This is my attempt to explain the term “bounded accuracy”.
Bounded accuracy is the term that WotC uses to represent a role playing game design concept. It is not a “rule” and you won’t find it in the Player’s Handbook, but it is the foundational design philosophy behind the core of 5 Edition D&D.
The “accuracy” part of the term refers to how hard it is to do something. For combat, this relates directly to armor class and bonuses to your attack roll.
The “bounded” part of the term refers to establishing upper limits.
What are the limits?
There is a maximum Ability Score of 20, a maximum Difficulty Class of 30, and a maximum Armor Class of 30. There is a maximum Ability bonus of +5 and a maximum Proficiency Bonus of +6 making a maximum total bonus of +11 (resulting in a maximum score of 30 on a roll of 19.)
Also, there is typically no more than +1 on magic items, with +3 being the cap and representing things of artifact power. The game makes no assumption that you have magical enhancement bonuses on your weapons and armor.
This is all about the Core Mechanic: To resolve an action roll a 20-sided die and add modifiers. If the result is greater than or equal to a target number then the action succeeds.
Regardless if this target number is a Difficulty Class (DC) or an Armor Class (AC), the concept is 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 |
To explain the effects of bounded accuracy on the game, it can be illustrative to compare its effect on three different characters.
Let’s start with a typical commoner. We’ll call him Fred. Fred is average in every respect. All of his ability scores are average (10) and Fred has no proficiencies or special skills. The table above was designed with Fred in mind. If any task is hard for Fred, it has a DC of 20. Fred adds no modifiers to his d20 roll when he attempts a task.
Our second character is Norman. Norman is a first level Fighter. The highest modifier Norman could add to his d20 roll would be about +5 (Ability +3, Proficiency +2).
Our third character is Conan. Conan is a 20th level Fighter. The highest modifier Conan could add to his d20 roll would be about +11 (Ability +5, Proficiency +6).
All three characters attempt to do something “hard”. They all need a 20. Fred rolls a 20 and succeeds. Norman’s roll is only 15, but with his +5 modifier he also succeeds. Conan only rolls a 9, but with his +11 modifier, he succeeds. So this “hard” thing is hard for Fred, not so hard for Norman and it is easy for Conan. Being normal PCs, Norman and Conan are better at some things than they are at others. They do not have maximum ability scores in all of their abilities, and they are not proficient at everything. At some tasks, they may not have a better chance of success than Fred does. Conversely, not all Non-Player Characters (NPCs) are as “average” as Fred. At some tasks, a NPC may have an ability score that is higher than a PC and a larger proficiency bonus. So most tasks within reach of specialist also fall within the ability of a lucky novice.
Higher level characters and tougher monsters are that way because they can do more damage, more often, in more ways than lower level characters.
If you are new to D&D, this may all seem obvious, and hardly worth more than a passing glance. However, this is a break from some earlier versions of the game. In some earlier versions, your PC’s “to hit” bonuses and Armor Class increased with each level and thus forced monster attacks/defenses to also increase with level. This resulted in lower level creatures being unable to have any possibility of hitting higher level PCs and visa-versa. This was done in the very reasonable goal of allowing higher level PCs to combat tougher monsters. D&D 5e accomplishes this goal, not by making tougher monsters harder to hit but by making them harder to defeat by giving them more hit points. So as PCs increase in level they do improve in their ability to hit higher armor classes (although at a much slower rate) but their ability to defeat tougher opponents comes mainly from their increased ability to inflict more damage when they do hit, and their increased capacity to survive stronger attacks due to their own increased number of hit points. So in this edition, characters can meaningfully interact with the same threats for most of their career, if they so choose. Lower level monsters will still be a threat at higher levels if they are encountered in larger numbers.
This was described by Rodney Thompson in Legends & Lore (June 4th, 2012) on the Wizards of the Coast website. This is no longer available on their web site, so I quote from it here:
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.
Now, note that I said that we make no assumptions on the DM’s side of the game about increased accuracy and defenses. This does not mean that the players do not gain bonuses to accuracy and defenses. It does mean, however, that we do not need to make sure that characters advance on a set schedule, and we can let each class advance at its own appropriate pace. Thus, wizards don’t have to gain a +10 bonus to weapon attack rolls just for reaching a higher level in order to keep participating; if wizards never gain an accuracy bonus, they can still contribute just fine to the ongoing play experience.
