Why D&D’s d20 Tests Make Experts Look Inept and How to Make the Best of It

Decades ago, I read game designer Steve Jackson explain why he swapped the d20 to-hit roll in Dungeons & Dragons for the 3d6 roll used in his alternative combat system Melee (1977). Steve considered the 3d6 bell curve so superior that he trashed the d20 without a second thought. His roleplaying games The Fantasy Trip and GURPS use 3d6 core mechanics. Then, I struggled to grasp Steve’s dislike of the d20.

Now, I understand Jackson’s disdain, but I love D&D. Like esteemed game designers such as Jeremy Crawford and Monte Cook, I find reasons to embrace the d20.

In Cook’s designer’s notes for his Numenera RPG, he describes the d20’s flaw. “Using the d20 introduces a great deal of randomness into a game. It’s difficult to use a d20 as a task resolution die and still have character aspects play a big part in success or failure without all of a sudden finding yourself using pretty big numbers.” He gives an example like this: Suppose two archers try to hit a bullseye by rolling a 20 or higher. An untrained person with a decent 12 Dexterity gets +1 and hits 10% of the time. In comparison, a 12th-level ranger trained in the bow and boasting an 18 Dexterity gets a +8, but still only hits the bullseye 45% of the time.

D&D games show this dynamic when the DM asks everyone to roll an Intelligence (Arcana) check to recognize ancient sigils, and then the brainy wizard fails while the barbarian knucklehead succeeds. That outcome may seem funny the first time, but similar scenes play frequently and can feel disappointing. Instead of rewarding the player who chose to make a character good at something, the d20 roll often makes experts look inept.

If D&D used bigger bonuses, then experts would get a boost. Suppose the expert archer gained a +25 and hitting the bullseye required a roll of 30. Now, the sharpshooter feels more like Annie Oakley. But that arrangement makes difficult tasks impossible for unskilled characters when we really want success to become rare.

Instead of using big modifiers, fifth edition’s bounded accuracy uses modest bonuses that give every character a chance of success at the price of making experts inconsistent.

Monte describes an alternative. “Now imagine that you used 2d10 instead. 2d10 gives us a more normal distribution. In other words, you end up with a much better chance of getting a 10 than a 20. Using the same bonuses, the archer still hits the bullseye 45% of the time, but the unskilled guy only 3% of the time. That makes more sense.” With a 2d10-based game, clumsy newcomers at Faerûn athletic competitions luck into fewer medals. (In one of my very first posts, I grappled with a related issue.)

This more natural range of outcomes leads game designer Steffan O’Sullivan to write, “I’m not fond of dice systems with a flat distribution. I’m solidly in the bell-curve camp.” O’Sullivan created the Fudge RPG, which became the basis for the popular Fate system. Both games use a set of four special 6-sided dice marked on two sides with a plus (+), two with a minus (-), and two blanks. “When you need to roll dice in Fate, pick up four Fate dice and roll them. When you read the dice, read every + as +1, every blank as 0, and every – as –1. Add them all together. You’ll get a result from –4 to +4, most often between –2 and +2.” No roll requires counting past 4, so even little kids add the results easily. “The fewer mathematical calculations used to figure out a dice result, the more likely you are to stay in roleplaying,” O’Sullivan writes. “So Fudge Dice were born, and I like them a lot. They’re a joy to use and don’t slow the game down at all, one of my early design goals.” The system’s bell curve makes results of -4 and +4 rare, but possible. So a +4 (1.23%) matches my real-life chance of a bullseye, while an Olympic archer scores a bullseye on any roll better than -4.

Despite the virtues of the bell curve, Monte Cook still opted for a d20 for Numenera and D&D creators Gary Gygax and Dave Arneson chose the d20 for to-hit rolls and saving throws. The d20 rolls beautifully, it generates a big range of numbers without adding, and the icosahedron feels deliciously different from the bland cubes in countless games like Monopoly. Gygax became particularly enchanted with the exotic new dice from Japan.

Most importantly, d20s yield predictable odds compared to mechanics that combine multiple dice. Monte Cook explains, “If you’re using a system where the GM has to assign a target number for a task, it’s a lot easier to do that on the fly with a d20 than, say 3d6 or 2d10. Why? Because with a d20, the difference between, say, 17 and 18 is the same as the difference between 8 and 9. They’re basically just 5% increments. With a bell curve, that’s a lot harder to figure for the GM, particularly on the fly.”

In 1974, D&D lacked ability checks. To decide between success and failure, Gary Gygax suggested that DMs estimate the chance of success, and then improvise a roll that fits the odds. A d20 roll made the math easy.

