The basic premise behind the bounded accuracy system is simple: we make no assumptions on the DM’s side of the game that the player’s attack and spell accuracy, or their defenses, increase as a result of gaining levels. Instead, we represent the difference in characters of various levels primarily through their hit points, the amount of damage they deal, and the various new abilities they have gained. Characters can fight tougher monsters not because they can finally hit them, but because their damage is sufficient to take a significant chunk out of the monster’s hit points; likewise, the character can now stand up to a few hits from that monster without being killed easily, thanks to the character’s increased hit points. Furthermore, gaining levels grants the characters new capabilities, which go much farther toward making your character feel different than simple numerical increases.

This extends beyond simple attacks and damage. We also make the same assumptions about character ability modifiers and skill bonuses. Thus, our expected DCs do not scale automatically with level, and instead a DC is left to represent the fixed value of the difficulty of some task, not the difficulty of the task relative to level.

We think the bounded accuracy system is good for the game for a number of different reasons, including the following:

  • Getting better at something means actually getting better at something.

  • Nonspecialized characters can more easily participate in many scenes.

  • The DM’s monster roster expands, never contracts.

  • Bounded accuracy makes it easier to DM and easier to adjudicate improvised scenes.

  • It opens up new possibilities of encounter and adventure design.

  • It is easier for players and DMs to understand the relative strength and difficulty of things.

  • It’s good for verisimilitude.

Rodney Thompson, WotC Designer, June 4, 2012
Read the full article here

Bounded Accuracy 5e

DnD 5e was created with an essential design principle as the foundation of its math and mechanics: Bounded Accuracy.

What is Bounded Accuracy?

Bounded Accuracy is a system where the difference between attack bonuses, armor class, ability scores, and saving throws remains relatively constant throughout the game, regardless of character level.

Accuracy refers to your chance to hit something (or, more generally, succeed at a task). Bounded refers to the hard(ish) limits on how well you’re able to do at ANY task.

What are the bounds? The upper bound of DnD 5e’s difficulty is 30, and the lower bound is 0 (well, technically -3, but it essentially counts the same as a 0).

In what way is accuracy bounded? Without magic items or additional effects, the highest modifier a player can achieve is +11.

With a roll of 19 and a maxed-out modifier, a player can just barely do the hardest tasks in the game.

Let’s get into the details.

What Are 5e’s Bounds?

On the modifier side of things, players are limited in several ways:

  • Ability score/modifier. Under normal circumstanes, players are capped at 20 for ability scores, corresponding to a +5 modifier.

  • Proficiency bonus. Proficiency bonuses run from +2 to a maximum of +6.

  • Magic items. 5e’s magic items never exceed a +3 bonus (in AC, attack roll, damage, etc.) However, the game never assumes you have magic items for balance purposes.

On the difficulty side of things, the principle is much the same.

DC-or-AC Difficulty To Break Armor To Hit
5 Very Easy a glass bottle an inanimate object
10 Easy a wooden chair No Armor a badger
15 Medium a simple door Leather Armor* a troll
20 Hard a small chest Plate Armor** a dragon***
25 Very Hard a treasure chest a tarrasque
30 Nearly Impossible a masonry wall(1 ft. thick) a deity
*with shield and +2 Dex modifier
**with shield
***Adult Red Dragon is AC 19

Notice something? The highest possible die roll on a d20 is a 19, and the lowest is a 2 (assuming that a 20 is an auto-success and a 1 is an auto-failure).

So your range of rolls goes from -3 (assuming a -5 modifier and a d20 roll of 2) to 30 (assuming a +11 modifier and a d20 roll of 30). Those are, in a nutshell, the “bounds” of DnD’s d20 math, and the difficulty of all activities, from hitting a monster to persuading someone, fall somewhere in that range.

How Does Bounded Accuracy Affect Combat in 5e?

