Population Distribution of Psionics

According to the math of 1e, Psionics are WAAAY more common than you thought. Hell, they're way more common than I thought, and I like psionics. Doing the math is really enlightening.

OK, so first of all, what is the basic probability of psionics? According to the Player's Handbook 1e, if you have an ability score of 16 or higher in INT, WIS, or CHA, you have a base 1% chance of having psionic powers. So the question then becomes, what percentage of people have ability scores that high?

First of all, from the basic odds of rolling dice: The odds of having a score of 16 is 6/216, or 1/36.

So, 1 in 36 people will have a 16 in, say, INT. 1 in 100 of them will have psionic power. Thus, 1 in 3600 people will have 16 INT and a psionic power. Think about what that means:

--In a city of 36,000 people, 10 of them will have 16 INT and a psionic power.

Now given that the base chance of having a 16 WIS or 16 CHA is the same as having a 16 INT, the 1% chance of psionics gives us the same number as well. Thus 1 in 3600 peole will have 16 WIS and a psionic power, and 1 in 3600 people will have a CHA of 16 and a psionic power.

--In a city of 36,000, 10 of them will have a 16 WIS and psionics, and 10 of them will have 16 CHA and psionic power.

Thus, in our city of 36K, we can expect 30 people to have psionic powers because of their single 16 ability score.

So what about people with scores higher than 16? It gets a little more complicated here because the Players Handbook gives different bonuses for high scores in the three different abilities. First, the basic probability of the dice: The odds of having an ability score of 18 is 1/216, and the odds of having an ability score of 17 is 3/216, or 1/72.

INT = 17

The score of 17 INT gives the person a +2.5% chance of having psionic powers. 1/72 has a 17 INT, and 3/100 of them will have psionics. Thus 1 in 2400 will have both. In our city of 36,000, we would expect to have 15 people to have INT 17 and psionic power.

WIS = 17

The score of 17 WIS gives the person a +1.5% chance of having psionic powers. 1/72 has a 17 WIS, and 2/100 of them will have psionics. Thus, 1 in 3600 will have both. In our city of 36,000, we would expect to have 10 people to have WIS 17 and psionic power.

CHA = 17

The score of 17 CHA gives a person a +0.5% chance of having psionic powers, but unfortunately, fractions are rounded down, so it remains the base 1/100 chance. 1/72 has 17 CHA, and 1/100 will have psionics. Thus, 1 in 7200 will ahve both. In our city of 36,000, we would expect to have 5 people to have CHA 17 and psionic power.

Thus, in our city of 36K, we can expect 30 people to have psionic powers because of their single 17 ability score.

INT = 18

The score of 18 INT gives the person a +5% chance of having psionic powers. 1/216 has a 18 INT, and 6/100 of them will have psionics. Thus 1 in 3600 will have both. In our city of 36,000, we would expect to have 10 people to have INT 18 and psionic power.

WIS = 18

The score of 18 WIS gives the person a +3% chance of having psionic powers. 1/216 has a 18 WIS, and 4/100 of them will have psionics. Thus, 1 in 5400 will have both. In our city of 36,000, we would expect to have 6.7 people to have WIS 18 and psionic power.

CHA = 18

The score of 18 CHA gives a person a +1% chance of having psionic powers. 1/216 has a 18 CHA, and 2/100 of them will have psionics. Thus, 1 in 10,800 will ahve both. In our city of 36,000, we would expect to have 3.3 people to have CHA 18 and psionic power.

Thus, in our city of 36K, we can expect 20 people to have psionic powers due to their one ability score of 18.



****In sum, because of single ability scores of 16, 17, or 18, we can expect a city of 36K to have 80 people with psionic powers. ****


Combinations of Ability Scores

Having multiple scores that are in the high range gives you a slightly higher chance of having psionic powers. The problem is, people are far LESS likely to have multiple high ability scores than just one high ability score. Thus, the people who have high scores in 2 or 3 abilities and a psionic power are much more rare.


17 INT (+2.5%) + 17 CHA (+0.5%) = 1/72 x 1/72, 4% base chance = 1 in 129,600
17 INT (+2.5%) + 18 CHA (+1%) = 1/72 x 1/216, 4% base chance = 1 in 388,800
18 INT (+5%) + 17 CHA (+0.5%) = 1/216 x 1/72, 6% base chance = 1 in 259,200
18 INT (+5%) + 18 CHA (+1%) = 1/216 x 1/216, 7% base chance = 1 in 666,514

17 INT (+2.5%) + 17 WIS (+1.5%) = 1/72 x 1/72, 5% base chance = 1 in 103,680
17 INT (+2.5%) + 18 WIS (+3%) = 1/72 x 1/216, 6% base chance = 1 in 259,200
18 INT (+5%) + 17 WIS (+1.5%) = 1/216 x 1/72, 7% base chance = 1 in 222,171
18 INT (+5%) + 18 WIS (+3%) = 1/216 x 1/216, 9% base chance = 1 in 518,400