Playing D&D means learning to embrace the d20’s swings. To help gamers love the d20, D&D’s current rules architect Jeremy Crawford offered advice on the October 3, 2019 episode of the Dragon Talk podcast. “Any time the d20 is in the mix, that is a swingy die so get ready for the unexpected. What I encourage groups, players and DMs alike to do, is rather than viewing that as something to chafe against or be unhappy about, embrace it as a storytelling opportunity. Over the years, the longer I play D&D and DM D&D, the more I have come to love the unpredictability of the d20, because so often it will create moments that will challenge the DM and the players to really stretch their storytelling ability to come up with a fun reason for why this transpired. Why did the ace rogue who triggered this battle, why did she end up going last?

“When the d20 throws you a curve ball, catch it and follow through with the curve. Just see where it leads you rather than saying, ‘this is dumb’ or ‘this isn’t how it should play out.’ No, in D&D, what the d20 does is really showing how this is going to play out. Let’s ride it and see where this craziness goes.”

If I were magically transported back to a version of 1974 that somehow lacked Gary Gygax and Dave Arneson, would my attempt to bring dungeons and dragons to the world use a d20? I might choose Fudge Dice, but I would never stop giving those new icosahedrons from Japan forlorn looks.

Related: D&D and the Role of the Die Roll, a Love Letter
When You Describe Outcomes, Flatter Your Game’s Heroes and Monsters
In D&D, Letting Everyone Roll Certain Checks Guarantees Success, So Why Bother Rolling?

17 thoughts on “Why D&D’s d20 Tests Make Experts Look Inept and How to Make the Best of It

  1. Frederick Coen

    I understand and agree with the math of your post. Bell Curve highlights mastery – and imposed difficulties – while the d20 is just plain “swingy”. I first felt the difference when switching from D&D to BattleTech (2d6 system) for a change of pace. +1 in D&D was kinda “meh”, but +1 in BattleTech was great (tripling your chance of hitting that jumping light mech through the trees). We got really good at knowing the 2d6 percentage tables (“7+” = “55%”). And expert pilots with a simple +2 bonus were *amazing*, and nearly godlike compared to greenhorns with a -1. [Actually, BattleTech uses minuses as “good” and plusses as “bad”, but you get the idea.]

    But I also understand and agree with Crawford’s storytelling angle. For example, if the archers are shooting at the bullseye (AC 20), maybe Frank Farmer flat out misses the target completely unless he rolls an 18, while Annie Archer still scores the 6pt ring with a “2”. Both “missed” the AC20 target. Or in combat, when the bard swings the orc chief’s massive greataxe, anything less than a “hit” is a complete miss, with comic results; the fighter who wields it also “misses” but his “miss” is “a glancing blow off the foe’s armor, staggering him for a moment, but inflicting no lasting damage…” Last night, the hobgoblin warrior “missed” the ranger by 1; I described it as “a hard blow to the shoulder that will leave a bruise, but didn’t pierce the armor – you’ll be fine.” The ranger’s return blow was also a miss (a “2”); his strike was “parried with minimum effort, your blade skipping off the parry to strike a spark from the hob’s chainmail, as its momentum carries you past harmlessly.” The Warlock’s spear strike – also a “2” – “You missed so completely the wolf doesn’t even know you attacked it.” The hobgoblin’s next attack was a Nat1, though, so I described him getting tangled up in his dead comrade’s limbs, and missing his chance to strike.

    We kinda decided to highlight expertise by stealing from the rogue, and letting all experts (Expertise, specifically) Take 10. The wizard is never going to get less than a 15 as he considers the strange runes, even if the fighter (“Nat 20!, whoo hoo!”) happens to remember seeing that rune once in a picturebook. The rogue pops the masterlock (DC15, from the PHB) in less than a minute, every single time; while the fighter gets a single chance after 2 minutes. Kinda stealing a page from Pathfinder 2e, which I think provides the best (if less memorizable) compromise: No matter what your skill BONUS is, your skill LEVEL determines what you can accomplish. Sure, the Fighter has seen that rune before, but all he remembers – despite his Nat20 – is that the book was about a Necromancer. The wizard *only* got a 13 due to a bad d20 roll, but his expertise in Arcana is sufficient to determine that this is a Glyph of Warding, not any kind of necromantic magic… (but maybe the glyph will summon undead guards?) The Wizard might be able to pick a lock on a tavern door with a great roll, but he can’t do it in combat situations – only the rogue’s constant training and practice on focus allow him to do that. Likewise, apparently all clerics have a natural talent for Perception (high WIS for their prime stat)… but the ranger’s training allows him to better interpret what he sees. Cleric: “look at all the birds over that copse of trees”. Ranger: “First, they just took off, so something spooked them. Second… some of those aren’t birds!”