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.
The link is back up on the Wizard’s site if you want to read Rodney Thompson’s comments in their entirety : Legends & Lore Archive | 6/4/2012
Dungeon Master Assistance 
Could you please correct the statement “maximum Ability bonus of +4″ to +5, in ” What are the limits?” section?
Otherwise, I found this article clarifying some ideas of 5th edition 🙂
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Thank you for your comment. I am glad that you found this useful.
I made the change you suggested. Thanks.
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Actually, ability scores can go up to +7, and proficiency can go up to +12 for bards, clerics, and rogues.
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Good catch on the proficiency bonus maximums, but what am I missing on ability score modifiers? A +7 would require an ability score of 24 and, as far as I can see, all ability scores are capped at 20. Perhaps you are referring to monsters? I should have made it clear that I was talking only about Player Characters.
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Barbarian at level 20 gets +4 to Str and Con. This can break the cap of 20.
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I commented on the original post by accident, but I asked if the writer ever clarified what he meant by being able to have a +7 ability score modifier. Also, how can bards/clerics/rogues get their proficiency up to +12???
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Expertise doubles the proficiency bonus
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Was this ever clarified? How can clerics get up to +12 Proficiency? And how can ability scores go up to +7 without magical items?
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Clerics with the knowledge domain, proficiency bonus is doubled for any ability check on Arcana, History, Nature, or Religion skills. There are other examples of proficiency bonus doubling. At 17th level, the Cleric’s proficiency bonus is +6. Double +6 = +12.
The only way to increase your ability scores above 20 without using magic is to be a level 20 Barbarian. At level 20, the Barbarian gets a feature that increases their Strength and Constitution by 4 and raises the cap on Strength and Constitution to 24 instead of 20. This gives them a +7 on those ability modifiers.
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Just a bit of info. I know its an older post. The DMG includes information on page 230 chapter 7 regarding Alternatives to Epic boons which allows ability scores to increase to 30. Magic items and artifacts also can increase this beyond 20. Page 209 also lists the Tome of Understanding (and similar tomes) which increases an ability score and raises the maximum by 2.
As for modifiers from ability scores the PHB shows them at +10 for a score of 30 in the character creation section on page 13.
Not certain you needed this but I felt a few citations would help. Though I might be missing the mark if this post only pertained to the “Bound Accuracy” information.
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5th edition is published by Wizards of the Coast. TSR doesn’t even exist any more.
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You are correct of course. It is Wizards now.
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Necrothread here, but my thoughts on this are here:
What they say they are doing, or trying to do, doesn’t actually map well to the math – and that’s before you add in the various class-specific exceptions to things mentioned in the comments above.
D.
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I read your post and it makes my head spin. I don’t know if 5e is better than 1e, but I like it better. If you prefer 1e, play that. If the math doesn’t work as well – I will leave it up to you to prove that. You haven’t convinced me yet.
Even if they haven’t perfectly balanced all of the different possible combinations, I will excuse them that. I think it is a noble goal to strive for and I think they did a pretty good job. I don’t think the answer is to add +4 and +5 magical weapons. Perhaps some of the class abilities, feats and monsters need to be adjusted, but I am not sure what I would do to make it better.
Are you finding this a problem that has come up in real games, or is it just theoretical?
If it is a real in-game problem, what would you suggest DMs do to handle it when it pops up?
I must confess that I haven’t yet ran a high level game, but in lower to mid level games I haven’t found this to be a problem.
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LOL, sorry for the head-spinning. The point I was trying to make is that mathematically the difference between +3 and +5 is actually pretty meaningless given how the rest of the math works out – unless you are handing out +4 and +5 weapons when the characters are still in single-digit levels. The deal is that is that they aren’t deal-breaking in any mathematically meaningful way if character gets them at reasonable levels (e.g. double-digit levels). There’s no real need to have them, but there is no real need NOT to have them either – you slightly more likely to hit something that you were already pretty certain to hit, and the extra point or two of damage you are doing with each of those hits is even less significant at that level than the Strike bonus is.
