Bounded Accuracy

Bounded Accuracy

This article was first broadcast in Episode Twenty-Four on 16th May 2018.

Ryu: Lennon? Why did we just get a delivery of 500 yards of parachute cord?
Lennon: Oh did that show up? Great! Yeah it’s a research project I’m doing about bounded accuracy.
Ryu: Okay…I think I know where you’re going there. I mean, you’re wrong, but I see where you got the idea.
Lennon: I refuse to be wrong without proof
Ryu: Ostron, have you done anything with bounded accuracy?
Ostron: Are you going to keep asking silly questions?


If you’ve looked into anything about the development or great ideas behind 5th edition, you’ve probably heard the term “bounded accuracy” thrown about. Then you probably wondered “what does that mean? It’s easier to hit someone who’s tied up? That’s already true.” However, bounded accuracy has nothing to do with tying up characters and everything to to with the math tied into 5th edition, and it mostly has to do with bonuses to attack, though it does have a knock-on effect on AC.

Bounded accuracy was a design philosophy Wizards adopted to counteract what happened with the 3rd and 4th editions of D&D. For those who weren’t involved or don’t remember, AC increased in those editions along with characters’ levels. This had two effects beyond simply increasing the characters’ AC. First, it meant that lower level monsters were mathematically unable to injure characters without a crit, and second it meant that characters HAD to be provided with magic weapons or they were going to be unable to injure monsters.

While it was nice for players who enjoyed having their characters be almost literally immune to damage from certain sources, it created some headaches. First of all, as mentioned, characters not using magic had to be sure their attack bonuses were being augmented by feats or magic items in order to keep killing monsters, requiring either a lot of looting, a lot of money, and/or a DM who regularly gave away such items. Also, it meant there were three types of opponents: ones players ignored because they couldn’t do anything, ones players would fight regularly, and ones the players had no hope of surviving combat with. It was basically Return of the Jedi – Luke was a high enough level to take on Darth Vader, but when he gave lip to the Emperor he just laughed and started cooking him alive and there was nothing Luke could do about it.

Bounded accuracy changed all that. At a simple level, the combat mechanics were modified so only three sources usually provide permanent increases to a character’s hit bonus: the ability modifiers, the proficiency bonus, and static bonuses from magic weapons or items. Those familiar with character mechanics will recognize that two of those are permanently limited; ability scores can never provide bonuses above +5 to characters, and the proficiency bonuses top out at +6 by level 17. Currently all of the magic weapons available from official sources have bonuses that top out at +3. That means, in theory, the highest permanent bonus a player character should have to hit is +14, and most characters are going to have an average of +7 or +8 to hit. The +7 or +8 figure is because many players build for a “balanced” ability score array and don’t max one skill up to 20, and from levels 5 to 12 they have a +3 or +4 proficiency score.

Because of the way the levels scale, the majority of players’ time in most campaigns so far are spent at those levels, and few campaigns right now are going into the higher teens.

It would seem like spells that require saves rather than attack rolls might have avoided the bounded accuracy limits, but since saves and spell save DCs are now tied directly to the ability modifiers and proficiency bonuses, they end up getting similar limits even though the actual math is different.

That mechanic dictated a lot of other things in the rest of the rules. First, most monsters received ACs in the range of 13 to 18, with enemies that are supposed to be harder to hit getting values from 18 to 23. With a 23 AC, players with the +14 value have a 2/3rds chance to hit, but the average builds only have about a 1/3 chance. So while the mechanics of bounded accuracy don’t directly affect AC, the reality is that it influenced the AC values monsters get.

Now monsters technically do not have bounded accuracy applied; a quick look through just the regular monster manual will show monsters with statistics far above 20. However, monsters sanctioned by official D&D sources will still follow the basic rules for limiting their attack bonuses because characters’ AC is now only dictated by either their Dex score or armor or both. Without magic items, the sturdiest classes can get “regular” ACs that top out at about 25. Adding in magic items boosts the max to 31 with a shield and magic plate, and then there are other spells and temporary effects that can theoretically boost it into the 40s, but only for the length of an encounter. Technically all of this is not part of the bounded accuracy system, but the designers did it so that monsters would be viable for longer periods of time. CR 1/8 kobolds still have a chance of hitting some level 20 characters and damaging them even without rolling a critical.

Beyond the way the system influenced the design, it also has effects in the way characters and encounters are designed by players and DMs. First of all, almost all players trying to maximize their characters’ combat stats go for a ranged fighter or ranger; the “Archery” perk they get gives a flat +2 bonus to ranged attacks, meaning they can conceivably achieve a +16 maximum bonus. Also, unless their DM allowed them to have it at creation, any characters building to be “Tanks” usually start immediately trying to gather the heaviest armor they can since it’s the only way their AC will increase. Also, during gameplay, it should mean that by the time players pass level 5 or so, some of them have at least a chance of scoring a hit on any opponent they come across, even without rolling a critical. Whether that’s wise or not is a completely separate issue.

DMs’ jobs actually got a little easier with the addition of bounded accuracy. Because they no longer have to worry about characters’ AC climbing with levels, they do not need to revise their menagerie of opponents every few levels to make sure they can still threaten the characters. Also, with much less need for magic items to bolster characters’ stats, DMs can pay less attention to making sure lootable gear is available and just use mundane coin or valuable items most of the time.

However, overly creative DMs now have to be more careful. Magic items that provide flat bonuses to attack bonuses or AC are now extremely powerful items, and any that allow characters to break the limits mentioned above should be used carefully. DMs also have to be careful of indirect bonuses too. For example, according to the Dungeon Master’s Guide, anything that grants resistance to a large range of damage (for example “magic”) effectively grants the creature an extra 2 AC (there’s lots of math to back this up but we took Ostron’s calculator, just trust us).

(Ostron wants his calculator back)

If you’re a DM who designs or modifies monsters you have to pay particular attention to their AC and attack bonuses. Monsters whose AC goes into the mid or upper twenties are going to be very difficult or impossible for characters to hit. Even if they mathematically have a 15% chance to hit, remember the gambler’s fallacy – it doesn’t mean that three out of every twenty attacks at your table will hit. They could very well miss every attack they make. Also, monsters with bonuses to hit over +10 or so are going to hit many characters the majority of the time.


Ostron: I’m going back to work now
Ryu: And I’m going to find something to do with all this rope