Wednesday, 8 May 2013

Writing on the numerical knife edge

I've long held the conviction that the difference between success and failure at the top of any game is a matter of tiny fractions of... something. The man who comes 20th in the Olympic 100m is still stupidly fast. The 300th best basketball player is incredibly good at what they do. And yet Mr 20th and Mr 300th earn a tiny fraction of what the Usain Bolts and Magic Johnsons do and very few people know their name.

J.K Rowling sold a million bazillion books. A.N Other sold a thousand... and yet give books by both authors to a collection of people who have never heard of either and A.N Other is the prefered writer 45 times out of a hundred...

How does that work?


I have a dirty secret... under my glossy writer exterior... I'm a physicist.

And every now and again my science side escapes and stomps over some corner of the writing lawn with its science boots on.

Today it wants to tell you about how the business of success is a highly nonlinear affair. The mathematician in me could waffle on about feedback loops and reinforcement but the physicist likes to keep it simple (believe it or not, simplicity is the goal of all physicists).

I'm going to use the science of spherical cows which is explained in this joke:

There was a farmer that was having trouble with a cow that didn't produce good milk. The farmer decided that he'd hire three experts to figure out what was wrong with the cow. He hired and psychiatrist, engineer and a physicist, and gives them each a day with the cow.

After the first day, the psychiatrist comes to the farmer and explains that the cow is not happy inside the barn, and that the inside of the barn should be painted green, so that the cow will feel more at home.

The farmer isn't sure so he asks the engineer to give it a try.
After the second day the engineer comes to the farmer and tells him that the cow isn't being milked efficently, and gives him draftings of a very efficent milking machine.

Still not convinced, the farmer asks the physicist.
After a day of study the physicist goes to see the farmer. The physicist walks to a chalkboard and draws a big circle and says "Imagine the cow is a sphere..."


So in short, I'm going to make a ridiculously simple model that I hope captures some essential elements.

Let's take two authors who each start with 100 readers (random pick-ups due to launch day publicity say). Now let's say from that point on new readers are gained by old readers convincing people to read the book.

Let's say that each reader convinces r new people to read the book and that they do so in the week after reading it themselves.

The total number of books sold after n weeks is given to us by summing a geometic series (a formula I was taught in school at age 16)

a + ar + a r^2 + a r^3 + \cdots + a r^{n-1} = \sum_{k=0}^{n-1} ar^k= a \, \frac{1-r^{n}}{1-r},
Let's take two authors, call them Maz and Mark (just for kicks).

Let's say Maz's readers each convince, on average, 0.95 people to read the book, and that Mark's readers each convince 1.05. These authors appear to have written books of pretty similar saleability. One is not great and the other bad. They are both good, and the difference between their ability to inspire their readers to recommend them is fractional. It's shown below as height.

Let's work out their sales after 18 months.

a = 100
r = 0.95 or 1.05
n =78 weeks

Mark sells 87,907 books.
Maz sells 1,963 books.

Here's that difference shown as height...

 So, yes, cows aren't spherical (though they can be rolled), but the fact remains that the difference between selling 10 books, 10,000 books, 10,000,000 books comes down to fractions. The work of many brilliant writers goes virtually unnoticed while we build temples of worship to others whose tales have just that fraction more ability to move us.

And the bottom line?
        It's down to you.
              Like an author's work?

                     Tell someone!


  1. Thanks for the lesson! I pimp my favourite writers with religious fervour. When someone comes and visits they usually leave with a book and the order to go read it, it's awesome.

  2. Given your premises, its hard to argue with your results, although Harry Connolly (based on his blog posts about pimping his work) would probably argue with the set up of your equation. Not to put words in his mouth, but from the way I understand his methodology and observations (based on sales data), word of mouth seems to briefly inflate a balloon, rather than snowball as you have here with your summing of a series.

    1. One might be 'buzz' - the thing that races around the blog-sphere. The other is the quiet work of individuals who aren't part of the forum-blog-twitter clique and who over lunchbreak at work just mention what they've enjoyed reading.

      In the end that latter group hold vastly more power.

    2. Or in the bus. One thing I'v learned since I work in a Natural Sciences department and take the Campus Line 5 days a week is that people in the natural sciences in Germany _love_ Fantasy books. Yours included.

      I've had discussions about Martin and Abercrombie and whether or not Gardens of the Moon or Deadhouse Gates is the best start into Erikson, and none of those guys and girls in the bus knows about online places like Westeros. A few days ago someone started reading Prince of Thorns - that should give you some more sales in my hometown. :-)

    3. good to hear! Hooray for buses! ... and natural sciences... and Gabriele C.!

  3. Geez, that really puts things into perspective! It's kind of mind-boggling to think that what starts out as much a small difference ends up so massive by the end. Very interesting post, and even if I'm not math-minded enough to double-check the results, I certainly don't doubt the premise!

  4. That's a great post but I think there are more to sales than word of mouth (the four Ps of marketing! Promotion, placement, price, and finally, product).

    1. It's almost as if you're arguing that cows aren't perfect spheres...

    2. Reminds me of the gravity model of trade which tries to correlate abundance of some sort versus a resistance of some sort. Loosely, the abundance creates a positive feedback loop, which Mark's word of mouth model predicts. Each positive makes the next positive easier to attain. Each sale makes the next sale easier up to a limit, aka the resistance. It is used a lot of in real estate to loosely estimate income potential. Large 'anchor' stores like Best Buy attract an 'abundance' of shoppers which then benefit sales of satellite stores in the plaza until you hit a natural limit of how far people will drive (resistance).

  5. This made me think too (armchair psychology here) that it depends upon the "quality" of the early readers. For instance, I imagine some women read 50 SHADES and admitted it to their friends. Most of them had never read a snippet of erotica before so they wanted to "confess" this guilty pleasure to their friends (and in confessing, also show they aren't the same boring Mom-type, they've still got their young wild side going on). If it's someone the listener admires and aspires to be like (common among women and it just gets worse as women get older; competition can be brutal; God, I hate my own kind sometimes) then that listener perceives it's the cool thing to do, and kinda naughty (like I said, competition plus what Mom doesn't want to be naughty?) so THEY go read it and then pretty soon the "confession" turns to bragging... Or this could be total bullshit. But it's how I anecdotally witnessed it in my Stepfordesque neighborhood. -- Bets

    1. I sometimes think that the "naughty" factor is what's helped a lot of grimdark take off, as well as New Weird ten years ago.

      People love feeling just a little naughty about what they're reading (romance still outsells all of us!).

    2. I think people like grimdark for the same reason Danny Boyle rails against the Pixar-ification of cinema, some readers want books that handle adult themes in an adult way. They (readers) don't want to have books toned down for a PG or PG-13 rating in order to maximize market size.

  6. This is great. I am working with two writer's groups on line and one in real time, and I am not sure we get this as a community, though some of us do. I am now pimping your blog post!

  7. @travisrgriffin9 May 2013 at 02:01

    This is really interesting. I tell everyone I know that is remotely interested in fantasy to try Prince of Thorns. Sorry to say though, almost all of my friends will never read a book in their lives. I have nobody to talk to about you or ericksons books. This is why I constantly harass you on Twitter. That and lots of alcohol.

  8. Mark, huh?. That's actually kinda funny.

  9. As a fantasy writer who is an engineer beneath the surface, I've got to go with the milking machine on this one.

  10. You know, I just love your posts. Even if I shouldn't be giggling in front of my PC this time of the day....:)