I do, however, submit that it's risky to assume Gary Gygax wasn't thinking in terms of statistics, probability, and damage-per-round when he drew up the AD&D combat tables. Gygax was one of the most successful and prolific hobby game designers around in the mid-70s. He certainly was on board with the idea that characters should face problems they couldn't hack their way through; it's a common scene from the S&S fiction he devoured. As a wargame designer, he also appreciated the drama of a desperate dice battle against overwhelming odds. I'm certain that he deliberately set up the game's math in a way that both enables and encourages players to sometimes deal with powerful monsters in a brute-force way. In this regard, playing OD&D with the Chainmail melee rules instead of the Alternate Combat System that became the basis for AD&D is illuminating.

      "It gets weird when D&D design becomes self-referential." I agree completely ... but I still enjoy doing it. There are times when I feel like a French movie critic analyzing an American reviewer's deconstruction of a German director's remake of an obscure Italian film based on a Russian poem. Still, it beats giving the dog a bath.

  5. Interesting!

    But that penultimate paragraph is the important one. “To hit” and AC are nearly distractions. What really matters is hp and damage.

    (If you’re just analyzing the combat system. I’d agree with Guy that fighting straight-up “fair” fights is as foolish in the game as in real-life. But it seems that’s a bigger discussion that what Steve is doing in this series of far.)

    And that’s why people get into trouble when trying to modify the system by thinking about “to hit”, AC, and damage separately and too literally. Like it or not, D&D combat has always been too abstract for that sort of reasoning about it to work.

  6. Certainly you can never look at any sequence of numbers in isolation. None of the analysis I've offered in this blog goes deep enough to show fully how the math works across multiple editions of D&D. All of this is leading up to something--but I confess that even I haven't yet followed it all the way to a settlement. I know where I expect it to land, but I've been surprised by my own conclusions often enough to appreciate the danger of pride.

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

    I certainly prefer the more orderly progression of the later levels, but that might just be a personality thing. Back in the day when we played AD&D, we'd pretty much never go beyond the sweet-spot of level 3-7 in that edition. That range seemed to be where the game's rules worked best; characters weren't too squishy and magic users weren't too powerful.