Image Credit — freeimages.com / Piotr Ciuchta

I’ve been holding off on this article for almost 9 months because I wanted to make sure I had an RPG connection. Last week, I finally found it.

2016: The Myth

2016 is perceived to have been a horror year for the loss of celebrities. One famous face or voice left us after another. It started with David Bowie early in January, and ended with the departures of George Michael, Carrie Fisher, and Debbie Reynolds late in the year. I think it was in late August (Gene Wilder) that I first saw social media suggestions that 2016 was a Horror Year, and that was when this article began percolating in the back of my mind.

First, though there were any number of people whose loss I mourn, who enlivened and enlightened my world, 2016 didn’t seem that much worse than 2015 had been; and second, it didn’t come as any great surprise to me. I’ll get to the latter point in a little bit, but first, let’s look at the question – just how bad was 2016 for celebrity deaths?

2016: The Statistics

Using the resources of Wikipedia’s list of deaths by year, I performed an only slightly scientific analysis. For the years 2012-2016, I counted up the number of deaths of people whose names I recognized, and because we’ve had four months of 2017, I also kept a separate count of the number of deaths for the first four months of the year. If my theories – which I’ll get to shortly – were correct, 2017 would be no better than 2016 or even 2015, or not much so, anyway. You can see the results to the right. It contains both what I expected to find, and a surprise or two.

The first thing that I noticed was in the April results, which showed a clear trend over the 2013-to-2016 range. That’s very close to a straight line.

The second thing I noticed is that 2013 was a very good year for celebrity deaths. Both the April and Whole-year numbers are significantly down on the years to either side of it.

The third point is from the overall numbers, showing that – in terms of the celebrities whose names I recognized, which include musicians, actors, directors, politicians, sportsmen, and authors – 2015 was indeed slightly worse than 2016, but they were close enough to be comparable. So why was 2016 perceived as being so much worse than 2015? The answer seems to me to lie in the peak in the end-of-April numbers. This created a subconscious predisposition that 2016 was going to be a bad year. In fact, the remainder of 2016 was not as bad – if the 2015 rest-of-year were applied to the 2016 start-of-year, 2016 would have a total of 41 significant losses, not the 35 that were actually recorded.

The end of April is 1/3 of the year, or close enough to it. So you would expect the April numbers to be about 1/3 of the total. In 2012, the ratio was 1/5; in 2013, 1/6; 2014, 1/4; 2015, just over 1/3; and 2016, a smidgen higher again. This is another key to the perceptions of both 2015 and 2016 – it wasn’t so much that they were worse than expected as that the three years before them were so much better.

It can be argued that in fact, the perceptions of 2015 and 2016 were the consequences of better-than-the-odds numbers of celebrity mortality in the preceding three years, that some of those who passed away managed to beat the odds long enough to claim a couple of extra years on this planet. From that perspective, the high number of celebrity deaths in 2015-2016 were something to celebrate!

But there’s more to the story. These results were (mostly) pretty much what I expected to see, even before I opened the website to do the research. What’s more, the reasons for that show that years like 2015-2016 will be happening again and again over the next few years. While the start of 2017 has not been as bad as 2016, it has been very much on-par with 2015, and I expect the rest of the year to follow a similar pattern.

Inevitable Mortality in the Modern World

As preamble to the reasons for expecting these things, it’s worth taking a quick look at the causes of mortality in the modern world.

Accident

While death from accident can and does still happen – Paul Walker in 2013, for example – for the most part, that is a relatively small contributor to celebrity deaths, a distinguishing characteristic relative to the general population. While having the financial resources to ensure the best care does help mitigate the consequences of accidents slightly, a far bigger factor is avoiding accidents in the first place. As a general rule – again with exceptions – most accidental deaths suffered by celebrities occur when they are doing something extreme, either in a relative wilderness setting (Lisa Lopes of TLC in 2002) or involving a vehicle of some kind (Walker again), and the reduction in mortality from accidental causes is more related to a reduction in incidence of lethal accidents in general for celebrities relative to the general population.

Violence

Relatively few celebrities die from violent circumstances, though there are tragic exceptions. John Lennon, for example, murdered in 1980, or Bob Welch, the former guitarist for Fleetwood Mac who had commercial success with “Ebony Eyes,” “Sentimental Lady,” and “Precious Love” in the late seventies, who died from a self-inflicted gunshot wound in 2012. While Celebrities may be the targets of violence, due to their perceived affluence, they can also usually afford better protection and security, so violence is an uncommon cause of death in this subpopulation.

Addiction

With two major causes of mortality relatively reduced in significance, those that remain are heightened in prevalence. Death from addiction, in the form of both legal and illegal substance abuse, remains a high risk for celebrities. A combination of the pressures of the various occupations that made them famous, the relative availability through the social ‘scenes’ they inhabit, and the financial wherewithal to satisfy such needs is responsible. This is a problem that particularly afflicts those at the younger end of the age scale.

I can never discuss this subject without thinking, first, of various interviews with Alice Cooper over recent years, secondly of Aerosmith, third of Keith Richards, fourth of Joe Walsh from the Eagles, and fifth of Stevie Nicks.

Cooper has said a number of times that it was discovering blood in his vomit that prompted him to give up alcohol, and that he then took stock and noticed how few of his hard-drinking friends were still alive. In particular, he attributes many of his problems to his friendship with The Who’s drummer, Keith Moon. ‘The difference with Keith Moon — with most celebrities, only ten percent of what you read about is true. With Keith Moon, you’ve only heard about ten percent of the stories and they’re all true,’ he said during his appearance on Top Gear (the quote might be slightly incorrect but is accurate in meaning and sentiment).

Aerosmith, famously, were growing in popularity until drug addiction took their toll on the band, Joe Perry and Brad Whitford leaving as a result. Eventually, the band reunited and completed successful courses of rehabilitation before reigniting their careers and resuming their upward trajectory in popularity through their well-known collaboration with Run-DMC. These days, they speak openly of the period when drugs ruled their lives and take great pride in being clean.

