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Bounded accuracy is a major feature of the new system. It promises that bonuses to rolls won't grow too much throughout a character's career. And indeed, a first-level fighter would have an apex skill of about +5 (Strength +3, proficiency +2), whereas a twentieth-level fighter would have the same skill at at most +11 (Strength +5, proficiency +6). Supposedly, such bounded accuracy allows characters to meaningfully interact with same threats for most of their career, if they so choose.

This wasn't always the case. In 3e, everything was modeled by the rules, and a level 20 character meeting a level 1 character would not require any change to the way either are represented by the system. Such interaction was unlikely to be meaningful mechanically, as level 20 characters would outclass level 1 characters thoroughly. Thus, level 20 characters in 3e were both in mechanics and flavor significantly more powerful in every respect.

In 4e, only the immediate vicinity of PCs was ever modeled, and there was no such thing as "level 1" people near them by the time they'd hit level 30. If they were to be modeled at all, "low-level" creatures would be represented as minions of higher level (For more on this particular reasoning see this blog post, though it's not that important to the question at hand). There were no conclusions of relative power level to be drawn from the mechanics, even though the numbers kept on growing, but flavor of becoming demi-gods at high levels preserved.

In 5e, it appears that the approach has moved back to modeling the whole world, as implementation of flat math indicates. But what about the flavor? Is the world's greatest athlete at +11 really only capable of winning about 3/4 of the time against a village strongman at +5? If that is not the case or the intention, how is this apparent disconnect reconciled? Is comparing them in such way actually valid?

If that is, indeed, the intent of the system (please provide some quotes if possible) that even at high levels PCs do not straddle like colossi over mere mortals, it is a serious departure from the past two editions I'm familiar with. As a qualitative change, it would impact the way I treat high-level characters and the role they play in the world, much more so than different class features or spellcasting methods of a new edition.

Does the bounded accuracy approach mean that max-level characters are no longer demigods compared to starting characters in everything other than killing?

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Thanks for precisely wording a question which also has been bothering me since I finished reading the D&D 5e rules! –  thomax Aug 22 at 8:39

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Yes.

This is, of course, intentional. One of the problems that D&D has always faced is that characters often have wildly different skill values, which can cause issues where some players get sidelined during skill-heavy sessions, because their characters don't have any of the right skills.

4e tried to rectify the problem of disparate skills in two ways: Skills were no longer based on Intelligence, and everyone got bonuses to every skill as they leveled up. 5e continues this trend: Players generally get the same(ish) number of skills, and the difference between skilled and not skilled isn't as large as it was in 3e.

The non-combat difference between level 1 and level 20 characters is not in how high their numbers are, but in their other capabilities. For example, a level 20 Rogue might not have an Athletics check that's that much higher than his level 1 counterpart, but his Second-story Work ability lets him climb much faster regardless. His Reliable Talent feature makes it so he never has a roll that's super bad. And his extra Expertise skills mean that even if he fails the Athletics roll, he probably has a high bonus in other skills that can help him finish his task anyway.

You are correct that the bounded accuracy rules mean that high level 5e characters aren't the invulnerable demigods that they were in previous editions. However, they are still versatile, powerful heroes that are still likely to (eventually) succeed at everything they do against a small number of low level characters.

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Another example: A 1st level Fighter with 12 HP and 1 attack per round is going to be pasted flat by the 20th level Fighter with 200+ HP and 4 attacks per round. But a horde of 1st level Fighters can endanger the 20th level fighter. –  Alan De Smet Jul 28 at 1:40

Yup.

So you've pretty much got it in one, there. The leveling system itself is a holdover from OD&D and power level diversity present in Chainmail, which is much better explained here. But really, basing your assumptions of how things should work in any edition on the previous editions is a Bad Idea. I really thought we'd learned that one after 4e.

Using your example, in the real world the difference between runners is not generally huge. The average human run time for the 100m dash is between 12-15 seconds, while the world record is just under 10 seconds. A noticeable difference, perhaps, but not huge. Its certainly not unbelievable that, when measuring times in 100ths of a second, Usain Bolt could have an bad day (stumble, trip, start late, or even simply be too tired) while Joe Schmoe, trying to make it back from the pub before his wife scolds him for the 5th day running, happens to have the best run time of his life; narrowly edging out his "competitor".

The problem with D&D becomes even more obvious when you compare pre-4e combat stats for low and high level characters. A 20th level character is effectively immune to a first level character and she could swat him like a gnat. But really, skill only goes so far and any single person, no matter how skilled, is likely to be felled in moments by three or four competent opponents; let alone dozens.

Well, almost.

Your math is a little off. I won't even try to calculate the combat probabilities, but the probability of the average athlete (+5) beating a record-holding athlete (+11) in this case is only 22.75%. If you go with beats or ties, it's 26.25%. A strictly average individual would probably be +0, where a village strongman (+3) is simply strong - not necessarily "athletic", and a world record holder might be considered as high as rogue's double-proficiency (+17). All of which means Joe Schmoe has a .75% chance of beating Usain Bolt (and an additional .75% chance of tying). That's 612 races to break a 99% probability of winning at least one or 305 races to break or tie at least once.

