Monday, 30 June 2014

Happy Canada Day, from Kati of Terra and Dodecahedron Books

Kati of Terra sends greetings back to her home plant, Earth (or Terra, as she prefers to call it).  And on Canada Day she sends particularly warm regards to her native land, for Kati is a Canadian girl.

Friday, 27 June 2014

Book Statistics Corner, Part 4 – Sales Trends of Ten of the Most Popular Book Series

In a previous blog, we looked at some statistics on sales for one particular popular book series, Patrick O’Brian’s Aubrey/Maturin series, a historical fiction series about the Royal Navy during the era of the Napoleonic Wars.  Now, we will extend this analysis, adding nine more of the most popular series in recent history.  The particular book series were selected from a wiki article, “List of best-selling books”. 
The author, series title and total sales (copies) are shown below:

Author and Series
J.K. Rowling - Harry Potter
Dan Brown - Robert Langdon
Stephanie Myers – Twilight
Suzanne Collins - Hunger Games
Robert Jordan - Wheel of Time
Stephen King - The Dark Tower
G.R.R. Martin - Game of Thrones
Veronica Roth – Divergent
Douglas Adams - Hitchhikers Guide
Patrick O'Brian - Aubrey/Maturin

Though this only constitutes 10 series, it represents nearly 1 billion copies sold and multiple billions of dollars in profit.  No wonder publishers love a breakout book series.  They are pure gold.
Since actual book sales are notoriously difficult to come across, we will again use proxy statistics from the Goodreads website to get a feel for how well these series did over time, and especially for how well sales held up from Book 1 to the final book of the respective series.  But first, we will examine the Harry Potter series a little more closely, since the wiki page had estimates of copies sold for each book in the series.  We can then see how well that compares to the Goodreads statistics.

Book Num  GR Reviews GR Ratings Sales (Wiki) First Pub GR Rating
1 40,793 2,580,696 107,000,000 1997 4.38
2 16,682 1,177,363 60,000,000 1998 4.28
3 18,824 1,219,695 55,000,000 1999 4.46
4 16,610 1,182,736 55,000,000 1999 4.46
5 15,789 1,136,636 55,000,000 2003 4.40
6 15,599 1,136,725 65,000,000 2005 4.48
7 37,191 1,175,133 50,000,000 2006 4.57
Total 161,488 9,608,984 447,000,000   4.43

As the table and graph indicate, the numbers of copies sold correlates pretty closely to the number of people who rated the books on Goodreads, once we have normalized the data.  We do that by defining the value of the statistic as 100 for Book 1, then comparing the following volumes to that index.   For example, Volume 1 (Philosopher’s Stone) sold 107 million copies, while volume 2 (Chamber of Secrets) sold 60 million copies.  Then 60/107 = .56, so Volume 2 is given the value 56, compared to Volume 1, which is given the value 100.  Similarly for the other books and measures.  The correlation coefficient between copies sold and number of ratings is .964, which is high.  Note that a value of 1.00 would indicate a perfect correlation between two variables.

Another way to see this is to divide the number Goodreads ratings into the number of books sold for each volume.  As you can see, the number is consistently close to 2 percent.  That also shows that Goodreads has a pretty wide reach among readers, at least as far as the Harry Potter series is concerned:

Book Num
Title (Harry Potter and the…)
Ratings pct of Sales
Philosopher's Stone
Chamber of Secrets
Prisoner of Azkaban
Goblet of Fire
Order of the Phoenix
Half-Blood Prince
Deathly Hallows

  As for the number of Goodreads  members who left reviews of the Harry Potter series, that also correlates nicely with the number of copies sold, up until the final volume (the correlation constant between copies sold and number of Goodreads reviews was .963 for the first six volumes) .  However, we can see on the graph that the number of reviews shoots way up for “Deathly Hallows”.  In this data at least, there appears to be a greater willingness to leave a review for the final book of the series.  I suppose a proportionately higher percentage of Goodreads raters want to do a “summing up” review, as well as leave a rating.  Intuitively, that makes sense.  We also noted a similar phenomenon in the Patrick O’Brian series in the earlier blog, though this time the effect is more pronounced.
We might also note that reviews became more positive as the series went on, from a 4.38 and 4.28 for volumes 1 and 2 to a high of 4.48 and 4.57 for volumes 6 and 7.   We can infer from this that, not surprisingly, the readers who continue on with a series tend to be keener on the books than those who don’t.  Again, we also noticed this tendency in the Patrick O’Brian series. 
Now let’s look at the book series in detail, focusing on the number of Goodreaders rankers vs the position of the books within the series.  We will go by series book sales, largest to smallest.
1 – Harry Potter (J.K. Rowling)
We see that the series followed a power law quite closely, with the second and the last books departing somewhat from the best fit curve.  The median book had about half the raters that the first book had.  As noted above, if we divide Goodreads raters into copies sold, we come up with a figure of 2.1%.  This relatively low figure may be a reflection of the fact that a substantial part of the audience did not participate on Goodreads, perhaps because they were too young.

