Friday, 15 May 2015

Ability Scores Revisited

I have not been deliberately neglecting the blog, it's just that other things have interested me more than D&D lately. If I'm going to provide players with a decent experience, however, I'll have to start doing some preparation instead of simply pulling things out of my arse the way I did last time we played. Mostly I've been engaged in paying my debt to society, and the primary means by which I accomplish this is coordinating part of the English program at a certain tertiary institution. One ongoing point of contention between the other parties involved in this process is the division of students into sections, or classes, according to ‘level’. The problem with attempting such a division is that we don’t have a large enough student body to divide anything but the most extreme outliers in any statistically meaningful way; that is to say, excluding a few students in the ‘highest’ group and a few students in the ‘lowest’ group, the overall performance each group isn’t much different.

So it is with ability scores in D&D: Without intimate knowledge of the way these scores are distributed among either the general population of the fantasy world or their analogs to capacities in the real world, we end up with a very faulty sense of comparison. 

It seems I didn’t make it clear last time that distribution of any ability score through a population is represented by a bell curve. The majority of the population will be in the first standard deviation by definition. If the range of ability scores is taken to be between generally 3 and 18 with 10 being the median, more than half of character scores will cluster between 8 and 12. (Bear in mind, however, that this median of 10 is not the mean or average for the population. More on that later.)

A number of points were raised at the session where the issue was first raised. First was the claim that advances in modern medicine have raised our overall health in such a way that the players present should have CON scores higher than average for a medieval or ancient world. I countered that in fact medicine has saved the lives of a large number of individuals who would not have survived to pass on their genes and reduce the overall CON of the population. The same goes for STR—few of us use it nowadays, preferring machines to do our heavy work, kill our food, and transport us long distances—we as players simply don’t, generally speaking, have the physical fortitude to withstand the rigours of premodern life.

I do, however, consider the innumerable maladies and lack of proper nutrients suffered by say, medieval peasants, and I roll their scores with a simple 2d6. In a feudal society, these make up the majority of the population. But this is not the stock from which player characters are drawn. Normal members of the well-fed, educated class into which PCs are generally born receive all stats on 3d6. Where access to information is severely limited and farming methods produce a three- to six-fold yield on seeds at best, this is generous. PCs themselves are yet above this still—they get 4d6, being allowed to discard the lowest die.

By this method, it is more likely than unlikely that every PC will fall in the third standard deviation on at least one stat, and usually more than one. In other words, PCs are by far among the best specimens of humanity.

Furthermore, players are allowed to allocate the final six numbers as they choose, in order to customise their characters. I have even been known to allow them to wheedle me into a point or two distributed differently because, for the sake of the game, I really want them to be happy with the characters they create. I want them to be attached and invest, caring about the characters advancement in order to be engrossed in the game.

A bit of personal history here. The first time in my life I rolled a D&D character, I was 12 years old and the DM was 11. Stubborn and high-handed as children that age can be, especially when they have a chance for some authority over someone slightly older, this DM was firm in the method he established for rolling characters: The six stats were generated in order, STR first, then INT, etc., each by 3d6. When it came time to roll my character’s CHA score and it came up a trio of ones, the DM said, without a trace of sympathy, ‘Rather repulsive, isn’t he?’

Now, we only played for about a year, during which I had only a smattering of poorly-executed and generally unsatisfying experiences in that campaign before rediscovering D&D in adulthood, but by the time I took over the role of DM for my current campaign I had already determined not to be that much of a dick.

The leeway my method allows for PCs superior to 95% of the human race. But since it seems really hard for some players to grok the deal they’re getting, I’ll have to provide some illustrative graphs.

Let me take a few seconds and roll up a stereotypical medieval peasant with 2d6. I toss my pair of dice six times and get the following numbers: 6, 4, 4, 3, 8, 8. Conceiving my peasant as a raggedy ploughman living in a squalid hut away from any opportunity to eat much or learn much, I arrange the scores thus:


He’s stronger and hardier than he is anything else, because his life depends on ploughing and he damned sure has to push that plough. As he lives on beans and peas, cabbage and watery ale, and is always a few calories away from starvation, he can’t bring his STR or CON higher than 8, and constant worry about survival has not given him much room for intellectual curiosity or any opportunities to make use of dexterity. As far as charm goes, the local gene pool is shallow and our man’s face shows it; besides, as his behaviour is a collection of nose-picking, farting, and poorly-articulated thoughts uttered in a cloud of halitosis through a mouthful of rotten and mangled teeth, his CHA score is lowest of all.

Now let’s move up an echelon and look at the ‘middle class’.

This is the stock whence most PCs come. Although they are a smaller demographic relative to the total population, their scores cluster around 10 because 10 is designated in the core rule books as average for adventurers. It is considered to be the median: While it is in the middle of the number set, it is far above the starving peasantry. The creators of the game had certain basic abilities in mind, such as average IQ being 100, an adventurer’s backpack being of a weight that a STR of 10 would allow him not to be encumbered by it, and so on. Among this demographic there are very few outliers of 3 or 18 on any score, so that any individual with either a very high or very low score is remarkable for it. The reason we have scores for, say, STR on parameters of 3 to 18 is to account for nearly-lame potential mages on one end and Conan the Barbarian on the other. There is a big jump from one point to the next. In IQ testing, 15 points is a standard deviation, and a difference between two individuals a standard deviation apart is often quite noticeable. Likewise differences in one point in any of the other five ability scores. 

