The “Big Three” Ability Scores: Another Reason Adventurers Are Rare What an Analysis of Pregen Characters Reveals about Ability Score Preferences
“Dungeons and Dragons” by Judit Klein. Used under Creative Commons (CC BY-ND 2.0).
Which ability scores are the most popular? Which are most likely to be dump stats?
You probably have some gut answers about this, based on what you’ve seen first-hand. I know I did.
But, to see whether my instincts were right, I recently analyzed the ability scores of 31 pregenerated characters gathered from the official D&D site (including the D&D Starter Set), as well as the winning pregen characters for D&D Adventurers League’s Elemental Evil scenario, and the winning pregens for the League’s Rage of Demons excursions.
The official pregenerated characters and the “cream of the crop” winning League pregenerated characters strike me as fairly representative of the larger pregenerated population — of what people choose to emphasize (or dump) when allocating a predetermined set of points. If you have doubts about that assumption, then you might not be persuaded by the rest of this piece. That’s fine. You might also quibble with the sample size (31), and that’s fine, too.
Why Did I Do This?
I wanted to test some assumptions I’d made back in 2014, when I created a system to estimate how many NPC adventurers of each class might live in a city.
When I created that “population engine,” I challenged several common assumptions. For instance, most previous models make a serious error when it comes to character levels. The number of 2nd-level fighters in a population should be higher than the number of 1st-level fighters. That pattern applies across every other class. (My 2014 article explains why.)
I also argued that the number of folks who could cut it as adventurers in a D&D setting would be naturally restricted by the low likelihood that they would end up with the right combinations of high scores. (This argument was inspired in part by Wallace Cleaves’ own observations on ability score distributions.) In one key sentence, I wrote that regardless of character class,
NPCs are unlikely to be adventurers if Dexterity, Constitution, or Wisdom are below 10. Otherwise, they’re likely to walk blindly into danger, fail to avoid it, and die from whatever hits them.
That may not sound like much of a limit, but think about it: Half of any population will have a Dexterity below 10. Half of the folks with high Dexterity will have Constitution below 10 (and many of those with high Constitution will have low Dexterity).
Once you start with the Venn Diagrams, in other words, the pool shrinks rapidly. Throw Wisdom into the mix, and you end up ruling out the vast majority of people in any demographic.
So I was wondering how often pregenerated characters had Dexterity, Constitution, or Wisdom scores of 8 or 9. Did the pregens match up with my assumptions? If a lot of pregens used Wisdom as a dump stat, I’d have to rethink parts of my population engine. Ditto for the other two abilities.
Results
The descriptive statistics appear to support my assumptions, but they also highlight some fascinating details.
- Not a single pregenerated character had a Constitution or Wisdom score below 10.
- Dexterity, Constitution, and Wisdom were the three highest ability scores on average (i.e., mean scores).
- Of these, Constitution had the highest average (a mean of 13.8).
- Constitution also had, by far, the smallest standard deviation–which is just a statistician’s way of saying that Constitution scores tended to be clustered around a very tight range. Two-thirds of Constitution scores landed between 12.1 and 15.4.
- Wisdom had the second-smallest standard deviation.
- The value most frequently assigned to Dexterity was 16. (Stats junkies: I’m referring here to Dexterity’s mode.) Dexterity’s average (mean) was lower than the average for Constitution entirely because Dexterity had a much higher standard deviation — when Dexterity wasn’t 16, it could range as far south as 8, which Constitution didn’t.
- Dexterity only ever dipped below 10 when Strength was 14 or higher. Presumably, the designers planned to have those characters wear heavy armor, making the low Dexterity irrelevant to AC.
- Dexterity was the only ability score to have a score above 16 (two 17s). (You can find the raw data here.)
- By pretty much every metric, Strength was the most common dump stat. (This is an odd turn, compared to distributions in previous editions.) It had the lowest average (11.4), the lowest mode (8), and the lowest median (10).