D.
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So you are saying that DMs don’t need to worry about breaking anything if they want to give a higher level PC a +4 or +5 weapon. That’s good to know. There are some players that would find that so awesome it would be worth it just to see their reaction.
Thanks for clearing that up for me. If you will pardon the mixed metaphor, sometimes I can’t see the forest for the trees and need to have it slap me in the face before I get it.
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f you are new to D&D, this may all seem obvious, and hardly worth more than a passing glance. However, this is a break from some earlier versions of the game. In some earlier versions, your PC’s “to hit” bonuses and Armor Class increased with each level and thus forced monster attacks/defenses to also increase with level. This resulted in lower level creatures being unable to have any possibility of hitting higher level PCs and visa-versa. This was done in the very reasonable goal of allowing higher level PCs to combat tougher monsters. D&D 5e accomplishes this goal, not by making tougher monsters harder to hit but by making them harder to defeat by giving them more hit points. So as PCs increase in level they do improve in their ability to hit higher armor classes (although at a much slower rate) but their ability to defeat tougher opponents comes mainly from their increased ability to inflict more damage when they do hit, and their increased capacity to survive stronger attacks due to their own increased number of hit points.
Low level monsters still get the shaft like mad. Bounded accuracy combined with heavily decreased HP gains per level would’ve done it.
Whether the AC of PCs is too high for monsters to hit, or PCs get this dumb ‘multiple attack’ garbage combined with massive HP, the low level monsters are out of luck either way.
So nothing was ‘fixed’ on this front if the point of your paragraph here was low level monsters’ ineffectiveness.
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Not completely “fixed” but it is a lot better, in my opinion. Adding several of even low level monsters to an encounter with higher level PCs now makes it a lot harder than the same encounter would have been in earlier versions.
There is nothing to prevent you, as a DM, from having house rules that eliminate PCs multiple attacks and decrease the the HP gained each level if you think that would improve the game. I might also prefer a game where the PCs didn’t get quite so powerful as they increase in level, but trying to balance it all out turns out to not be a trivial undertaking.
Of course some still prefer to play 3rd edition or Pathfinder. I personally much prefer 5th edition to any of the others.
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Where did you get the Max. AC of 30? Are you talking about Monsters? I’m planning to take a character at least temporarily above 30. If you know a trick, I want to learn it.
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I am talking here about the design philosophy of the game. I am not saying that in a particular game a PC’s armor class could never exceed 30, but it should be rare and would fall outside the bounds set by the designers of the game. For example, no monster should be un-hittable without magical weapons. There is a maximum Ability bonus of +5 and a maximum Proficiency Bonus of +6 making a maximum total bonus of +11 (resulting in a maximum score of 30 on a roll of 19.) So if a monster (or a PC) had an armor class higher than 30 no one could hit him without magical help unless they rolled a natural 20.
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unless that player is a fighter with the archery fighting style, in which case they have a +13 to hit with any ranged weapon.
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an unarmored blade singer wizard with 20 int 20 dex, the dual wielder feat, haste, shield, and mage armor can effectively have 31 AC for 3 straight rounds, a combo you could realistically have online at level 12, or earlier if you’re really lucky rolling stats. alternatively, a 17th level blade singer with 20 int, 20 dex, the defensive duelist feat, haste, and mage armor can have 31 AC for an entire minute before blade song runs out, all without magic weapons or items or any help from other players. So the accuracy isn’t exactly that bounded.
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OK – I surrender! I concede your point.
This was just my attempt to explain the design concept as I understand it. It does appear that, in some outlying cases, the designers do allow certain combinations of spells, feats or other features to exceed their stated design goals. However, I believe it is still useful as a Player or especially as a Dungeon Master to understand the design philosophy that the rules are based upon. Even though the designers themselves may bend or even break these ideals from time to time.
The basic idea is this: A PC should not require a magic weapon in order to be able to hit a Monster.
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Except there are plenty of monsters they include which can only take damage from magic or magical weapons.
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You are exactly right. That is a great example of how the designers have broken their own design goals.
Excellent point. Thank you.
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New reader here. This was very insightful, and the table in particular is a great reference. Thanks for the post!
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You are welcome. I’m glad you found it useful.
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