Reader Morghulis

TL;DR: Memento mori. After reading too much Seneca, I’m meditating on death like a statistician, by counting how many of GRRM’s readers did not even survive to see the HBO show (much less the end of the book series). Rough answer: around 40,000.
No disrespect meant to Martin, his readers, or their families—it’s just a thought exercise that intrigued me, and I figured it may interest other people.
Also, we’ve blogged about GoT and statistics before.

In the Spring a young man’s fancy lightly turns to actuarial tables.

That’s right: Spring is the time of year when the next bloody season of Game of Thrones airs. This means the internet is awash with death counts from the show and survival predictions for the characters still alive.

Others, more pessimistically, wonder about the health of George R. R. Martin, author of the A Song of Ice and Fire (ASOIAF) book series (on which Game of Thrones is based). Some worried readers compare Martin to Robert Jordan, who passed away after writing the 11th Wheel of Time book, leaving 3 more books to be finished posthumously. Martin’s trilogy has become 5 books so far and is supposed to end at 7, unless it’s 8… so who really knows how long it’ll take.

(Understandably, Martin responds emphatically to these concerns. And after all, Martin and Jordan are completely different aging white American men who love beards and hats and are known for writing phone-book-sized fantasy novels that started out as intended trilogies but got out of hand. So, basically no similarities whatsoever.)

But besides the author and his characters, there’s another set of deaths to consider. The books will get finished eventually. But how many readers will have passed away waiting for that ending? Let’s take a look.

Caveat: the inputs are uncertain, the process is handwavy, and the outputs are certainly wrong. This is all purely for fun (depressing as it may be).

So, we’ll need to answer a few questions. How do we define readers? How many readers are there? What are their demographics? And what are the mortality statistics for those demographics?

Readers: By the fall of 2013, around 24 million ASOIAF books had been sold in North America, but that includes all 5 books (so far). Furthermore, it seems that book sales went through the roof once the HBO show began in 2011, which will make it really hard to estimate trends in readership over time after that year. 2011 is also the year when the latest book in the series, A Dance With Dragons (ADWD), was published.

The first book in the series reached its one-millionth US-paperback-edition copy by the fall of 2010. So for simplicity’s sake, let’s say that by the end of 2010, there were at least 1,000,000 US readers. [This misses people who bought the hardcover instead or who read it as a library book; and this overcounts people who bought but never read it or who didn’t like it enough to continue the series. Still, it’s a nice round number and probably the right order of magnitude.] These are the grizzled veterans who were already fans before the HBO show (a.k.a. the hipsters who liked it before it was cool). Some started when the first book appeared in 1996, others as late as 2010. Let’s call these 1,000,000 US residents our core ASOIAF readers who really want to know how the book series ends. How many of them had passed away before the HBO show began and ADWD came out?

The first US printing of the first book had around 50,000 copies according to Martin. Instead of thoroughly researching how book readership tends to grow, let’s assume it’s linear (another crass oversimplification). Then over the 15 years from 1996 to 2010 (inclusive), we’d have to add around 65,000 readers a year to reach 1 million total readers. Since that’s not too far from the first print run, let’s go with it: we have 65,000 new ASOIAF readers every year over 15 years.

Demographics: I can’t find demographics for Martin’s readers specifically, but there are a few demographic summaries of fantasy readers in general. Readers of The Magazine of Fantasy & Science Fiction and Lightspeed Magazine seem to be roughly 10% ages 18-24, 50% ages 26-45, 30% ages 46-55, which I guess leaves around 10% aged 56 or older. (That ignores people under 18, but let’s face it, kids probably shouldn’t be reading the gruesome Game of Thrones anyway.) The sex breakdown is roughly 60% male, 40% female. Let’s assume this age/sex breakdown holds for our million ASOIAF readers, though here are several other summaries with slightly different demographics.