2 – Robert Langdon (Dan Brown)
In this case, we see that the function departs from the power law form by quite a bit.  That’s mostly because the second book of the series, The Da Vince Code was really the big breakout success.  In fact, most people think it is actually the first book in the series, which was actually Angels and Demons.  But the second book caught the public’s fancy more, probably because of the implications for the church. Note that the last two books seem to have lagged the first two quite badly, relative to the first two, at least in this data.  But it is hard to repeat that level of success.    If we divide the number of Goodreads raters into the number of copies sold, we come up with a ratio of 1.4%.  This probably reflects an older, less social-media driven audience for this type of a series (and perhaps a less enthusiastic one). 
3 – Twilight (Stephanie Myers)
This four book series followed a relatively flat power law very closely.  After the initial drop-off from Book 1, she seems to have held on to about 40% of the initial book raters, very consistently.   If we divide the number of Goodreads raters into the number of copies sold, we come up with a ratio of 4.2%, a middling-high figure. 

4 –Hunger Games (Suzanne Collins)
This series also conformed closely to the power law, though naturally that’s easier to do with only three data points to fit.  She also did a very good job of holding onto about half of the raters through the final two books of the trilogy.  If we divide the number of Goodreads raters into the number of copies sold, we come up with a ratio of 10.4%.  This would seem to indicate that readers of this series were very enthusiastic about sharing their ratings of the book and were very social media aware.

5 –Wheel of Time (Robert Jordan)
This series conformed fairly well to the power series, but with some bumps along the way.  From reading reviews, it seems that the series lagged somewhat in the latter middle part, then picked up again towards the end.  Nonetheless, it did an excellent job of holding onto raters as the series progressed, given its length.  Nearly half were still engaged for most of the latter half of a long series.   If we divide the number of Goodreads raters into the number of copies sold, we come up with a ratio of 2.2%.   Due to the length of the series, this might also reflect an older, less social-media driven audience.
6 –The Dark Tower (Stephen King)
This one is almost a textbook perfect example of a nice power law.  King did pretty well to hold on to a lot of raters over a long series as well.  If we divide the number of Goodreads raters into the number of copies sold, we come up with a ratio of 2.1%.  Again, due to the length of the series, this might also reflect an older, less social-media driven audience.

7 –Game of Thrones (G.R.R. Martin)
Yes, I know that’s not the real name, but that’s the name of the TV show, so I figure that’s how most people think of it.  Again, it is almost a picture-perfect example of a power law.  The last book has lagged a bit, but he still has two more books to go.  Again, he has done a good job of holding on to nearly half of his original audience, as inferred from Goodreads raters.  If we divide the number of Goodreads raters into the number of copies sold, we come up with a ratio of 7.6%.  Perhaps this is at least partially due to the series having a concurrent TV spinoff, with the consequent buzz and cross promotion.

8 –Divergent (Veronica Roth)
This is a pretty decent fit, but there are only three points to fit, so that has to be borne in mind.   If we divide the number of Goodreads raters into the number of copies sold, we come up with a ratio of 8.2%.  As with the Twilight series, this would seem to indicate an audience that is very enthusiastic about the books and keen to share their feelings on social media.
9 –HitchhikersGuide (Douglas Adams)
Again, this is a nearly perfect fit to a power law.  However, it has quite a steep drop-off, with the first book in the series getting far more ratings than the earlier books.  This seems to be a feature of older books and how they interact with Goodreads.  It may be that it is more a reflection of people’s recall of an older series, rather than being related to underlying sales.  However, if we divide the number of Goodreads raters into the number of copies sold, we come up with a ratio of 6.1%, which is quite high for a series whose author died quite a while back and whose audience probably skews older. 
10 – Aubrey/Maturin (Patrick O’Brian)
Again, this is a very good fit to a power law, especially given the length of the series.  We see a bump at Book 10 (that was the book that shared the title with the movie “The Far Side of the World”).  Book 2 is also a bit low.  If we divide the number of Goodreads raters into the number of copies sold, we come up with a ratio of 2.9%, which is what we might expect for a series whose author died quite a while back and whose audience probably skews older. 

Some Conclusions

·         It does appear that the number of Goodreads raters reflects the number of copies sold fairly accurately within a series (i.e. there is a good correlation).   At any rate, that appears to be the case for the Harry Potter series.  For that series, the number of Goodreads raters was about 2% of the copies that were sold.

·         However, a similar calculation went from a high of 10% for the Hunger Games series to a low of 1.4% for the Dan Brown series.  So, there is some considerable variability in different audiences to make their way to Goodreads and to share their opinions, via rating the books.