"Fixing" the theme.

Honestly, I think if they were going to go with this "flat-math" they didn't take the concept near far enough and should have eliminated the simple level-based numerical bonuses altogether (to make it more distinct from other editions). But if you really want to make your high-level heroes "demigods" again, simply apply advantage to any character more than your preferred arbitrary number of levels higher and disadvantage to the lower character. Although the lower level characters can (and should) still be able to beat the "demigods", you will make the probability about as close to zero as you can get without having to make any significant changes to the rules.

Bonus: If you cancel out the higher level character's advantage by giving him the disadvantage of tying his laces together, he should still handily win the race. That demigod enough for you?

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Bounded Accuracy is the culprit behind your observations. Rodney Thompson describes Bounded Accuracy and the why behind it.

These are the reasons behind bounded accuracy.

  • 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 is easier for players and DMs to understand the relative strength and difficulty of things.
  • It opens up new possibilities of encounter and adventure design.
  • It's good for verisimilitude.

Does the bounded accuracy approach mean that max-level characters are no longer demigods compared to starting characters in everything other than killing?

The key to the answer lies in the detailed explanation for

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

A 1st-level character might not fight the black dragon plaguing the town in a face-to-face fight and expect to survive. But if they rally the town to their side, outfit the guards with bows and arrows, and whittle the dragon down with dozens of attacks instead of only four or five, the possibilities grow. With the bounded accuracy system, lower-level creatures banding together can erode a higher-level creature's hit points, which cuts both ways; now, fights involving hordes of orcs against the higher-level party can be threatening using only the basic orc stat block, and the city militia can still battle against the fire giants rampaging at the gates without having to inflate the statistics of the city guards to make that possible.

20th level means the characters are highly skilled individuals capable of unleashing a wide variety and quantity of damage to their chosen targets. However they are vulnerable to attrition. To a degree not seen since the 1974 release of OD&D.

OD&D is built on the miniature wargame Chainmail. In Chainmail man to man combat was represented by 1 hit by a veteran warrior = 1 kill of a veteran warrior. The To-Hit probability was adjudicated solely on the basis of the weapon type vs the armor type. In Chainmail, a Hero was worth 4 Veteran Warriors and took 4 hits to kill. A Superhero took 8 hit to kill.

During the early Blackmoor and Greyhawk campaign this was found to be too deadly and too boring and it was expanded to 1 hit = 1d6 damage and 1 hit to kill = 1d6 hit points. The hit points was modified up or down on the basis of character class. The hero and superhero (along with Wizard types) were expanded to a range of levels from 1st into the teens.

OD&D offered two combat system. The first was based on Chainmail and was not commonly used. The second more popular system was the familiar cross-index level to the Armor class, roll 1d20, if equal to or higher than the number on the chart you hit. If you hit you do 1d6 damage, regardless of weapon. Characters to-hit bonus and hit points increased as they level. But NOT their ability to deal melee damage. The exception being magic items and higher level spells.

The interplay of the above produced a balance in OD&D similar to that of 5e. High level meant skilled characters capable of defeating tough monsters but were vulnerable to attrition by less powerful creatures or characters.

It was different with interim editions of D&D because high level meant not only a large amount of hit points but vastly higher armor class and to-hit bonus. The lower level opposition was outclassed in several key areas. 5e takes to hit bonuses and armor class out of the high level picture, High levels increases the amount and frequency of doing damage.

Bounded Accuracy also applies to skill and attribute test. High level characters are significantly better than lower level characters. But the lower level characters often have far better than a 5% (1 in 20) chance of overcoming their higher level opponent in a ability or skill contest.

My personal opinion is that this is good for D&D because it always been easier to add elements for a high powered fantastic campaigns. But as the example of D&D 3.X, Pathfinder, and especially D&D 5e it harder to subtract it without a lot of work on the referee part.

With 5e I have the option running a gritty Thieves World/Game of Thrones style campaign as well as a more fantastic campaign like spelljamming among the planets or visiting the hub of the outer planes, Sigil.

My impression is that the overall effect divides 5e characters into 3 or 4 broad tiers. Low, Mid, High, and possibly Epic. That while it is possible for a horde low level character to overcome (combat or non-combat) a epic level character it is not very probable. However it far more likely that a mid or high level group can overcome an epic character. That the difference between tiers are not dramatic in combat or out of combat.

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What does this mean for non-combat areas of focus? –  wax eagle Jul 22 at 3:22

A level 20 rogue gets a +17 to certain skill checks. Other classsed also can sometimes double their profieciency bonus.

Also, while the max DC for a level 1 char is 26, the max DC for level 20 is 37 thus making activities that are literally impossible for a level 1 char to be possible even ifnot always probable at level 20.