  2. Jacob

    So, if shooting a Free Throw is a DC 15 check, a scrub like me with a +0 has a 30% chance of success.

    We have stats on how well experts shoot.

    An average college baller with a +8 (70%) and an average player in the NBA has a +9 (75%). The best players have +10 or +11. A play with middling Dexterity like Shaq only has a +5.

    The same thing works if a 3-pointer is a DC 20.

    This works out if college ballers and NBA players typically have a +3 to +5 in Dexterity and +4 to +6 from Expertise in Basketball/Athletics.

    Rolling a single d20 works fine with pass/fail tasks that are not highly specialized, if you set an appropriate DC.

    The point where rolling a single die breaks down is when you use degrees of success. That’s when you need a bell curve, and why trying to use the result of an Athletics check to determine how many feet someone long jumps will give you bonkers results.

    The point where die rolling in general breaks down is with highly specialized tasks. Performing heart surgery may be impossible with training, but a specialist might have a high chance of success. But 5e already gives us a couple of examples on how to handle this.

    1. The lock item in the Player’s Handbook. The item’s description states that it can only be picked by someone Proficient with Thieves’ Tools: Problem solved.

    2. Spells and Feats. These are highly specialized actions. They often allow characters to perform “feats” that would otherwise be impossible for any other character. You chance of casting a spell you have prepared (short of Wild Magic) is zero.

    1. Frederick Coen

      Part of the challenge as a DM, though, is “level-setting the world”. Are “college ballers” paragons of physical performance (18 DEX to get +4) *and* high-level (in the Athlete class?) in order to get a proficiency bonus of +4? Or are they 1st level, with Expertise in “Balling” for “+2, doubled”? We *do* select NBA players from a pool of millions of people, and they train extensively, so I suppose this is possible/reasonable. While Frank Farmer is still “average”: DEX 10, maybe proficient for +2 because he spends all his non-farming time with an inflated cow stomach and a bottomless bushel basket.

      And then a 5th level bard or rogue comes along with 20 DEX and +3, +4, or +6 (depending on expertise / JoaT) and easily matches the expert who has trained all his life.

      And *then* – and this is David’s point – the Fighter in full plate (assumed DEX 10) with no skill rolls a Nat20, and sinks the 3-pointer on his first try, while the NBA baller and the “expertise in ‘Tools: Sports’ ” bard are sitting there with 18s because they rolled average 10.

      What should an “average” person be able to do? What should the “average professional” be able to do? What should the “specialist” be able to do? and how do you model that on a d20?

      Frank Farmer has a 30% chance of picking that DC 15 lock in the PHB. Is that right? Larry Locksmith (proficient, and nimble fingers DEX 12) has a 45% chance. And if he can’t do it, call in Shifty Sam from the next town over, with DEX 14 and expertise (+6)… And the 1st level rogue (DEX 16 or 18, expertise) is still better. And the Wizard can still beat them all with a lucky roll.

      1. Jacob

        Frank the Farmer has a 0% chance to pick the lock because Frank the Farmer is not proficient with “thieves’ tools.” See page 152 of the Player’s Handbook.

        You don’t model this on a d20, it requires the DM to exercise judgment.

        To your other point, yes, it’s entirely possible, just very unlikely, for some average person to sink a 3-point while the pro wiffs it.

        There’s a reason that most real life Archery/Shooting competitions, et cetera, involve multiple shots (which gives you the effect of multiple die rolls).

  3. Dylan James

    I’ve been reading your blog for years David, and I just wanted to comment that I really appreciate your insights and I don’t think enough people tell you how much they get out of what you write. It’s been great food for thought and has taught me about the history of RPGS and D&D and has given me some solid advice as a GM/DM.

  4. Stan

    It’s always annoyed me that 5e “experts” don’t seem all that expert. How about allow a reroll on unmodified die results <= character's base proficiency?

  5. Griffin Baker

    A good way to slightly tone down the d20’s randomness is to limit who can make rolls. Instead of having the whole party roll Intelligence (Arcana) checks, limit it to only one member of the party (the group chooses) or limit it to characters with proficiency in Arcana or some connection to the ancient sigils.

  6. David C

    Other people have mentioned the option to limit tests to people with proficiency in a skill where it makes sense. I’d just like to add that players make a choice about which parts of the narrative their characters are going to have a strong impact on when picking skill proficiencies, so especially for knowledge skill like Arcana, it makes a lot of sense to gate checks behind proficiency sometimes.

