Crossing the Equator 4: Small x Large, Publishing, and St. Petersburg Math

From the title, it doesn’t sound like this is an essay about writing. It is. More generally, it’s about successes and failures in publicity, and the mathematics involved.

Pop quiz: What’s a small number times a large number?

  • a large number.
  • a small number.
  • I have no idea.

There is a right answer. It’s “I have no idea.” It’s a poorly specified question. Yet, predicting the performance of creative work requires us to multiply small numbers by large ones. Let’s say that you’re a writer. What’s the probability that a person who goes into a bookstore looking to buy one book chooses yours? It’s small. It’s much less than 1 percent. What about the number of people who go into bookstores? It’s large. What does this mean? Well, it could mean anything.

I’ve spent more than a decade studying the economics of creativity. It pays– and it costs. The expected value (or mean return) of a creative effort is quite high. There are two problems:

  • Variance: most people would rather have $100,000 than a 50% chance at $200,000 or a 0.01% chance at $1 billion, even if all have the same average payoff. Most creative endeavors have high variance and $0.00 is not an uncommon result. If this is hobby writing, that’s fine. If one relies on creativity for an income, it’s dangerous.
  • Value capture: people who are good at creating value tend to be below average in the social skills involved in capturing value. So, the hardest-working and best people see most of their efforts enrich other people. This is a depressing social problem that I don’t expect to see solved in my lifetime.


I’ll do my best to keep this discussion accessible. This is about psychology, more than math. In general, people are bad with probabilities less than 10%.

Another pop quiz: which of the following probabilities is closest to that of being killed by a shark on a beach trip?

  • 0.01% (10,000-to-1)?
  • 0.001% (100,000-to-1)?
  • 0.0001% (1-million-to-1)?
  • 0.0000001% (1-billion-to-1)?

The answer is… the last. It’s very rare. Beach traffic kills far more people than sharks. You’re probably sucking down more micromorts if you lay on the beach and drink than if you get in the ocean, so long as you know how to swim. As humans, we’re bad when it comes to low probabilities. That’s part of why lotteries make so much money. We don’t have a resonant model for probabilities like “1 in 160 million”. When we multiply an out-of-context large event by a small probability, we have no intuition for what the result should be.

Why is publishing so hard?

I’m putting a finishing polish on Farisa’s Courage. This has put a lot of my mental attention on figuring out the publishing process. It’s not to be taken lightly. Self-publishing and traditional publishing both have pitfalls. They’re both very hard to do well.

The median outcome, for people who try either approach, is near zero. Most people who try to find agents never will. Most self-published books sell less than 100 copies. It’s the upside potential that keeps them going. Very few people make money on books. Some will improve their careers in other ways, and some view writing as a public service. However, we ought to be frank about the fact that the median book fares poorly. Perhaps it deserves to do so, because it’s easy to throw one word after another until one has 100,000 or so, but writing a good book is hard.

If I got Farisa’s Courage in front of a “Big 5” editor (chosen at random) in New York, I’d give it a very high chance (over 95 percent) chance that she recognizes it as publishable, professional-quality work. That doesn’t mean that I don’t get rejected. Publishers can’t afford to take every good manuscript. What about the likelihood that she picks it up and reads it for pleasure? Probably 1 percent. It might not be a genre that she cares about. She might be distracted and put the book down at page 20, never to pick it up again. That happens with books. To be honest, that 1 percent is a good number. I’m rating myself favorably, there. Anyone would could sell a book to 1 percent of the reading public would be set for life.

The painful truth about trade publishing isn’t that rejection is common. It’s the realization that it ought to be more common. Let me explain. Editors will go to bat for books they read and fall in love with, but that’s rare. It’s rare for all of us. Getting a trade publisher doesn’t mean that anyone loves your book. It could mean that, but it could also mean that you’re a “might surprise” and you’ll get no promotion. If you fail to earn out your (paltry) advance, you’ll probably never sell another book, even if it’s not your fault. The goal isn’t to “get published”, because much of what’s published is in the “might surprise” category that the publisher doesn’t really believe in, but to get a real deal (i.e., “all in” versus “might surprise”) that comes with a six-figure promotion package. That matters a lot more than an advance, which is just a signal. Even with an excellent book, the probability that someone has the reaction necessary to get that treatment is small.

I start reading about 120 books each year. I complete about 40. Perhaps 5 leave that kind of “this is so awesome” impression that I will tell others about them. Keep in mind that these are published books, often from highly selective houses. Those 115 others weren’t bad books. A publisher thought that they were good, and so did I, and I may have still felt that way after finishing. It just wasn’t enough to make me recommend it. Someone else fell in love with them; just not me. That’s 4%, and nothing was wrong with the other 96%.