Keith Richards had a reputation for drug use in the popular zeitgeist that far outstrips the reality. He kicked his heroin habit in 1978, and stopped using cocaine after requiring surgery when he fell out of a tree in 2006; when discussing the subject, he often says that he simply “got lucky” whereas a number of his fellow musicians such as Bryan Jones, did not.

In “The History Of The Eagles,” Joe Walsh spoke very poignantly about his addiction – ‘There was a time, very briefly, where it helped [creatively], and then it stops working and you start to chase it’. This always resonates for me with the Beatles and their experimentation with (then-legal) mind-expanding drugs in the mid-60s, when there was a perception that drugs could stimulate creativity.’ Without LSD, it was often said, Jimi Hendrix would not have been as brilliant or successful as he was; what no-one thought to ask was whether or not he might have been even better and bigger without them’ – I forget who gave that statement (which I am sure I am misquoting, but the gist of it is accurate) but it places the celebrity drug culture into real perspective. David Bowie expressed similar thoughts about his collaborations with Brian Eno and Robert Fripp in Germany.

Many others have spoken on the subject over the years, but these vignettes touch on most of the key themes common to these stories. It might be a false impression, but I get the personal feeling that such cautionary tales have seeped into the creative community over the years and drug abuse by celebrities is diminishing as a cause of death as a result.

Cancer

There are three medical conditions which are largely unresponsive to the better health-care available to the wealthy and famous, and hence figure more frequently (in relative terms) in celebrity mortality. The first of these is Cancer, one of the leading causes of death globally. One question that I have frequently debated is whether or not Cancer is a product of the industrial revolution, or whether the potential was always there for it to be a massive killer, but people died before that could manifest. I used to lean more toward the former, these days I think the latter is more probably true, but if you asked me again next week, you might get a different answer.

For a long time, Cancer was perceived as an old person’s disease, but it is now recognized that people in their twenties and thirties can experience the disease, and some forms can even afflict children. However, age seems to have a profound effect on survivability – my impression is that it’s a case of accumulated damage reducing the body’s capacity to cope with the side effects of the medication, while also increasing the number of compromised systems that can become terminal conditions.

Cardiac Arrest

The second of the major medical conditions is what is commonly known as a heart attack or heart failure. The fact is that, with prompt care, about 22% of those who experience a cardiac episode will survive; that’s the survival rate where the experience takes place in a hospital situation. Where the incident occurs outside of such a setting, without medical care at hand, survival rates drop to only 7%. And that’s despite the modern awareness of the dangers involved, and all the apparatus of ambulance services and early diagnosis of the risk factors.

Cardiac problems, in other words, usually kill too quickly for medical assistance to make any difference. The consequence is that cardiac arrest doesn’t play favorites.

Stroke

Between 1990 and 2010 the number of strokes which occurred each year decreased by approximately 10% in the developed world and increased by 10% in the developing world. In 2015, stroke was the second most frequent cause of death after coronary artery disease, accounting for 6.3 million deaths (11% of the total), worldwide. About half of people who have had a stroke live less than one year.

About 75% of those who experience a stroke suffer sufficient disability that enjoyment of life is impaired. Despite ranking as the number-2 killer, world-wide, around 75% will survive their first incident [Stroke Statistics: 9 Sobering Survival Facts You Should Know]. Putting that information together with that in the previous paragraph paints a grim picture: a stroke is probably a death sentence, but you may linger long enough to suffer before the end.

Strokes are principally an old-age condition. 2/3 of all strokes occur in people 65 years or older, and 95% of them take place in people 45 years or older.

AIDS

HIV is believed to have originated in west-central Africa during the late 19th or early 20th century. AIDS was first recognized by the United States Centers for Disease Control and Prevention (CDC) in 1981, and HIV identified as the cause a few years later. While there are tragic exceptions, in particular transmission from mothers to unborn children, the majority of human cases stem either from intravenous drug use or gay sexual practices. But that wasn’t known in the early 80s, as the documentary “Queen: Days Of Our Lives” makes clear. Through the course of the 1980s, the number of people living with the disease rose steadily to about 800,000 in the US, while the number of new cases steadily declined. For the next five years, the number of cases stabilized, indicating that deaths and new cases were roughly equal. From 1995 onwards, the number of new cases declined steadily while the number of cases of survivors grew steadily. At around 2006, the rate of increase began to slow, but still to increase steadily; by 2012, about 1.2 million people were living with the disease.

That is only possible if survival rates rise, i.e. if mortality rates decline. Celebrities will continue to die of AIDs, but more often it will be the result of AIDS-related complications to other medical problems.

AIDS deaths were not age-related, but with the problem becoming chronic more than directly-terminal, that is changing.

Other

There are lots of other ways for people to die, but between them, the selected list above accounts easily for the vast majority of deaths, celebrity or otherwise. What’s clear is that while celebrities are no more immune from them than anyone else, celebrities have the maximum opportunity to take care of themselves and thereby to delay or reduce the majority of the risks involved.

Susceptibility By Era

With that preamble, let me turn my attention to explaining the reasons why I was not all that surprised by the compiled results of my research. To do so, I need to look at when celebrities became famous.

The Pre-60s

Most people become celebrities in their 20s and 30s. A few manage it while younger, and a few when older, but that’s certainly the peak age range. Anyone who became famous before 1960 would therefore probably have been born between 1920 and 1939. That places them in the 77-96 age bracket in 2016. While there are a few who survive for that length of time, they are few and far between, and even fewer would also happen to be celebrities for some reason other than their age. It follows that every celebrity from this era is either gone or will probably leave us over the next decade. There were no less than 13 celebrities of this vintage who departed this mortal coil in the course of 2016 (whose name I recognized, the yardstick of celebrity that I am employing). 13 out of 36 is a significant percentage, almost one third. That can’t be particularly surprising. With every year that passes, there will be fewer representatives of this historical period remaining, and so this number is likely to drop precipitously in coming years. People like Cliff Richard and the remaining members of the Beach Boys are likely to soon leave us.