To illustrate, I generate two characters who could potentially become adventurers in a medieval English setting. Rather than rolling dice, these characters are generated automatically with set numbers one standard deviation apart: Rounding up, this equals two points of difference. 

Adam the Average has a 10 for each of his ability scores. His pack weighs less than 40 lbs. With average intelligence, he speaks only his native English, but he is trying hard to learn French because it would help him advance in the world. He is neither particularly wise nor dexterous, but neither is he a fool or a klutz. He has been fairly frugal and has worked hard, and has saved himself just enough to buy a decent sword and tent to start off on his trek. Since he was reasonably well-liked in his community, his friends and relatives might have given him a bit extra and helped advise him on other essentials he might need, like a whetstone and oiled scabbard, and a carpet for his tent. His chances of success on his adventures are moderate. After all, with 5 HP (half of CON), two median-damage stabs with a sword will do him in.

Stephen the Superior, on the other hand, has a 12 for each of his scores. His pack is still comfortable at 45 lbs., and he can carry 25 lbs. more over his head than Adam can. With an IQ of 120, he is well in the ‘exceptional’ range, and is fluent in English, French, and Catalan. He can read difficult texts and write articulately—and probably, with a CHA of 12, somewhat persuasively as well. His reputation is good, and by a combination of his popularity and finesse with his shrewd management skills, he has enough to buy a good sword, as well as a decent bow and several other accouterments, and he knows how to put them to good use. He has 6 HP, which means that the two hypothetical median-damage sword stabs that would certainly kill Adam would leave Stephen bleeding and in pain, but alive.

While any character can become a fighter so long as he has a STR of 9, he will be at a significant disadvantage in combat even against Adam the Average. When all ability checks are made against a d20, a difference of one point puts a 5% chance between success and failure. At two STR points lower than Stephen the Superior, Adam the Average is not ‘slightly weaker’. He is catastrophically weaker.

Strength differences appear as follows.

Adventurer stock strength distribution.

In ancient Greece, where our campaign takes place, a man of Conan’s strength is already extremely rare, existing perhaps once in several thousand individuals. I don’t have the data handy for distribution in our modern, mostly sedentary, society, but I’m persuaded that the median clusters closer to 5 than to 10, with a man of Conan’s strength being found singularly in closer to a million individuals. Extreme outliers, while they do exist, would be almost invisible on a chart of this type; men like Brian Shaw and ┼Żydr┼źnas Savickas are world famous precisely because only a handful of them exist in a population of several billion. They represent STR of perhaps 18/00, the highest theoretically possible for a human being. 

Intelligence, however, ostensibly remains constant throughout history; probably because IQ tests, whatever they measure, must be adjusted periodically as the general population gets better at taking tests. Regardless of which explanation you like to attach to the Flynn effect, though, average IQ is 100 by definition. 

Intelligence distribution.

Numerous websites claim IQs well off the chart for famous people—220 for Isaac Newton and Leonardo da Vinci, for example—but these are conjecture as these people died long before testing, but such claims reinforce that these individuals were clearly extreme outliers. The same standards apply to every score—including CHA, with the far left representing most lepers, through plain folks in the middle and extending through actors to politicians to world leaders. 

Charisma distribution.

With CHA of 4, the character draws taunts and abuse wherever he goes, and is shunned by society. People who come across as cold or 'standoffish' would represent the charismatic equivalent of dull normal. Adam the Average has an ordinary number of friends and gets along with half of the people he meets. Stephen the Superior has lots of friends and gets along with most of the people he meets. The fictional character of Don Juan has enough charm--or knack for manipulation, depending on your politics--to bed nearly any lady he desires; he could amass a handful of henchmen if he chose, but he prefers so substitute romance, with six love affairs at once being analogous. (The Players's Handbook gives a maximum number of six henchmen for a CHA of 14.) I hope I don't have to fill in all the spaces between Don Juan and Napoleon to make my point clear. Napoleon had a core of dedicated henchmen through which, in combination with military might, he managed ultimately to rule over several million people. 

So when I hear, ‘My character is worse than I am in real life’, it sounds like someone who has only been in a rickshaw saying, ‘Man, that Ferrari you gave me is slower than my legs’.

Edit: It turns out transparent .gifs don't show up so well on Blogger. If their illegibility fails to make my point, I'll fix them later. 

1 comment:

  1. This was enlightening. Thanks for taking the time to put this into perspective like that. I think the key thing (or at least what I hadn't really thought of) is that the scale goes from one extreme to the next in such a way that the space between the points is rather large. That is, a 10 and 11 being very different, even though at first glance it doesn't feel that way.