When an editor decides whether to publish a book, she has to guess at how many other people will have that falling-in-love reaction… or at least enough short-term limerence (or curiosity) to buy it. It’s a rare thing, but there are a lot of people in the world. So it’s a “small times large” calculation and, as humans, we often have no idea what we’re doing. Who can tell the difference between a book that 0.25% of people will fall in love with (enough to recommend it to their friends) and one that 5% will feel that way about? The former is a publishable book of above-average quality. The latter is the next Harry Potter.

When it comes to word of mouth, which is the only sustainable way to get a book out there, it’s the extreme but infrequent reactions that drive. A “7” and a “2” reaction are the same: no movement. But look at the 50 Shades series. People hate those books. The writing’s bad and the characters are terrible. Yet enough people really love them that they’ve sold hundreds of millions of copies.

St. Petersburg paradox

A lottery ticket that pays out $100 million with 1-in-200-million odds is worth 50 cents. A stock that has a 50 percent chance of being worth $78 tomorrow and a 50 percent chance of being worth $76 is worth $77. That’s expected value: 0.5 * 76 + 0.5 * 78 = 77.

Okay, so let’s say that we have a lottery ticket with a base payoff of $1. The bearer flips a fair coin and the payoff doubles for each head, until a tail comes up. So, if he flips three heads, then a tail, it pays off $8. Here’s a random sample of 20 payouts:

$4 $1 $2 $16 $1 $2 $1 $2 $2 $1 $1 $128 $8 $1 $4 $1 $1 $1 $2 $1

We see that the ticket’s worth at least $1, and probably not more than $20. In twenty trials, we made $207, so we might estimate an expected value of $10.35. However, most of that value is in one trial where we got very lucky and made $128. Take that out, and we’re at $4.16. So what’s it worth?

If one ticket is for sale, most people would pay about $5 for it. They’d lose 7/8 of the time, but win big when they win.

I ran a simulation: 20 trials in which I pooled together 100 St. Petersburg tickets. The median value was $501, or $5.01 per ticket. With 10,000 in each packet, the median payoff was $7.66 each. With 1,000,000 in each, the median was $9.56 each. In other words, the more tickets you can afford to buy, the more that they’re worth.

This is counterintuitive. We see it because improbable high-impact events (like that $128 above) dominate.

To a large extent, publishing is driven by the St. Petersburg phenomenon. Some readers might love a book but not tell anyone about. Others will tweet to their 50,000 followers. Some reviews will sell 20 books and others will sell 200,000. Making it harder for writer and publisher alike, no one knows what the rules are.

Some writers might bemoan the death of the advance. Writers used to be able to live off advances. Now, advances are low and mostly a source of anxiety, because even paltry advances are not always earned-out. Why are advances disappearing? Publishers no longer know what sells books. (Also, publishers lose if bookstores screw up and can’t move product, but that’s not new.) They used to know exactly whose numbers to dial when they thought they might have a best-seller on their hands. Now, it seems to be out of their control. Books with million-dollar advances and top-shelf reviews can flop.

A good publisher will deliver reviews, radio and TV appearances, and opportunities to speak without the author paying out-of-pocket. (If you’re not getting this package, and it’s increasingly rare, then self-publish. Trade is only worth it if they’re all-in on you. Otherwise, keep the rights. You might want them.) Promotion and intangibles still matter. They seem to matter less, is all.

What does this have to do with St. Petersburg math? Well, let’s say that you’ve written an excellent book and you convince 20 people to buy it. What happens then? Probably, nothing. Your book is great, but that “I love this and will tweet incessantly about it” reaction is uncommon. If it happens for 2 percent of people (and that would be a great book) there’s a 67 percent chance that it happened with no one. Of those 20, you might get four who sell one more book and one who sells three. That’s seven more. They might move two more copies. From that base of 20, you’ve sold a total of 29 copies. Now, let’s say that you convince 2,000 people to buy it (or give 2,000 copies away). Your likelihood of reaching a “super-spreader” is a lot higher. Then, you can set off a word-of-mouth explosion, reach escape velocity, et cetera.

In the old world of trade publishing, we knew who those super-spreaders were. They worked in prestigious houses, or they were reviewers at the New York Times, or they were agents who drank with the big fish. If you kept getting rejected, you saw them as choke-points, but once you got in, they were your biggest allies and the only people you needed to please. Those still exist, but they don’t have the propulsion that they once did. This is probably good for the world. Readers matter more. However, it makes for a more confusing world– and nobody really knows how it works.