The 1960s

The early boom in television took place in the course of 1960s. The Beatles instigated a seismic shift in music and popular culture in 1963-4; they and the many musicians who were inspired to enter the industry following their example skew the average celebrity age younger from this time onwards. The explosion in popular culture greatly increased the number of living celebrities.

If you became famous in the period 1960-1970, you would have been born in between 1930 and 1949, and in 2016 you would have been between 67 and 86. It should come as no surprise that a great many celebrities of this vintage have also passed away, but the vast increase in numbers ensured that a few would survive to this point. Virtually all of these early stars can be expected to pass away in the next 10-20 years, and most in the next decade. The surviving Beatles and The Rolling Stones amongst them.

A decade earlier, and members of this age group would have ranged in age from 57 to 76. While a number of the older members would probably have passed away, most of the younger ones would not be in extraordinary danger. This is the group most likely to figure prominently in the obituary columns over the next decade.

The 1970s

The seventies saw a further groundswell in popular culture. Television brought forth stars in ever-increasing number, as did popular music. If you became famous between 1970 and 1979, you were probably born between the years 1940 and 1959, and in 2016 you would have been aged between 57 and 76. This is the age bracket at which mortality becomes pronounced; most people can expect to live that long, accidents and addiction-related deaths excepted. There will always be exceptions, people who passed away despite youth, but people in this age bracket are just starting to enter the danger zone. This, therefore, is the group whose numbers are most likely to grow, year-on-year, in terms of presence in the obituary columns. And that, combined with the boom in numbers of celebrities, means that obituary lists are only likely to grow in length over the next decade.

Carrie Fischer was merely one of the early casualties of her generation.

The 1980s

The 1980s brought the commencement of cable television and MTV and a new explosion in popular culture, but many of the newly-discovered ‘stars’ had been around for years without achieving the celebrity prominence they enjoyed thereafter. This, then, was the decade in which the imbalance caused by the ‘youth factor’ in the 1960s and 1970s began to fade from prominence.

Celebrities who became famous between 1980 and 1989 were probably born between 1950 and 1969. In 2016, they would have been aged between 47 and 66 – young enough that death is unlikely enough to shock, and yet a certain percentage are always going to pass away. Larry Drake, Prince, and Jerry Doyle were celebrities of this age bracket who were lost to us in 2016. George Michael was at the younger end of the age bracket, having been born in 1963.

While a few celebrities aged in this bracket will pass away each year, unless AIDS, Drug abuse, or Accident are involved, most will be with us for at least another decade. That’s when it starts becoming more problematic. Celebrities of this vintage will dominate the obituary lists of 2026-2035.

The 1990s and Beyond

The younger the celebrity, the more cheated we all feel when they meet an untimely demise. Of the handful of individuals listed by Wikipedia as having passed away from this age bracket in 2016, none had names that were familiar to me – not even the Australian Tennis Player. In 2015, however, there were three names that I recognized from this age bracket.

Most people who became famous in the 1990s, or more recently, will still be with us for the next 20 years. Mortality rates will only become significant for this age bracket in 2036-2045, assuming no significant medical breakthroughs – but that’s twenty to thirty years from now, so that’s a rather fraught assumption.

The Passage Of Time

Each decade of the forty-year period 1950-1990 saw a new boom in the numbers of celebrities. Those celebrities are aging with each passing year. 2000 brought the celebrities of the 1950s into the age bracket at which mortality becomes significant. 2010 did the same for those who became famous in the 1960s. 2020 will do likewise for those whose fame began in the 1970s. Each of these waves of celebrity is larger than the one before. More television channels, more new TV shows, more channels for the promotion of music, more televising of sports – more opportunities for people to become famous.

On top of that, syndication and secondary channels and classic-TV channels and new distribution channels for movies and music tend to keep refreshing the fame of such stars. A quick glance at today’s TV schedule for my local region reveals repeats of Charlie’s Angels, Friends, Dr Quinn Medicine Woman, JAG, M*A*S*H, Hogan’s Heroes, DCI Banks, Bewitched, I Dream Of Jeannie, Who’s The Boss, Diff’rent Strokes, Married With Children, Heartbeat, Judging Amy, Becker, The King Of Queens, Rules Of Engagement, Everybody Loves Raymond, Frasier, Get Smart, Cheers, Matlock, Jake And The Fatman, Diagnosis Murder, Star Trek The Next Generation, The Nanny, Top Gear, Two And A Half Men, The Simpsons, How I Met Your Mother, The X-files, South Park and Mythbusters. On the movie front, we have repeats of The Pelican Brief, Speed, Beverly Hills Cop II, and the Monuments Men. And that’s all on free-to-air network television, not even looking at the various cable-tv channels dedicated to “oldies” and “classic movies” and so on. At least twelve of those TV shows star people who are now deceased but who live on through their work. Their celebrity – like those of the stars who still live from those shows – is being constantly rejuvenated.

The upshot is that, with each passing decade (for the next few to come, at least), there will be more celebrities to die and more of those celebrities will be in the higher-risk brackets for mortality – inevitably resulting in an increase in the number of celebrity deaths each year, until some measure of stability is reached in the middle of the century.

Mortality in an RPG

I promised at the head of this article that all this has some application to RPGs. No, I’m not going to suggest that RPG creators and bloggers are celebrities. Instead, I’m talking about famous NPCs within a campaign.

Let us say that 30 years ago, there was a terrible War. Or maybe it was 40 years ago. And another two decades earlier. How many surviving veterans of that first war would there be in your campaign? How many people would have memories of that time?