    I think the more problematic aspect of swinginess isn’t so much when incompetent characters get lucky, they’re heroes after all, it’s when supposedly competent characters roll badly a bunch of times in a row. In some cases, this can be mitigated by using thresholds to grant auto-successes, e.g. the high-dexterity thief trained in acrobatics doesn’t need to roll to see if they can cross the narrow beam from one rooftop to the next without slipping, but other characters might. A milder variant that retains uncertainty is to also award advantage if you are proficient in a skill (and/or maybe disadvantage if you aren’t).

    I think the most important thing is to always keep in mind the fantasy of competence matters a lot to many players; Same as it’s good practice to describe missed attacks from a highly trained fighter not as them suddenly being clumsy and incompetent to the point of slapstick, but their opponent getting in some last-second dodges or parries or unexpected external circumstances thwarting an attack, there are probably ways to make skill check failures from highly proficient characters feel less jarring just by how you describe them.

  7. Jeramie Cooper

    Thank you for the post. I heard about it on Mastering Dungeons. I’ve run a lot of D&D 5e since 2015 and I ran Pathfinder 2e for the last few years as well. My players, who are normally 5e players, also played Pathfinder 2e the last few years. They expressed that Pathfinder felt too difficult, so one of the solutions I implemented was to use 2d10 exploding 10s instead of the d20. This change combined with the Pathfinder 2e 4 levels of success made the game feel more like the 5e games. I enjoyed the exploding aspect of the dice and 4 levels of success system that I decided to bring it into my next 5e game. I haven’t had a chance to use the changes in 5e yet. I suspect it will make the characters feel more heroic.

    After playing with a 2d10 system I started to expand on the idea and ask, “What other curves would work well and represent an increase in proficiency?” Because I use Roll20 it doesn’t matter how many number of sides are on the die. So, I ran some curves on anydice.com and compared 1d20 to: 2d10 exploding 10s, 3d7 exploding 7s, 4d5 exploding 5s, and 5d4 exploding 4s. It looks like these could be used to represent both an increase in capability and repeatability of experience, but it also removes the wild swings you mentioned. The low and high swings help add a dynamic feel to an encounter. The results of 3d7, 4d5, and 5d4, start to feel too repeated and thus a little boring. So, in the end, I’m not going to propose a test of the added dice complexity, even though it creates a more stable character performance that one would expect with experience.

  8. S

    Barbarian recognizes rune, wizard doesn’t: wizard now has a new quests to go on; where the barbarian saw the rune. Now you have a new quest, new lore, world building and something cool happened – and there’s a problem?

    Peasant archer and Ranger shoot at targets: if you think the Ranger should hit, they do; If you want a role, the Ranger is rolling to hit the -bullseye- and the peasant to hit the -target-; or the Ranger’s target was 5x farther away making it a fair duel; hell, maybe the Ranger’s string broke and they roll again. bad roll again? Embrace the curse! new quest, new lore, world building and something cool happens.

    The problem is not with the swingy nature of the d20, that’s it strength. The problem is with taking a myopic view of situation.

    Of course you may have been trying to push a story through and don’t want to follow some interesting results because they are not on the road you are driving down, then you have a problem, but that’s not the d20’s fault 🙂

  9. Rob

    I had this problem just tonight. It didn’t feel right to not require a roll for what the particular PC was trying to accomplish but they rolled repeatedly bad rolls on the D20, literally 2,3,2,5…it made it very challenging as the DM.

    1. Frederick Coen

      Option 1: “go with the dice”. Come up with a story about why the expert was off his game. I have used illness, “you’re an Apple, this is a PC”, and hidden sabotage before.

      Option 2: “go with the skill”. Frank Farmer’s result of 19 vs. Eddie Expert’s result of 10 (nat 2 + 8 skill). Eddie’s result is still more knowledgeable/expert/accomplished. Frank couldn’t have succeeded (novice skill or untrained), but this particular thing was still difficult for Eddie. Depends on the skill/situation, but make the dice-based failure not about Eddie failing, but about the challenge or opponent being equally or more skilled. As a couple examples: picking a lock, only to find that someone else previusly failed, and jammed the tumblers. Persuading a guard, only to find he had been reprimanded just yesterday for being too permissive, and is outrageously strict today. Eddie did great, but George the Guardsman just wasn’t having it!

      (Option 2 is a bit harder when Frank comes along with the nat20, true, but you can also have skill thresholds. like “can’t attempt unless proficient”, or “must have a skill bonus of +5 or better to attempt”.)

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