Mortality: Okay, it’s time for the morbid part. Here are some Death Rates by Age and Sex (we’ll ignore Race since I didn’t find those reader demographics). None of them have changed dramatically since around 2000, close to the first book’s publication date, so let’s just use the latest 2008 numbers. The age breakdowns here don’t match ours exactly, so let’s also average together the rates for age groups we need to combine. Table 2 here suggests 25-34 and 35-44 had roughly similar numbers of people, so we can take a simple average of their death rates to get the 26-45 rate. But for people 56+, we’ll do a weighted average, weighted by the approximate population in each death-rate category. Using very rough weights of 25 (million) in population for 55-64, 20 for 65-74, 10 for 75-84, and 5 for 85+, we get
(25*1000 + 20*2500 + 10*6000 + 5*14000) / (25 + 20 + 10 + 5)
or around 3500 for the 56+ male death rate. For females, it’s
(25*1000 + 20*2000 + 10*4000 + 5*12500) / (25 + 20 + 10 + 5)
or around 2800.
Finally, the table gives death rates per 100,000 population, but let’s translate them to percent of people who will pass away that year. The results are

Males: .11% for 18-25, .18% for 26-45, .53% for 46-55, 3.5% for 56+
Females: .04% for 18-25, .06% for 26-45, .23% for 46-55, 2.8% for 56+

Let’s run these numbers through R.

# Death rates (percent of people in that group who die in a given year)
# rounded or estimated from Census tables
DeathRatesVec = c(.11, .18, .53, 3.5,
                  .04, .06, .23, 2.8)
DeathRates = matrix(DeathRatesVec, 4, 2) / 100
colnames(DeathRates) = c("M", "F")
rownames(DeathRates) = c("18-24", "25-44", "45-54", "55+")
DeathRates
##            M      F
## 18-24 0.0011 0.0004
## 25-44 0.0018 0.0006
## 45-54 0.0053 0.0023
## 55+   0.0350 0.0280

# Number of readers in each age/sex group
# estimated from fantasy magazine reader polls
AgePcts = c(.1, .5, .3, .1)
SexPcts = c(.6, .4)
ReadersPerYear = t(65000 * rbind(AgePcts, AgePcts) * SexPcts)
colnames(ReadersPerYear) = colnames(DeathRates)
rownames(ReadersPerYear) = rownames(DeathRates)
ReadersPerYear
##           M     F
## 18-24  3900  2600
## 25-44 19500 13000
## 45-54 11700  7800
## 55+    3900  2600

# Function to estimate the number of readers who die
# within a certain number of years
NrDeathsByYearsLeft = function(YearsLeft) {
  sum(ReadersPerYear - ReadersPerYear * (1 - DeathRates) ^ YearsLeft)
}

# Total number of reader deaths from 1996 through 2010
FirstYear = 1996
FinalYear = 2010
TotalYears = FinalYear - FirstYear + 1
DeathsByYearStarted = sapply(TotalYears:1, NrDeathsByYearsLeft)
round(sum(DeathsByYearStarted))
## [1] 36814

So it looks like almost 40,000 veteran readers didn’t survive even until ADWD was published or the HBO show aired. This is on the order of 100 times the number of characters who’ve died, whether in the show or in the books.

Finally, let’s show the breakdown by year, since we already calculated it above:

# Number of deaths by 2010,
# broken out by the year in which they started reading
plot(FirstYear:FinalYear, DeathsByYearStarted, type='h',
     xlab = 'Year', ylab = 'Deaths',
     main = 'Number of readers deceased by 2010\nwho started in a given year')

(The trend looks perfectly linear just because we assumed linear growth in the number of readers and stable demographics over time.)

No deep insights here. There’s just the stark (hah!) realization that a substantial number of Martin’s earliest readers have not survived the wait.

Let’s not worry about which characters will die; let’s not hurry Martin as he writes. Let us just savor our time on Earth before we make the same journey ourselves. After all, valar morghulis.

PS—A helpful librarian friend tells me that the Carnegie Library of Pittsburgh system has 102 copies of the books currently in the system (acquired from 2002 onwards), with about 2300 total checkouts all together. This could be extrapolated to estimate US readership by library patrons who didn’t actually buy the book. At some point I may also go through her data to see how readership seems to have changed over time (i.e., the number of checkouts over time for older vs. newer copies).

Manual trackback: Partially Derivative ep. 20 (around 33:09); FlowingData