Tag Archives: power curve

Bounded accuracy and matters of taste

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(This post continues a discussion I started in “What does D&D have to do with ironclad ships?”)

In my last post, I wrote about how to-hit and damage bonuses contributed to Dungeons & Dragons’ power curve. When we compare D&D Next to early editions of D&D, we see a key trade off: The Next design reins in the to-hit bonuses characters gain as they advance. In compensation, characters gain greater bonuses to the damage they inflict. This trade off stems from something the designers called bounded accuracy, which spurred controversy. While most of the discussion focuses on bounded accuracy’s place in combat, in “Two problems that provoked bounded accuracy,” I wrote about bounded accuracy and ability checks.

Months ago, I wrote to explain that the influence of ability bonuses was too small for ability checks, so you might suppose I would like to see characters earning big to-hit pluses as they advance levels. But characters engage in many combats and make countless attack rolls, so even small bonuses earn big payoffs, and I’m fine with that. However, I understand that aspects of the bounded-accuracy controversy hinge on matters of taste.

In fourth edition, as characters leveled, they enjoyed steep increases in to-hit bonuses matched with continuing increases in the damage each attack dealt. This led to characters increasing exponentially in power. If you hit twice as often, and each hit does twice the damage, than you boast four times the power. Of course, monsters follow a similar power curve, so you never notice unless characters face creatures outside their narrow level band.

In character, your logarithmic increase in power feels exciting as unbeatable monsters and impossible challenges quickly become possible, and then easy.

Repainted town guardIf you want to keep suspension of disbelief, do not dare to consider the world-building implications of the 4E power curve. I checked the stats for a town guard in a heroic-tier Living Forgotten Realms adventure. As scaled for party level 10, this rank-and-file guard has AC 26 and 106 hit points. Where were these super guards a few adventures ago when the goblins attacked the town? The goblins could only hit AC26 on a 20, so they would have needed to make an average of 262 attacks on each guard to earn a kill. Of course, you can suppose that in your world, you have no super guards, but what happens when you reverse the roles, and a lone giant shows up to defeat an army?  Obviously, many players never consider this balance of power, so the game hums along. Those of us who cannot help thinking of such things find it all distasteful.

What if there are no super guards? Nowadays, the D&D rules specifically limit players to non-evil characters. In the early days, no such limitation existed. D&D focused more on killing things for selfish gains than on heroically driving back the darkness. I remember players musing that it made little sense to loot the dungeon when easy pickings lay in town. What happens when a player decides to “role play” his evil character by singlehandedly massacring and looting a town full of level-0 folk? Fortunately, my players always honored the social contract and returned to the dungeon.

Beyond the exponential power curve, players have other preferences. How high a level do you need to be before you should be allowed to hit Asmodeus on a 19? (Keep in mind, since first edition, a roll of 20 always hits.) How much of a bonus should attributes provide as compared to your per-level bonuses? I don’t think I can sway you on these matters any more than I can coax you into a new favorite ice cream flavor.

Next: D&D Next trades to-hit bonuses for enhanced damage

Riding the power curve through D&D’s editions

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(This post continues a discussion I started in “What does D&D have to do with ironclad ships?”)

Signed Greyhawk CoverIn the very first set of Dungeons & Dragons (1974) rules, every weapon dealt 1d6 damage. Short of magic, characters could only improve their damage output by improving their bonus to hit. More hits equals more damage. Soon, Supplement I: Greyhawk (1975) gave different weapons different damage dice and introduced the strength bonus to damage. Since then, each edition seems to give characters more ways to hit for more damage.

By the fourth edition, as characters leveled, they enjoyed steep increases in to-hit bonuses matched with unprecedented increases in the damage each attack dealt. This contributed to characters increasing exponentially in power. It explains why 4E monsters only remain effective for narrow bands of levels, and it explains the nervous ticks of every DM who has run an epic table. In past editions, only the wizard saw that kind of power curve, and the non-wizards eventually grew tired of serving as wand caddies for the Wiz.

D&D Next aims to create a power curve in line with earlier editions, while preventing the runaway power traditional for wizards. If you prefer the exponential power curve created in 4E, then you might have to look for a legendary hero module in Next, or stick with 4E and bless any dungeon master eager to run a high-level game.

Greyhawk also introduced Weapon Armor Class Adjustment, a chart that granted bonuses to hit based how well your particular weapon worked against a style of armor. The table only makes sense because, in the original game, armor class really represented a particular style of armor, such as leather or chainmail. Obviously, dexterity and magical bonuses to armor class quickly turned the table into nonsense. (If you want to make sense of the table, you must apply the dexterity and magical modifiers as penalties to the attack roll.) In practice, no one used the table and the “class” in armor class lost significance.

While D&D Next thankfully steers clear of weapon armor class adjustment, the system returns to the older practice of making armor class a measure of actual armor, or at least something equivalent.

The D&D Next approach brings back a problem that has bedeviled every edition of the game except fourth. In D&D, to-hit bonuses rise automatically, level after level, while armor class remains roughly the same. Sure, as characters acquire better equipment, armor class improves a little, and in most D&D editions AC starts a little ahead. But characters gain to-hit bonuses automatically, and eventually, inevitably, to-hit bonuses outrun armor class. Everyone begins to hit all the time. As I explained in “Hitting the to-hit sweet spot,” D&D works best when combatants hit between 30% and 70% of the time.

Fourth edition fixes the problem by granting everyone automatic increases to AC to match their automatic increases in to-hit bonuses. Now armor class becomes a function of a character or monster’s role and its level. Any reasonably optimal character would boast the same AC as peers in the same role. Armor exists as the flavorful means that some characters used to reach the armor class dictated by their role. This kept armor classes on par with bonuses to hit, while making monster design simple.

armorD&D Next attacks the old problem from the opposite direction. Instead of matching automatic increase with automatic increase, D&D next limits to-hit bonuses so they never overwhelm the relatively static range of armor classes.

In 4E, in defense as in offense, characters increase exponentially in power. The fixed AC bonuses that 4E granted with each level combined with rising hit points to grant everyone steady increases to two forms of defense. You automatically get harder to hit even as the hits do less effective damage. If you’re twice as hard hit and you can sustain twice the damage, your defenses are four times better.

D&D next attempts to straighten out the logarithmic power curve by refusing to let characters double-dip. Rather than gaining steep bonuses to hit along with increases to damage, you just get increases to damage. Rather than gaining constant improvements to armor class along with additional hit points, you just gain addition hit points. Of course, I’m simplifying to make a point. Characters still gain bonuses to hit as they advance, but they gain at a fraction of the rate seen in third and fourth edition.

When we compare D&D Next to early editions of D&D, the design reins in the to-hit bonuses characters gain as they advance. In compensation, characters gain greater bonuses to the damage they inflict. Like any design decision, this strategy makes some trade offs, which I will explore in an upcoming post.

Next: Bounded accuracy and matters of taste