In combat, bounded accuracy ensures that, assuming no magic items, a player’s to-hit chance remains relatively even at 65%, across all tiers of play. More specifically, the player’s natural bonuses to hit (increased by Ability Score Improvements and Proficiency Bonus increases) scale at the exact same rate as the ACs of each tier of monster Challenge Rating.

Let’s look at a table (credit to RPG Bot) to see exactly how this plays out across levels:

Player Bonuses Monster
Level/CR Ability Mod. Prof. Bonus Total AC Hit %
1 +3 +2 +5 13 65%
2 +3 +2 +5 13 65%
3 +3 +2 +5 13 65%
4 +4 +2 +6 14 65%
5 +4 +3 +7 15 65%
6 +4 +3 +7 15 65%
7 +4 +3 +7 15 65%
8 +5 +3 +8 16 65%
9 +5 +4 +9 16 70%
10 +5 +4 +9 17 65%
11 +5 +4 +9 17 65%
12 +5 +4 +9 17 65%
13 +5 +5 +10 18 65%
14 +5 +5 +10 18 65%
15 +5 +5 +10 18 65%
16 +5 +5 +10 18 65%
17 +5 +6 +11 19 65%
18 +5 +6 +11 19 65%
19 +5 +6 +11 19 65%
20 +5 +6 +11 19 65%

Note that this assumes a player uses their Ability Score Improvements at levels 4 and 8 to increase their relevant ability attack modifier. Assuming the player started with 16 (+3 modifier), they’ll reach a +5 modifier by 8th level, when their ability score reaches 20.

Proficiency bonus increases 4 times, starting at +2 and increasing at levels 5 (+3), 9 (+4), 13 (+5), and 17 (+6).

Together, ability score improvements and proficiency bonus scale at exactly the same rate as the expected challenge rating of monsters at your tier. Barring level 9, which is an anomaly in the otherwise smooth math, when your assumed to-hit is 70%.

Why is Bounded Accuracy in 5e?

Bounded accuracy was born from earlier editions of the game, where numerical bonuses scaled linearly with character level. One major downside of this system was that players were limited to a narrow set of challenges that were “level appropriate” — anything higher was impossibly difficult, and anything lower was not challenging at all.

Additionally, the assumed increase in enemy power levels meant that players were on a “treadmill,” where increased power-ups didn’t actually make them feel more powerful; they just kept pace with whatever tier of play they were meant to be in for their level.

d&d 5e dice

What Does Bounded Accuracy Accomplish in 5e?

Many of these are me paraphrasing Rodney Thompson’s 2014 post on the subject, but I’ve included a few additional benefits of the system to the bottom of this list:

  • Increases value of increasing a modifier. Difficulty, armor classes, and monster accuracy don’t scale with level, so a +1 bonus is and remains impactful. For example, a +1 magic item puts you 5% ahead of the assumed 65% to-hit chance of the game’s math, regardless of what tier you get it.

  • Allows non-specialists to attempt things. Modifiers range from 0 to +11. On a hard task (DC 20), a novice (+0) still has a remote chance of succeeding (5%), a non-specialist (+5) has some chance of succeeding (30%), and a specialist (+10) will succeed most of the time (55%).

    This is in contrast to a system where DCs that scale with players leave non-specialists no chance of succeeding. For example, a DC 35 would be totally impossible for a character in such a system unless their character were specialized to deal with that challenge.

  • Monsters stay relevant. Because monsters’ to-hit and AC bonuses don’t have a huge variance, hordes of lower-leveled remain a threat to higher-leveled players. They’ll still hit sometimes (even if they don’t deal much damage), and players will still miss them sometimes.

    Conversely, lower-leveled players still have a chance to hit uber-powerful enemies, even if they won’t deal much damage. The design goal here is interesting, as it “opens up new possibilities of encounter and adventure design,” where repelling a dragon with dozens of town guards becomes a legitimate strategy, rather than pointless folly.

  • Easier for DMs to improvise. If you’re a DM, you don’t have to remember a whole table of scaling DCs and ACs to make sure your encounters are level appropriate. No matter the level, if the task is supposed to be hard, it’s got a 20 DC; if it’s meant to be medium, 15.