Lastly I'd like to point out that while accuracy is bounded, and that is one way to measure success, damage output is not. A level 1 fighter can be expected to do 10 damage while a level 20 fighter can be expected to do 154 damage. (roughly speaking), the survival of characters also increases dramatically, from a Max of 15 hp at first level, to a max of 300 hp at level 20. Simple environmental dangers, such as falling great distances, are no longer such a deadly threat to higher level characters.

While the question focuses on ability checks of specific skills, it is missing out on the larger world narrative. At level 20 a Cleric can call on direct divine intervention without error, a Rogue can have amazing luck, automatically getting a 37 on an ability check, Fighters can jump further than is otherwise possible, and wizards have access to amazing spells. The power level is flatter than 3e or 4e, but it is not flat.

As for the intended level of power, there is a section in the rules called "Tiers of Play" which clearly delineates what is expected.

In the first tier (levels 1–4), characters are effectively apprentice adventurers. They are learning the features a that define them as members of particular classes, including the major choices that flavor their class features as they advance (such as a wizard’s Arcane Tradition or a fighter’s Martial Archetype). The threats they face are relatively minor, usually posing a danger to local farmsteads or villages. ...

At the fourth tier (levels 17–20), characters achieve the pinnacle of their class features, becoming heroic (or villainous) archetypes in their own right. The fate of the world or ev en the fundamental order of the multiverse might hang in the balance during their adventures.

The intent is not to become demigods, but rather to become heroes, or villains, who deal with problems that might involve demigods. The Characters themselves though, are still mortal heroes, who are capable of doing the impossible, but are not beings of a different caliber.

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It's not as different as the raw numbers make it seem.

The bounded accuracy rules allow for "meaningful interaction" of PCs from disparate levels with the same, or similar, threats.

The hit points and damage scaling system almost completely locks out a low level PC from defeating a high-threat monster, or they do so at tremendous personal risk.

However, a team of low-level PCs now have a better chance of tackling a bigger threat, comparing with e.g. 4E where high-level monsters were practically unassailable due to low chance of hitting them.

In 5E, a 10th-level fighter can tackle minotaurs and ogres. A 4th-level fighter is likely to need his or her buddies to fight these hard-hitting brutes.

Class features and spell levels also make a big difference between high and low level characters.

So, the only real difference from bounded accuracy is skills and hit/miss mechanics:

  • The low-level characters may get a hit on a high-level opponents more often under this system, but they will typically not have enough of an effect for that to be meaningful.

  • There are less "hyper-skills" than in 3E and 4E versions. I personally will feel more relaxed not trying to invent and justify DC 40 skill challenge, or figure out what +30 to Athletics should mean.

Is the world's greatest athlete at +11 really only capable of winning about 3/4 of the time against a village strongman at +5?

For opposed checks, if you want to model a challenge that the most skilled person should win, you need to set up the challenge to favour skill or background values over the randomness of the D20.

For a start, if someone has dedicated years of their life to a particular use of a skill, then I would give them Advantage on the roll. In that case, your comparison between village strongman and world's best athlete closes down to 87% chance of the athlete winning.

If that is not enough for what you want to express, split the challenge up into skillful parts that apply. Even for a 100 metre sprint can be split:

  • The warm up. Trained athletes (anyone with the "athlete" background) allowed to warm up double their proficiency bonus on Acrobatics and Athletics checks in competitive sports. This is similar to the Rogue's class feature. The numerical advantage is now +17 vs +5.

  • A good start. Opposed Acrobatics check. Advantage applies to anyone who has specifically trained (in their "athlete" background) for racing sports. This strong man now also needs a pretty good Dex and Acrobatics. Let's assume he does, so this is +17 vs +5, with advantage on the higher number.

  • The race. Two opposed Athletics checks (NB this comes out nicely as one per round). Advantage applies to anyone who has specifically trained (in their "athlete" background) for sprinting sports. This is +17 vs +5, with advantage on the higher number.

Winner of the race is whoever wins the most opposed tests.

With that more detailed model for the race, the odds come out much more in the athlete's favour. Each opposed test is now 97% in favour of the athlete. This favours our world-class athlete to the point where odds on him or her winning are more than 99.999% - not only that, if we decide to model the worlds next-best athlete as having 1 point less proficiency, we would still get a 93% chance of winning for the world's best. We have made skill and background matter a lot.


NB I don't recommend running a challenge for PCs with the odds skewed so heavily, it would be quite boring (instead I would simply rule that the highest skill won the race, as obviously it should). The above is just an exercise in trying out 5E's game model and how it can be adapted to fit expectations.

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Note also that just having repeated contests exaggerates any difference. Simply running the contest as five rolls with the winner being the one who wins the most would skew the odds substantially in the athlete's favour. No need for advantage/disadvantage. –  Paul Hutton Jul 23 at 0:59
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@PaulHutton: Whilst true, it is harder to narrate what each skill roll represents. I also find it encourages players to spam skill rolls, with "I try again", whilst I prefer an in-game justification such as a description of what the PC is doing extra or differently for each roll. –  Neil Slater Jul 30 at 6:25

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