To answer this question, you need to compile actuarial tables for your campaign world. And that’s not quite as simple as it sounds, because these tables need to reflect your campaign history. And there are all sorts of tools that you might need.

For example, let’s say that you have an expanding Kingdom, and that the dangers are three times as great in a fringe around the edges of the civilized lands. Let’s say that the Kingdom has been doubling in area every eight years, and each time it does so, the fringe increases in width by 20%. Let’s further state that 65 years ago, the civilized Kingdom was 31,416 square miles in area and the ‘fringe’ was a fifty-mile-wide band around the perimeter.

This is a pair of fairly basic geometric progressions describing some simple geometry. The kingdom’s civilized areas are a rough circle. The area of a circle is pi times radius squared. So 65 years ago, the civilized area was a circle with the average radius 100 miles, and the “wilds” were a band of further radius 50 miles around this circle.

In eight years, the inner-kingdom area doubles. In 16 years, it doubles again. That effectively doubles the radius to 200 miles. In 32 years, it doubles again, to 400 miles. In 48 years, it doubles a third time, and in 64 years it doubles for a fourth.
So it’s now 1600 miles average radius – or about 8,042,500 square miles in size.

The wilds increase 20% in radius after the first eight years, and again after another eight years. So in 16 years, they are x1.2×1.2 =x1.44 in additional radius. In another 16 years, or 32 years in total, the size would be x1.44 x144 = 2.0736, and after 48 years it would be x2.0736 x1.44. After 64 years, the wilds have increased in depth by x2.0736 x2.0736 = very close to 4.3, and would now be 215 miles in additional radius. So the total average radius of the Kingdom is 1815 miles, and the total area is 10,349,113 square miles. That’s more than 2 million square miles of semi-civilized ‘fringe’ where adventure comes a-calling.

Let’s say that the inner kingdom has a population density of 5 people per square mile, while the average in the ‘wilds’ is only 2. How many people are in the Kingdom now, and how many of them live in the wilds? 40,212,500 in the inner Kingdom. and 4,613,226 in the fringes. More than 10% of the population, in other words. But 65 years ago, those numbers were only 157,080 and 78,538, respectively – almost exactly a third of the populace lives in the wilds.

Note that both these numbers are extremely high. More typical would be for the inner kingdom to double in size every 40 years or so (the population level rises faster, but some of the newcomers will migrate to the cities), with the ‘wilds’ increasing about 50% in that sort of period.

The only reason to distinguish between the two types of area is so that you can estimate the danger levels separately, i.e. the mortality rates. But that’s getting ahead of ourselves.

Average Biological Lifespan

There are all sorts of ways to define the typical lifespan, and most of them are useless to us, because mortality rates are different for different age brackets. Simply stating an average, which gives the most intuitive ‘feel’ for the race, is really hard to translate into meaningful mortality rates. It’s actually a lot more useful to define the average usually quoted as the medical value, the average that would apply if nothing intervened to hasten death, i.e. the average under ideal circumstances, because that then lets us completely ignore it except as a guideline.

What we really need is a statement that reads, ‘at age X, Y per cent of the population have died.’ That lets us determine a series of mortality rates, and an average family size in order to achieve whatever growth rate of the society that has been decreed, simply by virtue of the number of survivors needed.

Interval Length

The lifetime of individuals is broken into intervals for the purposes of calculation. The most sensitive and nuanced approach is year-by-year, but the more intervals you have, the more work is involved. It’s not hard work, it’s just onerous, and makes for a boring article. So, for the purposes of this article, I’m going to use 15-year intervals, but in reality I would use 3- or 5-year intervals.

Base Mortality Progression

Let’s say that we have decided that 90% of the populace is dead at the age of 50. This is indicative of quite a dangerous life, even in the inner Kingdom.

The first step is to count the number of intervals required to reach that measurement age. So, 0-15 is one interval; 16-30 is two; 31-45 is three; and 50 is therefore three and one third.

The basic formula is

M = m ^ I

where M is the defined mortality rate (90%, or 0.9 in the example), I is the number of intervals (4 1/3 in the example), and m is the average mortality per interval. Since 0% of the population are dead at the age of 0, I and m define a simple geometric progression, or in this case, a base mortality progression.

0.9 = m ^ 3.3333333

Looks messy, doesn’t it? This can be quite a tricky calculation to solve. But there’s a simple way of restating the calculation so that it becomes a lot easier with a scientific calculator:

Log (1-M) = I x log(m)

or, using our example:

log (1-0.9) = 3.33333333 x log(m)

which becomes

-1 = 3.3333333 x log(m)

or log (m) = -1 / 3.3333333333 = -0.3

So, m = 0.501187233627 = 50.1187233627%. Call it 50.11%.

That means that for every interval that passes, only 50.11% of the population will survive. Or, if you prefer, the base mortality rate is 49.89%.

I find that it is useful at this point to set out a table showing intervals and the net mortality rate based on this base progression.

I=1, 1-15 years, 50.11% survive.
I=2, 16-30 years, 50.11% = 25.11% survive.
I=3, 31-45 years, 50.11% = 12.58% survive.
I=4, 46-60 years, 50.11% = 6.31% survive.
I=5, 61-75 years, 50.11% = 3.16% survive.
I=6, 76-90 years, 50.11% = 1.58% survive.
I=7, 91-105 years, 50.11% = 0.8% survive.
I=8, 106-120 years, 50.11% = 0.4% survive.
I=9, 121-135 years, 50.11% = 0.2% survive.
I=10, 136-160 years, 50.11% = 0.1% survive.

The first % shows the number that we calculated, i.e. the number who survive to the end of the interval. The second percentage is the net survival rate from birth to the end of the interval.