    Conversely, players can have a more intuitive understanding of their world based on DM descriptions rather than mechanical expectations — plate-wearers have 18 DC, so they’re hard to hit, always.

    On top of this, DMs don’t need to feel pressured to create ever-increasing stakes for their players just because they level up. If they want to bring a hobgoblin-based campaign past level 10, they can do that — no need to send every adventure to the Nine Hells just to keep things interesting.

  • Realism. DCs being fixed values rather than needing to scale with player power levels makes the world feel more real. A pack of goblins is never a joke that has zero chance of hitting your high-level character. Get swarmed, and you’ll die like any other mook.

    On the ability check side of things, you don’t have to create this weird narrative thing where, for some reason, doors keep getting sturdier the higher the party’s level, or other nonsense like that.

  • Ability-focused, rather than numbers-focused. Bounded accuracy places a greater emphasis on characters feeling unique because of the capabilities and features they have, instead of flat numerical bonuses. The aim here is to lean into roleplaying, rather than number-crunching, as a way of expressing ever-increasing power levels.

    You never have to worry about keeping up with the assume power level of your tier — by just playing your character and making normal, intuitive choices, you’ll keep pace with the game’s difficulty.

  • Makes advantage a big deal. Having advantage on a roll — rolling 2d20 and picking the highest — is a big deal in a system of bounded accuracy. It works out to between a +4 and +5 average result, which is a major swing. Advantage is also usually short-term or situation specific, so it encourages players to look for tactical ways to gain the upper hand rather than relying on a huge and consistent modifier.

  • Get everyone off “the treadmill.” This was a pejorative term for 3rd and 4th edition’s system, whereby players HAD to get certain numerical bonuses at certain levels if they wanted to, well, actually progress in the game. DMs were forced to shoehorn in appropriate magic items to make sure the next tier of play wasn’t too challenging, rather than simply relying on players’ natural level-ups and attendant features do that work for them. (Disclaimer: I’ve never actually played these additions, so this is hearsay on my part).

    In other words, there’s no pressure on players to “keep pace” with certain numbers or else become useless. That’s more beginner-friendly, and more roleplay friendly.

    This design choice is also a big reason why 5e assumes that players have no magic items at all — much simpler to balance the game that way. And why magic item bonuses are usually small (but still significant), and why attunement exists as a limiting factor.

  • Makes die-rolling more impactful. In previous editions, a modifier could easily be over 20. Meaning your d20 die roll literally meant less than the number on your character sheet. With a +11 max modifier (under normal conditions), the result of a d20 almost always matters (barring some game-breakers, discussed below).

Common Complaints About Bounded Accuracy in 5e

While bounded accuracy did fix many issues with earlier editions, it’s not without flaws. Here are some of the most common things that players and DMs complain about with regard to bounded accuracy:

  • Your character doesn’t get stronger in a satisfying way. Without proficiency in a skill or saving throw, your character is basically the same at 1st-level as they are at 20th. Similarly, your AC doesn’t really change much, barring magic armor.

    For example, a 4th-level Fighter in plate armor is rocking 18 AC. A 20th-level Fighter? Also 18 AC. At 4th level, enemies have maybe a +6 to hit; at 20th-level, +15. That’s a massive +9 progression, while your character’s AC stayed the same. You’re pretty much guaranteed to get hit more often the more challenging monsters you face, and there’s not much you can really do about it, build-wise.

    As a counterpoint, defenders of bounded accuracy will say that higher hit point pools means that it doesn’t matter if the 18 AC fighter can just as easily be hit by a goblin at 20th-level as they can at 4th-level; they barely feel the damage anyway.

  • Saving throws don’t follow bounded accuracy, which breaks the system as a whole. Enemy spell and ability save DCs scale as they become more challenging, but your chance to shake them off, barring proficiency in the appropriate ability, becomes worse. Take a DC 19 Wisdom shut-down effect like an Ancient Dragon’s Frightful Presence. If Wisdom is a dump stat for you (and it is for most melee characters), you don’t really have tools to cope with that.

