Confession Time: This is not the article I intended to post today. I simply ran out of time – after my sense of the day-of-the-week was thrown off by the Holiday Season, leading me to start late. Normal service will be resumed as soon as possible!

Over the last few weeks, I’ve re-read the Foundation series by Isaac Asimov. I’m sure most of you are familiar with the premise: scientist develops a statistical treatment for predicting the future, discovers that the Galactic Empire is past saving, but develops a plan by which the intervening dark ages can be cut from 30,000 years to just one millennium. In later years, he revisited the original trilogy with additional titles such as Foundation’s Edge which modified and expanded the core concept a little, reflecting the somewhat simplistic view presented originally, but that remains the core premise of the stories. From that foundation (no pun intended), the narrative describes the history of the “Foundation” which is to form the nucleus of the new Galactic Empire.

Every time I read this series, I am reminded of how much Psychohistory resembles some of the rules of an RPG – or should that be the other way around?

The Statistics Of A World

Most fantasy games don’t bother with whole-world statistics; being conducted at a more “human” level, there’s no need. Most science-fiction games, on the other hand, deal in multiple worlds, and therefore need some means of describing them and their relationships. This has been true ever since original Traveller, and I don’t expect it to change any time soon. The simplest such systems cover planetography, population levels, socio-political structure, planetary wealth, tech level, and law level – and most people reading this will already know what those terms mean, they are reasonably self-explanatory. More complex systems may deal with biosphere, climatology, ecology, and any number of other sophisticated and complex subjects. In order to make these useful in a game setting, they need to be reduced to a series of quick tables, one per subject, describing the standard characteristics of a particular type of world within the parameter specified. The most sophisticated systems actually use hidden logic to bias the results on subsequent tables according to the results of earlier tables, restricting randomness in the name of rationality and conceptual cohesiveness. For example, if you picked “Desert World”, the system would consider the impact of that environment on the society and modify the likelyhood of a given social structure accordingly, then use that result to modify the Law Level, and so on.

As GMs, we are interested in generating one world at a time, and as a result, we don’t tend to tend to see the forest for the trees. This is where “psychohistory” and RPG world generation go in different directions: We use the equivalent of “psychohistory” to develop profiles of individual worlds, rather than gathering statistics on hundreds, thousands, or even millions of worlds and using them to generate statistical profiles.

Does that mean that there would be no value in our using a computer program or spreadsheet to generate a statistically-significant number of worlds and then analyzing the results? Most GMs would say yes, but I have a different opinion.

You see, another of our characteristics as GMs is that we love to tinker with rules, especially when it comes to random-generation tables for things like worlds. But because in those sophisticated semi-random systems, changing one variable’s probability profile can have significant flow-on consequences, we are often in the dark as to the large-scale ramifications.

For example, if we decided that dry worlds and water worlds were both just a little more probable than the sort of “balanced” world that we live on (because they are exotic and a little more interesting), that could alter the number of planets with a given social system, or law level, or any number of other factors. It would mean that certain forms of technology would be more economically productive than others. It would mean dietary changes – fewer land animals and more seafood. Spices derived from shells would probably be more common, and hence cheaper, while other spices might be more exotic and expensive. “Farm worlds” with substantial arable land would be politically more significant, and wealthier – they would be objects of desire in wars. All that would tend to concentrate military power in such locations, and political power usually follows – so the galaxy is divided up into small fiefdoms consisting of a farmworld “capital” in the centre and a surrounding halo of desert worlds and water worlds.

If we knew all this in advance, we could tailor campaign backgrounds appropriately, and generate appropriate adventures that feel like they “fit” the environment, adding to the verisimilitude of the whole campaign.

If we don’t, the campaign background will not quite fit the galactic “environment” and the adventures will not quite ring true. This can undermine the campaign in ways that the GM can’t predict, and he will never be entirely sure of why it didn’t work.

The Simulation Of A Nation

National simulations tend to be a lot less developed, and may even be omitted altogether. Many games tell the GM to pick a government type and a wealth level and leave it at that. That can be because the authors realize that many of the genre conventions tend to fall apart when analyzed closely, especially in fantasy games.