The value, in trade publishing, was that of having a super-spreader in your corner. St. Petersburg math tells us that if you sell 50 copies of an excellent book, you’re still probably going to be forgotten, because super-spreaders are rare and you probably won’t reach one. If you sell 50,000 copies of a shitty book, you’ll be a blip that fades out (celebrity books tend to do this). On the other hand, if you sell 50,000 copies of a great book, it’s only a matter of time before you sell 50,000 more. You might to be able to reach escape velocity with a smaller print run than that. There’s a critical point in initial propulsion (and, as importantly, initial social proof) that makes the difference between obscurity and success.

The death (?) of trade publishing

Is trade publishing going to die? No. It will evolve. I think that it’s going to be smaller and a lot more selective.

In every guild-like industry, the profits are made on people in their mid-career years. You lose money training novices, and paying them when they’re not producing salable work. You make some money from advanced professionals, but they’re free agents who can command market rate. Publishing used to have a similar model. They knew that they wouldn’t make their money back when they put a six-figure marketing campaign behind a first-time author, until she finished up her third or fourth book.

As in the rest of the corporate world, conditions have become somewhat better for free agents but worse for those expecting employers (or, in this case, publishers) to invest in them. The publisher’s not going to throw a six-figure marketing campaign behind a first-time author, out of fear that she’ll bounce to another publisher offering a better rate for her second book. Those relationships don’t seem to exist anymore.

So, how is trade publishing going to change? I think that we’ll see fragmentation as self-publication becomes more common, and as the infrastructure connecting readers and writers directly becomes more mature. Mass-market fiction authors who can sell millions and have turned their work into utilities, they’ll find trade publishers. We’ll also see trade publishers holding on to historical nonfiction and biography, where the research and fact-checking demands are high and the validation of being traditionally published still matters. Established literary authors will probably continue to be traditionally published, even at a loss for the house. This is probably the last generation for which a first-time author can get traditional publishing. Look at where the system is now. Getting the right to submit to a publisher requires finding an agent. Now, agents don’t even read manuscripts. Interns, who function like agents for agents, do that. It’s decentralized and unplanned, but it’s a lot of bureaucracy. It’s still navigable, but just barely, and a lot of talented writers are looking at what it offers (small

That’s not to say that one shouldn’t pursue trade publishing and query agents. For one thing, there’s still a prestige benefit. That, actually, might grow. It’s a lot more competitive to get into Harvard now than it was in 1987. What does that mean? It means that everyone who went there in ’87 had his stock go up. Likewise, as trade publishing contracts, the prestige of having used it successfully might increase. Further, when it works for an author, it works very well. A deal that comes with a six-figure promotion budget is usually worth taking.

The standard package that most authors get isn’t worth giving up the rights. Let me explain why. Most trade-published books are just over the line and get a “might surprise” package. The publisher isn’t going to promote those books. In fact, they may ask for a marketing plan in addition to a manuscript. The author does the work. Essentially, it’s self-publishing but with important rights given up and shitty royalties– in exchange for a paltry advance. The only reason why authors take such deals is that the publishing process is so exhausting and time-consuming that they’re just relieved to be done with.

If you’re in the “might surprise” category, publishers demand that you have a social media presence, because they’re not going to market the book. Now, social media marketing is going to do, in the 2020s, what traditional marketing did in the 2010s. That is, it’ll lose effectiveness. What is unlikely to lose effectiveness is giving high-quality stuff away: gift copies, lowered prices, free chapters, and search-engine indexing if free material is posted online. If you use trade publishing, you can’t do any of that. You’ve given up those rights. You can’t offer your e-book at 99 cents on your protagonist’s birthday. Your strongest option is to ask people in 140 characters to buy a rectangular solid made of plant matter and chemicals.

Ten years ago, few talented authors self-published. These days, most say that they will self-publish if they can’t find a trade publisher. Over time, self-publishing (which may be renamed to entrepreneurial publishing, because to do it right, one has to do things like hire professional editors and cover designers, and that’s business) will likely be the default way for talented authors to break out. Trade publishing will be for victory laps only.

2 thoughts on “Crossing the Equator 4: Small x Large, Publishing, and St. Petersburg Math

  1. This is well written. As you said, writers find it difficult to make living from writing, and visual artists fare better. I’ll soon start reading farisa. If I feel anything remarkable from the book, I will tell.

  2. Pingback: Quotebag #119 | In defense of anagorism

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