    Bounded accuracy assumes that players “to-hit” increases at the same rate as enemies defenses. But in failing to scale player defenses with ever-increasing spell save DCs, this assumption falls apart.

  • Experts can get shown up by mooks. For example, take a hard skill check to break a door down, with a DC of 20. Your maxed-out Barbarian with a +11 Athletics modifier succeeds on a 9 or higher — 60% of the time. That random NPC you brought along with a +1 modifier? They have a 10% chance of success.

    In other words, a complete door-smashing novice has a 4% chance of doing better than a near-superhuman warrior. 4% may not be likely, but it’s still too likely for some people’s tastes.

  • Running swarms of relative mooks is boring for everyone. While bonded accuracy allows for a DM to keep using goblins, if they want, as players reach higher levels, they’re not a threat unless their numbers are enormous. Fights are usually best (read, most efficient and pleasurable) when they’re over in five rounds or fewer.

    Fighting wave after wave of non-threatening enemies is not most players” (or DMs) idea of a good time, meaning that low-level monsters DO get phased out as players level, regardless of whether they’re still technically viable.

Things That Break Bounded Accuracy in 5e

While Bounded Accuracy is a core design principle of 5e, there are several ways to break the +30 upper bound of the system. Here are a few ways to break Bounded Accuracy in DnD 5e:

  1. Expertise. Expertise is a feature available to Bards, Rogues, and anyone with the Skill Expert feat that doubles the proficiency bonus you add to skills you’re proficient in. This brings the maximum proficiency modifier to +12, which, with a +5 ability score modifier, translates into +17 on a roll. With a +17 bonus, your character exceeds at nearly impossible tasks (DC 30) 40% of the time.

    Most people don’t mind this, as broken skill checks aren’t usually as game-breaking as broken attack modifiers or AC. Plus, if a player commits that much to being an expert at something, they probably should be that good at it.

  2. Magic Items. Since 5e’s difficulty curve was designed under the assumption that players have no magic items, they don’t factor into the essential math of the game. Regardless of what tier a player gets a +1 weapon, they’re essentially 5% ahead of the curve (70% chance to-hit). The same principle applies to +2 and +3 weapons and magic armor.

  3. Stacking bonuses. This goes for attack rolls (Bardic Inspiration, Bless, Flash of Genius, etc.), ability checks (Bardic Inspiration, Flash of Genius, Guidance, etc.), and saving throws (Bardic Inspiration, Bless, Flash of Genius, Aura of Protection).

    For real examples, consider a Paladin/Peace Cleric. With Bless, Emboldening Bond, and Aura of Protection, they’d have a 2d4 + 5 bonus to all saving throws — +10 on average, before taking their normal modifiers into account.

  4. Pass Without Trace. A flat +10 Stealth modifier for the whole party, basically ensuring success for any character who is even partially optimized for sneaking.

Want an extreme example of breaking Bounded Accuracy? Be a 17th-level+ Artificer:

  • Dexterity modifier. +5.

  • Infuse Gloves of Thievery. +5 bonus to Sleight of Hand checks and Dex checks to pick locks.

  • Use Flash of Genius. +5 bonus to the roll (based on your Intelligence modifier).

  • Tool Expertise (passive). +12 bonus to the roll (double proficiency).

  • Cast Guidance. +1d4.

  • Have Stone of Good Luck. +1 on ability checks and saves.

  • Have Ioun Stone of Mastery. +2 (normally +1 proficiency bonus, but +2 with Expertise).

Congrats, you now have +31 to +34 bonus on your skill check. Any lock in the world that is nearly impossible to crack, you can break with a roll of 2 or higher (95% success rate).

Your maximum roll result is 54.

Plenty more things break Bounded Accuracy in some way or another — the above are just a few examples.