If this is for humans, it looks out of whack. No-one I know of has ever lived to 160 years of age. But that’s fine, because we are not locked in stone on this beyond the I=4 number. Well, actually, beyond I = 3 1/3. We can vary the other numbers to whatever seems reasonable:

I=1, 1-15 years, 50.11% survive.
I=2, 16-30 years, 50.11% = 25.11% survive.
I=3, 31-45 years, 50.11% = 12.58% survive.
I=4, 46-60 years, 50.11% = 6.31% survive.
I=5, 61-75 years, 3% survive (from 47.5%).
I=6, 76-90 years, 0.5% survive (from 16.67%).
I=7, 91-105 years, 0.01% survive (from 2%).

The first four values are unchanged. The values for the 5th interval were determined by setting the net % to whatever I wanted and then determining what the interval mortality rate had to be to achieve it. For example, to make the 5th interval come out to a net 3% survival rate, you have to apply a (3%/6.31%=47.5%) adjustment – in other words, 3% is 47.5% of 6.31%. The previous net mortality rate and the new net mortality rate determine the interval mortality rate.

Multiplying these values by the higher value in the age brackets and adding up the total actually gives the average lifespan, taking into account all the circumstances that are incorporated into the mortality rate.

50.11% x 15 = 7.5165.
25.11% x 30 = 7.533.
12.58% x 45 = 5.661.
6.31% x 60 = 3.786.
3% x 75 = 2.25.
0.5% x 90 = 0.45
0.01% x 105 = 0.0105.

Total = 27.207 years.

Variable Geometric Progression

But, for that matter, why use the base progression? In most populations without advanced medicine, infant and child mortality rates tend to be much higher than those of young adults, and those of the middle-aged tend to be greater than those of young adults. With the numbers we already know, it’s easy to adjust these tables as we wish. The key is that whatever we do one way, as a factor, has to be balanced by an equal and opposing adjustment somewhere else.

I=1, 1-15 years, 50.11 / 1.75 = 28.63% survive.
I=2, 16-30 years, 50.11 / 1.25 = 40.09% survive.
I=3, 31-45 years, 50.11 x 1.5 = 75.17% survive.
I=4, 46-60 years, 50.11 xX = % survive.
I=5, 61-75 years, 47.5 / 1.3 = 36.5% survive.
I=6, 76-90 years, 16.67 x 1.3 31.67% survive.
I=7, 91-105 years, 2% = 0.01% survive.

Above, I’ve paid a x1.3 adjustment with a /1.3 adjustment. I’ve listed a /1.75 and /1.25 adjustment and paired them with a x1.5 and a xX adjustment – so I need to calculate X:

1.75 x 1.25 = 1.5 x X
2.1875 = 1.5 x X
X = 2.1875 / 1.5 = 1.46.

So, I get:

I=1, 1-15 years, 50.11 / 1.75 = 28.63% survive.
I=2, 16-30 years, 50.11 / 1.25 = 40.09% = 11.48% survive.
I=3, 31-45 years, 50.11 x 1.5 = 75.17% = 8.63% survive.
I=4, 46-60 years, 50.11 x1.46 = 73.16% = 6.31% survive.
I=5, 61-75 years, 47.5 / 1.3 = 36.5% = 2.3% survive.
I=6, 76-90 years, 16.67 x 1.3 = 31.67% = 0.73% survive.
I=7, 91-105 years, 2% = 0.01% survive.

28.63% x 15 = 4.2945
11.48% x 30 = 3.444
8.63% x 45 = 3.8835
6.31% x 60 = 3.786
2.3% x 75 = 1.725
0.73% x 90 = 0.657
0.01% x 105 = 0.0105

Total = 17.8005 years.

So, by increasing child mortality rates and compensating in a later age group the average age has dropped substantially.

Minimum Family Size

The final calculation that is possible from these numbers is the size of the average family in order to achieve a given rate of population expansion. We know that some will be childless, whether they are a couple or not; so the initial calculation will look at 50 families with children, and we will then adjust for the ratio of families to childless pairs of people.

If we start with two people, it’s easy to calculate how many children they need to have in order to end up with two children surviving to the 16-30 age bracket, the age at which those children can take up the burden of maintaining population numbers:

2 / 11.48% = 17.42.

This calculation shows quite clearly that our adjustments went too far. No matter, that’s easy to correct with some more adjustments:

I=1, 1-15 years, 28.63% x1.25 = 35.79% survive.
I=2, 16-30 years, 40.09% x1.5 = 60.14% = 21.5% survive.
I=3, 31-45 years, 75.17% = 15.32% survive.
I=4, 46-60 years, 73.16% = 11.21% survive.
I=5, 61-75 years, 36.5% /1.25 = 29.2% = 3.27% survive.
I=6, 76-90 years, 31.67% /1.5 = 21.11% = 0.69% survive.
I=7, 91-105 years, 2% = 0.01% survive.

35.79% x 15 = 5.3685
21.5% x 30 = 6.45
15.32% x 45 = 6.894
11.21% x 60 = 6.726
3.27% x 75 = 2.4525
0.69% x 90 = 0.621
0.01% x 105 = 0.0105

Total = 28.5225 years.

Family Size: 2 / 21.5% = 9.3.

You might think that this number says that we still haven’t gone far enough, but it’s misleading. This is the number of children required for a couple to be sure that two of them will reach the age of 30. We only need them to live long enough to have two children who in turn will live long enough to have another two children. To find that out, we need two things – the year-on-year mortality rate and the age at which marriage becomes legal. The first can be calculated:

i x log (f) = log (p2 / p1)

where i is the number of years in an Interval, f is the result we are looking for, p2 is the cumulative mortality rate at the end of the period being subdivided, and p1 is the mortality rate at the start of the period. In the case of this example, i is 15 years, p2 is 21.5% and p1 is 35.79%. In fact, we already know that p2/p1 is 60.14%.

15 log (f) = log (0.6014), so
log (f) = -0.220836576236 / 15 = -0.0147224384157, so
f = 0.966668488301 = 96.667%.