What struck me as most interesting, however, was that Strength fared worse than Intelligence did. Given that Strength is a key ability for three classes (Barbarian, Fighter, and Paladin), I had expected muscles to do a bit better than Intelligence, which is the key ability only for the Wizard. Even if you factor in the specializations, figuring that eldritch knight and arcane trickster would want a high Intelligence, you then have to factor in cleric domains that grant proficiency with heavy armor and martial weapons.
Moreover, four of the PC races published by Wizards of the Coast offer a +2 bonus to Strength*, while only gnomes get a +2 to Intelligence. One could quite rationally expect a pool with a diverse range of races to favor Strength for that reason, too. But nope. Even with three Strength-oriented characters in the pool I analyzed (a goliath, a dragonborn, and a half-orc) and only one gnome, it didn’t work out that way. (* Mountain dwarves, dragonborn, half-orcs, and goliaths.)
Here’s what I suspect is happening. Dexterity and Strength compete with each other (over attack bonuses, over Athletics/Acrobatics, and over AC). But Dexterity has the tie-breaking feature of being a common saving throw. It also is the better option for the many classes that cannot wear heavy armor. So Dexterity kills Strength and eats its lunch: character-designers make their characters either Strength-builds or Dexterity-builds. Whichever one isn’t supporting the build gets to be the dump stat. That means Intelligence can be the next-score up from “dump,” which is a 10.
And, as it happens, the most common value for Intelligence was … 10.
On that note, meet Biff.
Biff represents the archetypal adventuring character, as determined by the values most often assigned for each ability score (i.e., according to their modes). The score most often assigned to Strength, for instance, was an 8, so Biff has an 8 Strength. Biff is a composite of all of the pregen characters.
| STRENGTH |  |
8 |
| DEXTERITY | |
16 |
| CONSTITUTION | |
14 |
| INTELLIGENCE | |
10 |
| WISDOM | |
13 |
| CHARISMA | |
12 |
What This Implies for Adventurer Demographics
Although a more robust investigation might yield different findings, what the analysis so far suggests is that adventurers are even more unusual than you already think they are.
See, across a population of NPCs who aren’t optimizing themselves, ability scores will be randomly distributed.
For them, it’s all just one big genetic lottery. Most NPCs will have a low score in at least one of the “big three” stats, Dexterity, Constitution, and Wisdom. Moreover, many of those who have low Dexterity won’t have the high Strength necessary to wear heavy armor. Many of those who do will be, by lottery of birth, too poor to buy heavy armor.
Now, don’t get me wrong: As I noted in the earlier article, PCs might very well go adventuring anyway because selling shoes is boring. But I’m thinking about the adventuring demographics of the overall NPC population. And NPCs don’t have the benefit of a GM who kindly matches each encounter to their party level. Weaknesses in critical areas are likely to drive them away from adventuring or into the grave, depending on their life choices. The decisions of careful and competitive character designers suggest that Dexterity, Constitution, and Wisdom cannot be dumped without consequences. Low stats in those areas may well affect NPCs in ways that they wouldn’t hamper a PC, particularly one buoyed by other PCs and a GM who follows encounter guidance.
Gus, for instance, might have a high Intelligence. But with low Dexterity and Wisdom, he’s not likely to be an adventuring Wizard. More likely, he’ll be a clerk or moneychanger. Ursula might have a high Charisma. But with a Constitution of 6, she’s more likely to end up bartering over supplies for her shop than slaying dragons.
When Gus and Ursula look up from their daily business to see your party of PCs, then, they’re looking at individuals who were lucky long before they ever succeeded at a saving throw. It isn’t just that they have high ability scores (like 16s). And it isn’t just that they have no scores below 8 (the floor for all pregens, point-buy, and standard array characters). And it isn’t just that the adventurers (hopefully!) have a GM who takes their levels into consideration when setting up encounters.
No, adventurers are disproportionately likely to have ended up with their high scores in all the right places.
They have won the Dexterity-Constitution-Wisdom lottery. ‡
your STR and DEX analysis is spot on. But all pregens are terrible – odd stats (unless it’s a 13 in a multiclass pre-req) are terrible decisions – wasted points. A 17! Dex??? Terribleness in extremis. So many wasted points!