17 WIS (+1.5%) + 17 CHA (+0.5%) = 1/72 x 1/72, 3% base chance = 1 in 172,800
17 WIS (+1.5%) + 18 CHA (+1%) = 1/72 x 1/216, 3% base chance = 1 in 518,400
18 WIS (+3%) + 17 CHA (+0.5%) = 1/216 x 1/72, 4% base chance = 1 in 388,800
18 WIS (+3%) + 18 CHA (+1%) = 1/216 x 1/216, 5% base chance = 1 in 933,120


--17 INT (+2.5%) + 17 WIS (+1.5%) + 17 CHA (+0.5%) = 1/72 x 1/72 x 1/72, 5% base chance = 1 in 7,464,960

--17 INT (+2.5%) + 17 WIS (+1.5%) + 18 CHA (+1%) = 1/72 x 1/72 x 1/216, 6% base chance = 1 in 18,662,400

--17 INT (+2.5%) + 18 WIS (+3%) + 17 CHA (+0.5%) = 1/72 x 1/216 x 1/72, 7% base chance = 1 in 15,996,342

--17 INT (+2.5%) + 18 WIS (+3%) + 18 CHA (+1%) = 1/72 x 1/216 x 1/216, 7% base chance = 1 in 47,989,029

--18 INT (+5%) + 17 WIS (+1.5%) + 17 CHA (+0.5%) = 1/216 x 1/72 x 1/72, 8% base chance = 1 in 13,996,800

--18 INT (+5%) + 17 WIS (+1.5%) + 17 CHA (+0.5%) = 1/216 x 1/72 x 1/72, 8% base chance = 1 in 13,996,800

--18 INT (+5%) + 17 WIS (+1.5%) + 18 CHA (+1%) = 1/216 x 1/72 x 1/216, 8% base chance = 1 in 41,990,400

--18 INT (+5%) + 18 WIS (+3%) + 17 CHA (+0.5%) = 1/216 x 1/216 x 1/72, 9% base chance = 1 in 37,324,800

--18 INT (+5%) + 18 WIS (+3%) + 18 CHA (+1%) = 1/216 x 1/216 x 1/216, 10% base chance = 1 in 100,776,960

Population Type and Distribution of PC Classes

The DMG 1e mentions (pg. 35) that only 1% of humans will have character-type classes (among other races, the ratio is 2%). Much like the typical game has way too much magic, I get the impression that the typical game also has way too many skilled NPCs.

The distribution of classes is listed as follows:
Clerics 20% (Druids 1/6 of those)
Fighters 44% (rangers 1/10, paladins 1/10 of those)
Magic-Users 20% (Illusionists 1/6 of those)
Thieves 15% (Assassins 1/6 of those)
Monks 1%


Thus, in a decent-sized small city of 10,000 people, we can expect a total of only 100 adventuring class NPCs:
17 clerics
3 druids
40 fighters
4 rangers
4 paladins
17 magic users
3 illusionists
13 thieves
2 assassins
1 monk

Pretty low numbers, if you think about it. In a small town of 1,000 people, there would only be 10 people with adventuring classes:
2 clerics
4 fighters
2 magic users
2 thieves

Think about the implications of that. It would take a small town of a couple thousand people just to equip the most basic of adventuring parties. In a village of 100 people, you would expect to find only find 1 person with a character class.

Any human is capable of picking up a sword and swinging it around, but the fact is, such PC equipment is bound to be pretty rare too. I mean, really, why would the average citizen have a sword lying around? They wouldn't have the money to buy it, nor the money and skills to maintain it, and it might be illegal to own in the first place.

In reality, the average citizen is going to have only "peasant's weapons", and no armor to speak of. For self-defense purposes, the average citizen would have a wooden club to bash things with, and a sharpened stick or second-hand spear to poke things with. In a pinch, they might swing an axe or scythe. There is a small chance they would have a small shield lying about, but that is it.

Finding a henchman or a pal to adventure with is going to be difficult. Only about 10% of those with class skills will be interested in adventuring employment at a given time, the rest being satisfied with their current situation. Thus, I think we can see the logic in why most fictional adventures took place solo, or just the hero with one sidekick.

Our idea of a "well-balanced party" is more or less just the product of the power-gaming mentality, wanting to be able to effectively hack-and-slash through any dungeoneering challenge. Adventuring with only one or two PCs makes the game playing much more challenging and high stakes. Thus, even Conan resorts to sneaking around, using his head, and planning good strategies, when it is just him and a couple low-level followers.