Family size if ‘instant’ = 2 / 35.79 = 5.59. Assume 1 year to have each child, adds 5.59 years to 16 years, the start of the age bracket being subdivided, which equals 21.59. Add 1 year for each year the age of marriage is over 16.

Historically, 16 was a very common age for marriage and 14 was not uncommon. 18 or 21 as ages of consent are relatively recent social developments.

In this case, given the child mortality rates, I’m going to assume that social pressures would favor wedlock sooner rather than later, with the assumption that the bride would be with child as soon as possible thereafter. This would also discourage experimentation and children born out of wedlock, both potential drains on the state. It’s even possible that there would be a small cash bonus paid – say, 5 GP upon falling pregnant, another 5 on the birth of a healthy child, and 2 GP a year until the age of apprenticeship – which could be anything from 8 to 14. Twelve is a reasonably common age, historically, with ascent to journeyman status at 16 (apprentices should not be distracted by a bride or a husband). So let’s say 16.

In which case, 21.59 + 0 = 21.59 – so 22 years old should get us to the point of success.

15 years = 35.79%
16 years = 35.79% x 96.667% = 34.6%
17 years = 34.6 x 96.667% = 33.444%
18 years = 33.444 x 96.667% = 32.33%
19 years = 32.33 x 96.667% = 31.25%
20 years = 31.25 x 96.667% = 30.21%
21 years = 30.21 x 96.667% = 29.2%
22 years = 29.2 x 96.667% = 28.23%

2 / 28.23 = 7.08.

Seven children by the age of 22 is just possible if the first is conceived at the age of 16. But 7 mouths (plus two adults) to feed is a heavy burden; children would be put to work on behalf of the family as soon as they were old enough to understand what was required from them. Only a paying apprenticeship, returning money to the family, would excuse a child from his share of the workload.

It is also more than most couples had, even historically – that’s a consequence of the harsh child mortality rates, which are higher even than medieval history (9 in 10 survivors, or 6 in 7 according to some accounts, is closer to the historical average).

Couples Percentage

Next, out of 100 adult individuals, how many are members of a couple? You want this to be a reasonable percentage, and the smaller it is, the larger average family size has to grow to compensate. Social pressures are sure to result from families of 7 children, even if only 35.79% of them reach the age of 16, and these would favor something close to universal marriage.

If the ratio is 98/100=0.98, divide the 7.08 by 0.98. It follows that so long as R is not enough to increase the requirement to 8, the situation is socially tolerable. In other words, 8 = 7.08/R, i,e, R= 7.08/8 = 88.5. Since couples come in pairs, 88 is not enough but 90 is acceptable. That means that there would be socially acceptable reasons for not marrying – but not many and they would be hard to qualify for.

Typical Family Size

As a rough rule of thumb, if 7 children is the minimum required to achieve a static population level, assuming only 28.23 of them live long enough to produce grandchildren, a couple can bring about population growth simply by ‘replenishing’ and ‘replacing’ any who fall victim to mortality before the grandchildren stage. Adding more children to the brood only increases the effect. If a couple has 15 or 20 children, even with the 28.23% survival rate, 4.3-5.6 people per couple will comprise the next generation – more than doubling and almost tripling the population every 31-36 years.

That’s an unsustainable rate of growth. But it’s far short of the doubling every eight years that would be required to sustain the population density. It follows that either much of the land is unoccupied, even within the central Kingdom, or that subject peoples have to be added to the mix.

In a way, that’s only reasonable – someone would have laid claim to the lands into which the Kingdom is expanding; having the land already populated is the fastest way to grow the population.

This would explain another phenomenon, too – the population density that I selected for this example is way less than would be historically accurate. Medieval France, with its fertile plains and rolling hills, had a population density in medieval times of 25 people per square mile. England, with far more rocky and inhospitable terrain, was 8-10. For this kingdom, I specified 5 in the “densely packed” inner core and 2 in the outer fringe.

Additional Dangers & Their Impact

A similar technique, to the one used for previous adjustments, without the ‘compensating effect,’ enables the tables to be adjusted to incorporate any dangers that aren’t already factored in – like wild critters crashing the party. As a general rule of thumb, mortality rates will be much higher in the outlands. It can even be argued that cross-adjustments should be applied – for every reduction in survival rates in the outland, an increase should be applied to the inner kingdom. That’s getting a bit fussy and technical, but it would certainly be realistic.

For the sake of brevity, and because it doesn’t present much in the way of novel features to be understood, I’ll forgo that this time around. Given the relatively low population density, it’s questionable just how well the inner Kingdom has been cleared, anyway, and that tends to suggest that the mortality rates would be similar in both parts of the Kingdom. So I’ll simply assume that the numbers derived above apply universally.

Demographics

Time intervals can be matched to intervals to derive pseudo-generations. The percentage who survive the previous interval can be deemed to be the surviving numbers of the base population of that interval. Deriving a population growth rate measured in intervals then permits a complete breakdown of the demography of the Kingdom by interval bracket.

This is exactly what I did – with minimal numbers – when discussing the decades of the twentieth century in which celebrities became famous.

Here are the actuarial tables I worked out above once again, for reference. You’ll need them for reference.

I=1, 1-15 years, 28.63% x1.25 = 35.79% survive.
I=2, 16-30 years, 40.09% x1.5 = 60.14% = 21.5% survive.
I=3, 31-45 years, 75.17% = 15.32% survive.
I=4, 46-60 years, 73.16% = 11.21% survive.
I=5, 61-75 years, 36.5% /1.25 = 29.2% = 3.27% survive.
I=6, 76-90 years, 31.67% /1.5 = 21.11% = 0.69% survive.
I=7, 91-105 years, 2% = 0.01% survive.

If you look at any given interval to work out the Demographics, something interesting happens. Let’s assume that we have a growth rate of G – I’ll show you how to work it out, in just a minute – and a base population 7 ‘pseudo-generations’ ago of B.