·         Nearly all of these very popular series fit a power law very well.  The main exception was the Dan Brown series, in which The Da Vinci Code was the exception to the rule.  But that book truly was exceptional, on a lot of grounds.

·         Most of the newer series managed to have 40% to 50% of the Goodreads raters involved by the midpoint of the series, relative to the first book.  The older series had a much greater rate of drop-off, though this may also be related to the fit between the audience of the series and the members of Goodreads.

Next time we will look at whether these findings hold for Amazon reviews, or whether things are different in the Kindle world.
Note that I will put up the raw data that these graphs are based on a little later in the week.

Friday, 20 June 2014

Book Statistics Corner, Part 3 – The Decay Curve of a Book Series

These days, a lot of writers are doing series.  There are good reasons for that - once you have built up an audience for a certain setting, cast of characters and genre, you would like to maintain that audience.  It seems natural that a series would be the way to go.  But what might you actually expect from a series?  For example, how many people will move on from book 1 to book 2, book 2 to book 3 and so on?  It seems likely that you will lose some people along the way, but is there a pattern to that?  To get a feel for this, let’s look at some results for some well known long running book series.  Naturally, we can only look at a few “ideal type” cases, but with luck that will give us some insights that are typical for most series.
First, we will look at Patrick O’Brian’s Aubrey/Maturin historical fiction series.  That is the series of books that the recent (released in 2003) movie “The Far Side of the World”, featuring Russel Crowe, was based on.  They are about a Royal Navy captain and a ship’s doctor/spy, set during the era of the Napoleonic wars, roughly 1800 to 1815.  Why did I pick this series first?

·         I have read them all, so I have a good sense of how the series evolved.

·         It’s a long series (20 books) so it really tests the idea of loyalty to a series.

·         It has sold a lot of books, and has had a lot of fans, so the statistical power of the analysis should be high (that just means that the numbers are big, so the results are probably grounded in some underlying realities, not random noise).

·         It has spanned the era of print books sales in book stores to the era of ebooks sales in on-line stores, so we might be able to see whether the change in how stories are stocked and delivered has affected how people consume series.

To begin, we will look at how the series did via a number of Goodreads  measures.  As you may know, Goodreads is a site where readers can leave reviews, ratings, and recomendations of the books they have read.  The measures that we will look at are Numbers of Reviews, Numbers of Raters, Average Rating, and Number of Editions.   The results, as taken from the Goodreads website are shown below.  The year that the book was first published is also shown, to give some idea of the time scale involved.  There’s a reason the first four books are highlighted, which we will get to later.

Book Num


 GR Reviews

GR Ratings

GR Rating


First Pub


Master and Commander







Post Captain







HMS Surprise







The Mauritius Command







Desolation Island







The Fortune of War







The Surgeon's Mate







Treason's Harbour







The Ionian Mission







The Far Side of the World







The Reverse of the Medal







The Letter of Marque







The Thirteen Gun Salute







The Nutmeg of Consolation







Clarissa Oakes/The Truelove







The Wine-Dark Sea







The Commodore







The Yellow Admiral







The Hundred Days







Blue at the Mizzen










As you can see, for most measures there was a fairly steady decline from Book 1 to Book 20, though some books in the latter part of the series seem to have done better than the book that immediately preceded it - in mathematics, we would say that it is not a monotonic series, but in statistics we might say that it comes pretty close to one (it is quite well modelled by a power law, in fact).