Don’t believe me? Try this exercise for size:

One-in-five D&D adventurers (let’s say) survive to progress to the next character level. The rest either retire or are killed. Let’s further assume that one in four retire, and three in four are killed; and that it takes an average of 6 months to gain a character level. When characters reach 20th level, there is nowhere else to go, so they will retire and start doing something else. If humans start earning character levels at the age of 16, and the average human lifespan is 35, how many adventurers of a given level are there in a Kingdom of 100,000 people?

First of all, one in five progression means that for any given character level, there are proportionately five times more characters at the next character level down. So, we can do a table relating character level to population representation:

20= 1
19= 5
18= 25
17= 125
16= 625

…and so on, until we reach:

1= 19,073,486,328,125 (a blatantly ridiculous number).

Next, we can count the number of retired or dead adventurers by subtracting the results of each level from the results one level higher:

19= 5-1=4
18= 25-5=20
17= 125-25=100

… and so on, until we reach:

1= 15,258,789,062,500 (still an outrageous number).

Applying the 1-in-four retirement vs. death ratio gives the number of these who survived and retired:

19= 4x 1/4 =1
18= 20x 1/4= 5
17= 100x 1/4= 25

Recognize this? It’s the same pattern we started with, just stepped down one level. Eventually, we will reach:

1= 3,814,697,265,625 (yet another outrageous number).

Next, let’s look at the aging progression: At 6 months per character level, it takes 10 years to reach 20th level. Presumably, all survivors who reach 21st level will retire, as described in the assumptions. Starting at 16, the characters will be 26 years old or less when they retire – leaving them with 9+ years before they reach the average age of death, and then an increasing likelyhood of death over the next 35 years.

You can look at the 6-month timeframe as establishing a “school term” length for adventurers (presumably the school of hard knocks) [assuming a stable population level, for simplicity]. What we have looked at so far are the relative proportions for just the students who enter in a given “school term” – six months later, there will be another, and six months after that another, and so on.

With this approach, it can be seen that the number of retired adventurers of any given character level will be the number from the current ‘school term’, plus the number from the previous one, and the number from the year before that, and so on.

1 (current) + 1 (previous) + 1 (before that) and so on gives 20 “school terms” whose members still have active adventurers, plus (9 years / 6 months = 18) more who have not reached the average death age, plus an equal number past the average age of death (by definition), or:

2 x (20+18) = 2 x 38 = 76 = the multiplier to convert the single class numbers to the whole-population numbers.

But, since we’re only interested in the proportions, and this multiplier applies to all character levels, we can ignore it, and stick to our already-established ratios.

When you do the math, it works out that 81% of retired adventurers are 1st level, 15.4% are second level, 2.9% are 3rd level, and the remaining 0.7% is spread amongst the other character levels.

Or, to put it another way, out of every million adventurers:

810,127 will be 1st level
153,924 will be 2nd level
29,165 will be 3rd level
5,509 will be 4th level
1,037 will be 5th level
194 will be 6th level
36 will be 7th level
7 will be 8th level
1 will be 9th level
And everyone of higher level is swallowed in rounding error – so there’s less than 1 of them..

Without knowing the ratio of adventurers to non-adventurers, that’s as far as we can go.

Why This Doesn’t Work

Characters tend to encounter enemies of roughly their own character level. If you’re 8th level, you can expect most encounters to be with characters of 6th to 10th level. This is done because anything else is less interesting to play. But it’s not reflected in the population stats.

So the entire concept falls apart when any sort of basic mathematical analysis is applied to it. That means that there is something wrong with our base assumptions, or there is something wrong with the game system that we are modeling.

The key number here is the “1 in 5”. Not only is this not very reflective of the typical PC experience, it is the reason we get such ridiculous numbers for the first level population. Now, I’ve seen suggestions over the years that this number should be as high as ten-to-one and as low as 2 to 1.