Dex certainly is the big mamma jamma. And str and int at the bottom (barb and wiz only) sure. But con is almost always a dump stat – if you are Dex or Cha or INT or wis based, becuase you plan to avoid the action. Druids wild shape so they dump physical; Dex clerics are ranged casters; sorcerer warlock and bard are ranged casters; Wizards are ranged casters; rogues use stealth to dart away from combat; Dex fighters are archers.
The number of classes that rely on cha as a primary or secondary stat is second only to Dex.
John has some excellent points. Just a couple of nitpicks–concentration checks are a very big deal in this edition. Smart enemies will target a caster specifically to break their concentration. They might even just target them however possible because they see them as a threat in terms of AoE damage, crowd control, or healing their enemies. I’ve only seen a caster dump con once and the rest of the table easily talked them into changing it. (In an AL game, you can change your character up through lvl 4)
Moon druids dump physical stats. Land druids don’t necessarily because they will primarily be using their wildshape for utility outside of combat. Moon druids are popular because they’re clearly mechanically superior but there are playstyle reasons to play a land druid and I’m finding them to be more popular than I expected. My first druid was moon. My current druid is land.
Thanks for the comment, Dalebert! (And apologies. Our automatic spam filter dropped yours — for reasons I don’t know — into the Spam folder. I’m glad I caught it!)
Very good point about concentration. I think I’d call that a contribution rather than a nitpick. The thing you’re bringing up isn’t a nit; it’s a good point. I’ll add that to the list of reasons for the higher Con scores. Also a good point about moon druids. There’s only one druid in the current sample, and it went for high Dex, high Con, low Str. It’s 1st-level, of course, so I cannot say what the designer’s plan was, but maybe it’s not moon druid? 🙂
When I posted this, I expected maybe 10 readers. But given the interest it’s generating, I may now be compelled to do a more robust (and more statistically principled) exploration. If I start digging through more pregens, I’ll keep an eye out for the two different druid-build strategies. Thanks!
Part of the problem is how much is tied these stats. When you account for them, you’ve successfully dodged out of most saves. Wisdom covers a large amount of the “Save or Suck” things and is tied to your perception. Con covers “Save or Die” and HP. Dex has your AC, AoE saves and, in some cases, your to hit bonus.
Also, the Int based skills tend to be lackluster for the prepared players making these characters.
Locally though, my group tends to have higher average strengths and dumps charisma and intelligence. A large portion of my player base wants to smash things in the face…
I suspect that groups like yours are common. It’s an open question whether they are common enough that — if I were to somehow gather and analyze all point-buy and all standard array characters — the results would change significantly. Personally, I’d hypothesize that point-allocation habits vary significantly by “generation” — that is, by which edition a player started in. Folks who started with AD&D may still have a gut instinct, for instance, to go for that 18 Strength. (And then reach for the percentile dice. 🙂 ) My hypothesis could be wrong, of course. It’s certainly happened before.
Graham – as you probably well know I never take STR as a dump stat. I consider myself a West Coast Barbarian – i.e. there is no need for a good defense if you can kill it fast. I won’t bore readers with the Andy/Wallace high damage output combo and the havoc it wrought.
I think there is an interesting deeper dive here where we could look at stat dependency across game mechanics and find out if stats are balanced proportionally.
The fundamental problem with your assumptions is that, while you’ve nailed the stat distributions, you’ve failed to consider the laws of large numbers. To take medieval France into consideration, the population was about 20 million people. Even if the adventurer population was a mere 1% of that total (which is way lower than your values of 50% of 50% of 50% i.e. 12.5% eligibility), there would still be 200,000 of them. I’d further contend that by and large, the average level of an adventurer would be 3.4 or so, as that’s functionally about the time survival is optimized against the average common threat. Relatively few adventurers would be level 1… essentially people in their first year maximum…
The only thing I disagree with that you’ve said, Jesse, is that you think somehow you’re disagreeing with any of my assumptions. (You might want to read the population-engine article that this was a sequel to. There’s a lot of stuff that you’re getting into here that I didn’t re-dredge because I was attempting to build on the previous article, rather than repeat it.)