In any given interval, you will have 0.01% (the survivors) x B, from 6 pseudo-generations earlier.
You will have 0.69% x G x B, from 5 pseudo-generations ago.
You will have 3.27% x G^2 x B, from 4 pseudo-generations ago.
You will have 11.21% x G^3 x B, from 3 pseudo-generations ago.
You will have 15.32% x G^4 x B, from 2 pseudo-generations ago.
You will have 21.5% x G^5 x B, from the previous generation.
You will have 35.79% x G^6 x B, from the current generation of children.

(note that by putting these in the order of increasing powers of G, the mortality rates are reversed relative to the earlier tables).

Every interval, you simply have to multiply each of the results by G to get the total numbers in the new generation. Add them up, and you always get the total population at the end of the current interval. So long as there is no change to your actuarial tables, the demographic breakdown by age is that simple.

Determining Growth by Interval

We had already specified that the Inner Kingdom doubled in size every 8 years. We know the geographic size that it was, 64 years ago – 100 miles radius. We know that the population rate is not matching this expansion in geography through internal growth, but it is presumably doing so through assimilation of captured nations/kingdoms.

So let’s work with doubling every 8 years. That means that it is increasing four-fold every 16 years. 16 is a little longer than the interval we have to work with, so we have to adjust this growth rate to determine the rate of growth every 15 years (because that’s out chosen interval).

Two relatively simple calculations do the job:

N log (R) = log (G1)

where N and G1 are the numbers specified for the quadrupling in size. So (in this case) N = 16 years and G1 = 4. R is worth noting down, it’s the annual growth, and you’ll need that number every calendar year of in-game time.

So,

16 log (R) = log (4) = 0.60206
log (R) = 0.602/16 = 0.03763
R = 1.0905 = +9.05%.

Then,

I x log (R) = log (G).

So, for the example, we have I = 15 and log (R) = 0.03763, which gives us:

15 x 0.03763 = 0.56445 = log (G)
G = 3.668

So the kingdom is growing at just under +267% every Interval.

The calculation to standardize population growth rates is exactly the same, you just have to substitute in the known values and whatever estimates seem appropriate, apply the (in this case) 22-year survival rate to the average number of children per family, and determine a 22-year (N) growth level (G1). Knowing I and the resulting log (R), it’s easy to calculate G.

Our example case is even simpler, because we’ve said that it matches growth in area, as a result of conquest of existing settlements. So the population growth per interval is exactly the same as the geographic growth by interval – both G values are 3.668.

It’s convenient at this point to work out the G-factors for each pseudo-generation:

G = 3.668
G^2 = 3.668 x 3.668 = 13.454
G^3 = 13.454 x 3.668 = 49.35
G^4 = 181
G^5 = 664
G^6 = 2,435.4

Base Population

We know that the total population is currently 40,212,500 – that was one of the first things that we worked out. But that’s not the Base Population.

We need to apply the demographics with B as an unknown variable, add them all up, and then determine B.

Growth = 3.668 per Interval
From 6 pseudo-generations ago: 0.0001 x B.
From 5 pseudo-generations ago: 69% x G x B = 69% x 3.668 x B = 0.0253 x B
From 4 pseudo-generations ago: 3.27% x G^2 x B = 3.27% x 13.454 x B = 0.44 x B
From 3 pseudo-generations ago: 11.21% x G^3 x B = 11.21% x 49.35 x B = 5.53 x B
From 2 pseudo-generations ago: 15.32% x G^4 x B = 15.32% x 181 x B = 27.73 x B
From 1 pseudo-generations ago: 21.5% x G^5 x B = 21.5% x 664 x B = 142.76 x B
From now: 35.79% x G^6 x B = 35.79% x 2435.4 x B = 871.63 x B

Adding those up, you get 1,048.1154 x B, and we know that equals 40,212,500, so B must be 38,366.

Plugging that number into the individual calculations and putting them back into the usual order gives:

Growth = 3.668 per Interval
I=1, 1-15 years = 33,440,956
I=2, 16-30 years = 5,477,130
I=3, 31-45 years = 1,063,889
I=4, 46-60 years = 212,164
I=5, 61-75 years = 16,881
I=6, 76-90 years = 971
I=7, 91-105 years = 4

These are the actual numbers of the current generation, broken down by age. To get the numbers for any earlier era, simply divide by G for each interval into the past. To get the numbers for any point in the future, simply multiply by G for each successive Interval. (That’s why I listed G at the start of the demographic breakdown).

Multiracial Demographics

In a multiracial region, if the input values – growth rates, mortality rates, etc – are different, you need to track each race separately. And be prepared for some interesting dynamics; we’re dealing with exponential and geometric growth rates here, and it’s entirely possible that you will discover that you need to extend your campaign background to include racially-specific plagues or other calamities just to keep a fast-growing race from crowding out everyone else, or from totally dominating the campaign. Unless, of course, that’s what you want.

Shutter Events

Every now and then, there will be a ‘shutter event’ – an event that makes a significant adjustment to the population levels. A plague, a way, a famine, a flood. Disaster of some kind. This is an event that permits some part of the population to pass through (relatively) unscathed while blocking another part completely.

To apply a shutter effect, you need to know two things: the proportion of each population group who are exposed to the shutter effect, and the survival rate of the event by age of participant at the time.

For example, in an attempted invasion from without the Kingdom that penetrates the inner Kingdom before being rebuffed, a certain percentage of the population in the wilderness will confront the event, as will a certain percentage of those resident in the Inner Kingdom. These are the residents of ‘ground zero’ of the event. In addition, from other parts of the inner Kingdom, an army will be raised of a certain size. Those who are NOT part of this group can be deemed to automatically survive the event; those who ARE have to be subdivided by interval bracket, and then be reduced in number according to the survival rate you have set.