At 2 to 1, there will be 4 characters of 16th level for every million population, so this is a far more reasonable number. But it has a marked effect on the average level – it goes from what is obviously 1-point-something-low to 3.6. Or to put it another way, more than half the population have at least 3 levels.

Economic Impact

You get even more interesting numbers by applying the average character wealth from the DMG to the different population levels. The results show a marked “lower class” at low levels, to a dominant economic class, and then a diminishing share of the overall economy as levels rise still further. There are lots of calculations and assumptions that go into these results, but the general pattern remains – characters at or near the average number of levels have substantially more economic power than those removed from that average. Higher level characters have more wealth but this is offset by a paucity of representation; Low-level characters have little wealth but great numbers; and somewhere in-between, there is a ‘sweet spot’ in which these two factors give a single population subgroup many times the economic power of anyone else.

The Value Of Understanding

In fact, by using the average wealth, you can work out from the overall wealth of the country how many adventurers they have (on average), and from that, the population.

But how much more useful would it be to have a set of tables or calculations that combined national wealth, socio-political structure, and a base population level, to determine the relative representation of different character levels? To know, up-front, that there was (say) a 4% chance – one-in-twenty – that any given NPC would have 8 character levels?

How would such knowledge affect player behavior?

How would such knowledge – assuming it was comprehensive and not limited to this single factoid – affect the way the GM thinks about his game world?

Population Dynamics

Sadly, this sort of analysis is not available, and it doesn’t take much analysis of the quoted numbers in any rulebook to determine that the reason is that it wasn’t done by the designers. Instead, they usually seem to pluck numbers out of thin air that “seemed reasonable at the time” without testing them for validity.

In fact, I’ve only ever seen one game product that even made a start on the subject – “Medieval Demographics Made Easy”. This was a PDF that I obtained through RPGNow, from memory, but at the moment it is not available from there – even if memory is not playing me false. Fortunately, it lives on through this website and the tools that it links to.

The reason for this is simple: it’s extraordinarily hard to do. It takes easily ten or twenty times as much time and effort per page of game supplement – and I speak from experience, as I have such a project currently sitting on the backburner at 20,800 words or thereabouts. It was supposed to be about 10,000 words and take a month to write; instead, it will be three or four times that length (when finished) and have taken well over 6 months. Along the way, I’ve easily done 100,000 words of analysis and logic that won’t appear in the game product when it’s finished, beyond a quotation of the end results.

The Reactions Of Fictional People

Everything in a rules system can be subject to this sort of statistical analysis. For example, taking rules for NPC attitude adjustment and applying them to a statistical population can be used to determine how the general population will react to any given situation, in broad terms, how favorable treaty terms will be, how successful that population group will be in negotiations, and so on. It doesn’t take a huge understanding of the history of the 20th century to observe the impact that these things can have on a population – one of the major reasons for World War II was the impact of the Treaty of Versailles on Germany.

Elves are often described as being a “fair” race, very attractive to look at, well-spoken and facile of tongue. How many GMs have considered what that means in terms of the diplomatic prowess of the race, and the accumulated impact of who-knows-how-many negotiations with outcomes slanted in the Elvish favor?

Throw in the average lifespan information provided, which shows various races as living much longer than humans. Yet, this doesn’t seem to show up in their skills – an elder Elf should be an expert in a dozen or more fields and a dilettante or hobbyist in at least twice that many. There should be specific details given with the race concerning this; there isn’t. There should be specific rules about characters with out-of-date skillsets; there is not.

How much more formidable does an Ambassador become after an extra 50 years or more of experience?

Too few GMs take the time to think about these aspects of their game world and its populations, then extrapolate to a broader political and social expectation.

This Means War!

It was by applying these techniques to the rules of standard combat that I developed the game systems that I presented in my multipart Blog Post, ‘This means WAR! Making huge armies practical’ in March 2009. I can’t think of a better illustration for the principle (or conclusion to this post) than pointing readers who have not come across it in the past to that 6-part series of articles.

Have a great week at the game table!

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