But let’s get to the part where it seems clear to me that you’ve misread what I said in the article that you have read.
I made the point that the percentage of the population that is adventuring drops off fast with each additional restriction. You and I agree on this basic principle, I suspect, but you think I stopped at just the 50% of 50% of 50%. I didn’t say the whittling stopped there. I said it drops off fast as you start adding Venn Diagrams. In that sentence (the one you are pointing at), I simply pointed to the top of the metaphorical slide.
But throughout the article (and in the previous article) I talk about the rest of that slide. To wit:
Characters with point-buy or standard arrays have minimum scores of 8, and each of those minimums reduces the pool still further.
Adventuring characters likely have at least a 14 in their primary stat. That also reduces the pool — more if you assume a 16.
If we make no other assumptions at this point, we’re looking at 2.8% of the population have a distribution equal to or better than 14,10,10,10, 8, 8.
But we’re not done. As I noted at the end of the article above, to have a reasonable chance of surviving, the character needs to have the higher scores in the right places. That adds another Venn cross section, because half of those characters will end up with at least one of their 8s in Dexterity, Constitution, or Wisdom.
Now our pool is 0.6% (less than your 1%).
Now we get to your second assumption: You assume that my argument says something about how many adventurers there are, total, rather than how often we bump into them. Those are different concerns. If the United States had 20 million people in it, and all of them were adventurers, you could cross Montana without encountering a single soul. Population density and percentage of population are the key variables here.
You’re making a second, unspoken assumption, too — one that I address in the previous article: Not every NPC who qualifies under these parameters is going to go adventuring. For instance, plenty of high-Intelligence people might become financial wizards rather than spellcasting ones, or translators rather than transmutators. I note in the previous article, for instance, that not everyone with a high Wisdom is going to be chosen by a deity to channel divine magic. Almost every character class casts spells, so the more restricted a world makes magic, the tighter that population gets.
But just for kicks, because I like this stuff, let’s go ahead and play around with an imagined adventuring population in medieval France.
And for bigger kicks, let’s assume that every qualifying character with a 14 or higher Wisdom gets recruited by a god. Every high-Intelligence character meeting the above qualities gets the tutoring that she requires in order to learn arcane magic. Every character with Strength higher than 14 gets training with martial weapons and medium or heavy armor. Etcetera. These are, of course, implausible. But let’s go with it anyway. Just for kicks.
You cite 20 million as the population of medieval France. Wallace Cleaves (my medievalist collaborator on this site) might have better sources than I do, but I’ll go with one I can cite, which gives 12 million for France in 1450. We’re talking about 83, 323 adventuring-class characters in a territory that’s nearly 250,000 square miles. When I calculate the Adventurer Population Density, I get .335.
So we’re talking about one adventuring-class character for every 3 square miles.
I have no idea whether that agrees or disagrees with the point you were trying to make. (Again, I think we’re agreeing on more than you think we’re agreeing on. It’s a fact of human nature: People read with their cynical hats on, prepared to look for what they are sure is wrong, and then, due to confirmation bias effects, sometimes read in ideas that aren’t actually there. And it’s entirely possible that I’m now doing the same thing back to you. If so, it’s not deliberate! 🙂 )
But I do think those numbers are interesting.
On one final point: You and I are completely in agreement about the relative scarcity of level 1 adventurers. I can’t tell whether you’re actually trying to disagree with me on that point, but in case you were, nope — we said the same thing. But I’m interested in your sourcing (or thinking!) for your estimate about “the time survival is optimized against the average common threat.”
That’s not a “show your cards” challenge. I’m truly interested in what you were thinking there.