The data is graphed above, with the various measures (Number of Editions, Number of Goodreads Ratings, and number of Goodreads Reviews) scaled in such a way that the measures for the first book are assigned the value of 100, and the measures for books after that are assigned numbers proportional to that initial value.  So, for example, the first book had 90 editions printed, while the second book had 63 books printed.  In our scaled variable we have assigned 100 to the first book, and 70 to the second book (63/90 = 0.70, so the second book is given the value 70).  The reason for using these scales (it’s called normalizing) is so that we can compare the three line graphs on the same scale.
There are a lot of interesting results here.  First off, we see that all of the graphs decline steadily (each shows a decay curve), but they fall off at different rates.  The fall-off for the number of editions is slowest.  That’s interesting, since the number of editions is probably the measure that best tracks the number of books sold and read.   After Book 5, the number of editions printed falls to about 40% to 50% of the number of editions printed for the first book.  So, Patrick O’Brian appears to have held on to about half of his initial book purchasers as the series matured.  There was an uptick at Book 10 - that’s “The Far Side of the World”, which was also the title of the movie starring Russell Crowe.  So, that clearly seems to have given the book a bounce.
There was also an uptick for the final book of the series “Blue at the Mizzen”.  A reasonable hypothesis is that those extra editions may represent sales to people who followed part of the series and dropped out, but who might have decided to buy the final book to see how it turned out.  However, in some ways Book 19 was really the end of the series (Napoleon is defeated) and book 20 could be thought of as the start of another series that featured the same main characters in a different setting (the plot moves from the Napoleonic wars to the wars of liberation in South America).  But the author died shortly after Book 20, so there was no chance for a “next generation” follow-up.  So the final book uptick might be related to people buying into a new series or it might be related to the wrap-up of the original series.  We’ll never know.
There are some other interesting features of these decay curves - first, how the decay curve of Goodreads ratings falls off more rapidly than the decay curve of the number of editions and secondly how the line representing the number of Goodreads reviews falls off even more sharply.  So, it appears that people might be less willing to invest the time and energy into rating or reviewing books that they read in a series, as the series goes on.  Also, it appears that they are more willing to invest the time in a rating than in a review.  That makes sense, as a rating only takes a few seconds, while a review can take five or ten minutes - even much longer than that, for those who take their reviewing very seriously indeed.
One other interesting aspect of the decay curves is that they are well modelled by our old friend the power law, of which I have written previously.   The fitted lines next to the jagged data lines are these power functions.   The R-Squared values next to the respective lines indicate that the fits are quite robust, in a statistical sense (an R-Square of 1.00 would indicate that the data fit the power-law function perfectly, so values in the 0.85 to 0.95 range are really quite good fits.
The above data also shows that after the first few books, the number of reviews and rankings correlated rather nicely with the number of editions of the book.   Since we assume that the number of editions printed correlates fairly well with the number of copies sold,  we can therefore have some more confidence in the notion that the total number of reviews a book gets scales fairly well with its total sales.  This assumes, of course, that each edition had more or less the same number of copies printed and sold.   This can be seen in the graph below.  Note, however that for the initial books in the series, the number of reviews was higher than would be expected from the relationship in the graph.  Again, this indicates that people may be more enthusiastic to review/rank near the beginning of a series than later on.

It is also worth noting how the average rating of the books went, as the series progressed.  As you can see, the first couple of books actually had the lowest rating, and after that the ratings were quite consistent, at a bit under 4.4, for the most part.  So, it would appear that as the series went on, the readers who dropped out were (not surprisingly) those who were less satisfied with the books, and the readers who stayed with the series were those who were more satisfied.   So, the audience was smaller, but more loyal as the series continued.

Now lets have a look at the Amazon Kindle numbers for Patrick O’Brian’s Aubrey/Maturin Series.  In this case, we will look only at the trend from Book 5 to 20, since the publisher has not yet released the first four books in ebook format.  I suppose they are going with the reasoning that ebook sales could “cannibalize” print book sales, but they are only concerned about that happening to the earliest books in the series.  I don’t know if that logic is still valid, but traditional publishers seem to be holding on to it in this instance.  We are also going to assume that the number of Kindle reviews correlates reasonably well with Kindle sales - i.e. a book with twice as many reviews as another, probably sold twice as many copies, at least to a first approximation.
As we can see, the number of reviews in the Kindle store do not show the decay curve pattern that was evident in the Goodreads data, which was probably primarily based on legacy print book sales.  In the Kindle store, the last two books had about as many reviews as the first two, and the others had 50 or more reviews, compared to the 85 or 90 for the top reviewed volumes.  So, perhaps the always available nature of the ebooks in the Kindle store has altered the underlying sales dynamics of the series.  Of course when it comes to ebook sales for books published before 2000, we are always looking at the “long tail”, so we might be seeing the dynamics of the long tail, which are generally thought to be underlain by a much flatter power law than initial book sales.

These are all good things to keep in mind when you evaluate the success of your own series, if you are a writer or publisher, especially if you are a self-publisher or small scale publisher.  To summarize:

·         There is a power-law like decay curve (in sales and other measurs), or at least there was in the legacy system.

·         The slope of that curve varies depending on the measure, with the tendency to rank or review probably falling off faster than sales, as the series goes on.

·         If your book gets made into a movie, you will most likely get a bump in sales J.

·         There may be a bump at the end of a long series, as people who dropped out of some of the middle books come in to see how things turned out.

·         Numbers of reviews and or numbers of rankings (not average rankings) probably scale reasonably well with sales.

·         The dynamics of print book series and ebook series may be quite different, with the ebook series possibly having a much flatter decay curve (or none at all).

Well, that’s just one series (a highly successful one) whose sales dynamics we have attempted to infer from Goodreads and Amazon Kindle data, available to the public.  In later blogs we will see whether these results hold for some other series in other genres, such as Robert Jordan’s Wheel of Time series or J.K. Rowling’s Harry Potter series.   We will also try to test some recent ebook only series, to see if the dynamics of those are different.