I started this part of the article by asking about veterans from a past war. That is quite obviously a shutter event. So let’s see what happens. Just to have some way to refer to it, I’ll toss out a random name: “The Julien Divide”. For some reason, the notion of something corrupting children into murderous monsters who turn on their family – how that relates to the title of the conflict, I have no idea. I put a little more thought (by about 20 seconds) into the composition of the Kingdom Army. For a start, I decided that the army is about 20% of the citizenry. From there I plugged in values that seemed about right to give a reasonable command structure. One of the good things about a 15-year Interval is that you can be reasonably sure that each interval represents an elevation in the command structure.

To start with, we have to work out how many intervals into the past we’re talking about. Let’s try 30 years, because that’s a simple example – two intervals.

Two intervals means that we are dividing the population numbers by G^2. Normally, you’d have to work that out from scratch, but as it happens, I just did that – 13.454.

Commencement Of The Julien Divide
Growth = 3.668 per Interval
I=1, 1-15 years = 33,440,956 / 13.454 = 2,485,577
I=2, 16-30 years = 5,477,130 / 13.454 = 407,100
I=3, 31-45 years = 1,063,889 / 13.454 = 79,076
I=4, 46-60 years = 212,164 / 13.454 = 15,770
I=5, 61-75 years = 16,881 / 13.454 = 1,255
I=6, 76-90 years = 971 = 0
I=7, 91-105 years = 4 = 0

Exposure I: Victims
I=1, 1-15 years = 2,485,577 x 25% = 621,394
I=2, 16-30 years = 407,100 x 17% = 69,207
I=3, 31-45 years = 79,076 x 5% = 3,954
I=4, 46-60 years = 15,770 x 3% = 473
I=5, 61-75 years = 1,255 x 1% = 12

Exposure II: Armies
I=1, 1-15 years = 2,485,577 /5 x 12% = 59,654
I=2, 16-30 years = 407,100 /5 x 30% = 24,426
I=3, 31-45 years = 79,076 /5 x 8% = 4,745
I=4, 46-60 years = 15,770 /5 x 3% = 95
I=5, 61-75 years = 1,255 /5x 1% = 3

The next step is to determine the casualty rates, and then apply them to the two exposed groups.

Exposure I: Victims
I=1, 1-15 years = 621,394 x 33.333% = 207,129
I=2, 16-30 years = 69,207 x 75% = 51,905
I=3, 31-45 years = 3,954 x 80% = 3,163
I=4, 46-60 years = 473 x 90% = 426
I=5, 61-75 years = 12 x 95% = 11

Exposure II: Armies
I=1, 1-15 years = 59,654 x 35% = 20,879
I=2, 16-30 years = 24,426 x 25% = 6,107
I=3, 31-45 years = 4,745 x 15% = 712
I=4, 46-60 years = 95 x 5% = 5
I=5, 61-75 years = 3 x 34% = 1

Next, you have to reduce the starting population at this point in time by the amount of these losses.

Commencement Of The Julien Divide
Growth = 3.668 per Interval
I=1, 1-15 years = 2,485,577 -207,129 -20,879 = 2,257,569
I=2, 16-30 years = 407,100 -51,905 -6,107 = 349,088
I=3, 31-45 years = 79,076 -3,163 -712 = 75,201
I=4, 46-60 years = 15,770 -426 -5 = 15,339
I=5, 61-75 years = 1,255 -11 -1 = 1,243
I=6, 76-90 years = 0 -0 -0 = 0
I=7, 91-105 years = 0 -0 -0 = 0

The second-last step is to age these back one interval toward the contemporary time period. Transpose each population number down 1 slot and multiply by the mortality rate of the old slot and the growth rate. To get the new 1st slot, multiply the old 1st slot value by the growth rate.

15 years after The Julien Divide
Growth = 3.668 per Interval
I=1, 1-15 years = 2,257,569 x 3.668 = 8,280,763
I=2, 16-30 years = 2,257,569 x 3.668 x 35.79% = 2,963,685
I=3, 31-45 years = 349,088 x 3.668 x 21.5% = 275,297
I=4, 46-60 years = 75,201 x 3.668 x 15.32% = 42,258
I=5, 61-75 years = 15,339 x 3.668 x 11.21% = 6,307
I=6, 76-90 years = 1,243 x 3.668 x 3.27% = 149
I=7, 91-105 years = 0 x 3.668 x 0.69% = 0

The last step is to do that again.

30 years after The Julien Divide
Growth = 3.668 per Interval
I=1, 1-15 years = 8,280,763 x 3.668 = 30,373,839
I=2, 16-30 years = 8,280,763 x 3.668 x 35.79% = 10,870,797
I=3, 31-45 years = 2,963,685 x 3.668 x 21.5% = 2,337,221
I=4, 46-60 years = 275,297 x 3.668 x 15.32% = 154,700
I=5, 61-75 years = 42,258 x 3.668 x 11.21% = 17,376
I=6, 76-90 years = 6,307 x 3.668 x 3.27% = 756
I=7, 91-105 years = 149 x 3.668 x 0.69% = 4

Compare these results to the original “current population” and you can see what a huge impact this conflict had on the Kingdom.

I=1, 1-15 years = 33,440,956
I=2, 16-30 years = 5,477,130
I=3, 31-45 years = 1,063,889
I=4, 46-60 years = 212,164
I=5, 61-75 years = 16,881
I=6, 76-90 years = 971
I=7, 91-105 years = 4

The Value Of Demographics

Demographics can give you another tool to bring your campaign to life, because they reflect your campaign’s history and its consequences in the modern game world. They also make a formidable analytic tool; unexpected patterns and tensions can be revealed that you didn’t even realize were present. You can either revel in these, or take action to defuse them; either will add to the verisimilitude of the campaign. Best of all, once the information is compiled it needs virtually no maintenance, thanks to the use of intervals. Years of game time will have to pass before the information is out-of-date.

Print Friendly, PDF & Email