Well, since you called me in, here is my medievalist comment. The maximum population of France in the period generally labeled medieval (and I’m excluding the “dark ages” here so lets say 1000 to 1500) was 17 million. I’ve seen claims higher and lower, but that’s a reasonable figure. That peak occurs at around 1300, what I refer to as “Peak Medieval” as the population had yet to decline as a result of the Little Ice Age (which handily starts right about the turn of the century) and the Black Death (1348 and on). Since I’m talking about it here I’ll shamelessly plug my own article on the subject of medieval periods in the “Get Medieval” series:
https://ludusludorum.com/2015/01/31/get-medieval-what-were-the-middle-ages/
I’ll leave aside the question of what exactly we mean by “France” in this period, and assume we’re talking about the geographic area covered by the contemporary country. In the middle ages France had some territorial issues, but the 17 million figure is for the modern country region at peak population. However, that was pretty dense for the middle ages and not really representative. I’d also argue, and have on this site, that D&D posits a much more unsettled background, but I digress.
Now, as to thinking about adventurer demographics, I actually think I may have an example or two to lend insight. It’s not a perfect analogy, but we might think of professional soldiers as being roughly equivalent to adventurers. Now, I can already imagine the screaming responses that most soldiers would be non classed conscripts. That would be wrong. Medieval armies actually tended to be pretty professional. They weren’t generally levied in the same way modern armies have been and large portions of those who fought in medieval engagements were serious professionals. I’ll try to explain my rationale and “show my work” below.
Lets take the Battle of Crecy as an example. I’ve chosen it because 1) it was one of the great conflicts of the Hundred Years war so people have heard of it, 2) it took place in 1346, just before the plague and still near the “Peak Medieval” population, 3) we have some pretty good stats on it.
The English forces were (and these are the conservative numbers) composed of about 2,500 men at arms. These are heavily armed and armored fighters. Their kit was expensive and they were highly skilled. If you want to argue that these aren’t adventurer-class fighters you are going to have to do some mental gymnastics to explain away their weapons and armor as they have all the heavy armor and martial weapon proficiencies of a fighter. They had 5,000 longbowmen. That weapon also takes serious proficiency built up over years, so again I think it’s reasonable to think of these as fighters. There were around 3,000 hobilars, or light horse. I’d still call these guys fighters as they were mounted and well equipped. The last group was 3,000 spearmen. There we have our levies, who arguably wouldn’t have class levels, but they are less than a quarter of the overall force. I’d say conservatively we have 10,000 very skilled, well equipped soldiers, most of whom have years of experience. These guys had been fighting all sorts of border wars and chevauchees for decades. They are adventuring-class fighters in my book. You can disagree, but then I’m not sure what the whole class idea means in the counter argument.
On the French side, the army was much bigger. Chroniclers put it between 80,000 to 100,000, but even the most conservative estimates put it at 30,000 men. The French had 12,000 mounted men at arms alone. These weren’t just professional soldiers. A significant portion of these were landed nobles and their highly trained and exquisitely equipped knights. If these aren’t adventuring-class fighters, I don’t know what is. They probably did have more levies and there are so many debates about the number of Genoese crossbowmen that I won’t even engage with that issue. Still, the French must have had something like 15,000 very highly skilled fighters using the kinds of armor and weapons that take years of training to use effectively, and they did use them effectively (the English far more so than the French, but that’s another issue).
What’s my point here? Well, in only one (admittedly big and important) battle at least 25,000 skilled fighting professionals duked it out on the field of battle with another 20,000 or so soldiers of various levels of proficiency. (If you are curious, about 300 English died and probably more than 2000 of the French men at arms, mostly nobility – a lot more of the regular troops probably died, but we don’t have reliable figures there.)
If we want to think about how many adventuring-class characters could exist in an area the size of France, I think these numbers at least give us something to go on. Having 83,000 or so adventuring-class folks might not be that far off. Sure, you can argue that many of these guys were from another country, or that they wouldn’t actually be adventuring-class, but I think we’re arguing semantics at that point. It’s also worth remembering that the 25,000 adventuring-class types in that battle was just overtly military folks. In a world with spell casting priests and wizards, I’m guessing there will be a lot more adventuring-class characters. I’ve discussed those numbers in the article Gray was kind enough to cite in his own excellent piece.