Sales of the book have accelerated so much that we’re about to sell out of the first printing of Modernist Cuisine. As we prepare to order a second printing, we face a big question: how many more copies should we print?

Several crucial parameters go into this calculation. After we order the printing, it takes about four months to manufacture and ship them, so ordering now gets books from the second printing to us in June. That is not as early as we would like, but that’s how it goes.

At a minimum, we should order enough books to handle four months’ worth of sales; otherwise we would need to order a third printing the moment the second arrives. We need more than this, however, because customers will place new orders between mid-March and mid-June. Taking that into account, we ought to order at least as many as we expect to sell in seven months.

But seven months’ worth of books would run out in October 2011. We would have to rely on a third printing to cover the holiday season. That seems like a risky proposition. If we make a mistake, we could run short of books just when more and more people want them. Complicating matters further, in order for the third printing to arrive in October, we would have to order it in June. Although we’ll know more about the level of demand for Modernist Cuisine in June, we won’t know as much as we would like.

Together, all these factors create a pretty strong motivation for us to order enough books in the second printing to meet demand all the way through the holiday season and into January 2012. Doing that means ordering 10 months’ worth of books, and taking into account that those 10 months include holiday gift giving.

How many books is 10 months worth? That is the big question.

We have always believed that word-of-mouth communication would be critical to sales of Modernist Cuisine. The book is hard to describe, and it is a big enough purchasing decision that many people will need to hear from a friend or see the book in a friend’s kitchen before they buy it. It is hard to tell how well people like the book until people have experience with the book.

That process is just starting. So far, we only have experience with pre-orders. A few hundred copies of MC have been in people’s hands for perhaps a week. That is not enough copies (and not enough time) to get a good handle on how strongly the word-of-mouth buzz will build. We’re trying to get the first printing out as quickly as possible, and by the end of April we’ll see what happens when 6,000 books get into the market.

Unfortunately, a reputation takes time to spread by word of mouth. Customers may need to spend weeks dipping into MC enough to start recommending it to friends and acquaintances. It also takes time for word-of-mouth interest to translate into orders. The first printing will give us a good read on whether the person-to-person buzz around the book is going to be powerful or not, but it is unlikely that we’ll get that read until some point in May or June.

A countervailing factor is that the book is currently back-ordered. Some people don’t want to wait; rather than getting in line, they say “I’ll order when the book is in better supply.” That won’t happen anytime soon, so the volume of orders we see in April and May might not reflect the true demand.

When we faced the same decision for the first printing, we had exactly zero experience. Several publishing companies told me to print 2,000 copies. I wanted to make 10,000, but what at the time seemed to be wiser heads on the MC team prevailed, and we compromised at 6,000 copies. It seemed inconceivable that we could run out of 6,000 copies before we could get a second printing done, so it seemed safe.

In retrospect we clearly should have printed more, but hindsight is like that. It’s unfortunate that 4,000 people will have to wait a couple months longer than if I had followed my initial instinct, but it now seems that a second printing was inevitable regardless. Even more crucially, I would have no more data now to make that inevitable decision on the size of the second printing.

Over the course of the last couple weeks our ideas about how many copies to order for a second printing have increased as sales of the book have soared. Earlier this week, the book hit number 45 on Amazon’s ranked list of all books by sales; it reached number 6 in the cookbook category. But we still don’t have much of an idea of how this translates into sales across the year.

As one example, one could postulate that there are a fixed set of people who want the book, so they will order at a high rate, but once they all have their copies, orders will quickly dry up. I hope that isn’t true, but it is certainly possible. But even if it is true, what is that number? If the total possible market is 10,000, then I really have to worry about it. If the number is 100,000, that is a different story.

An even simpler model is to assume that the current rapid sales rate is driven by the publicity and media coverage surrounding the book. That effect is certainly real, and it is highly likely that the media interest will start to fade in another month or so. So maybe we shouldn’t order that many. On the other hand, while we know that press and broadcast coverage will diminish with time, we also know that it will be supplanted by word of mouth. I don’t know how to quantify the strength of that replacement.

Here’s another imponderable: how big a holiday sales spike should we expect? Normally, cookbooks are timed to come out in September or October precisely so they get a big boost from holiday gift sales. In our case, we started to ship nine months before the holiday season, so a lot of people who would be perfect candidates to get MC as a gift may well buy it for themselves, or get it for their birthday. So maybe we won’t get a big holiday boost. Or maybe we will get one, but it will be offset by a decline in late summer.

Some people on our team started out suggesting a second printing of 10,000 to 15,000. Now they are suggesting 20,000, whereas my instinct is that 25,000 is the right number. That’s probably what we will order, but I wonder whether I am thinking too small (again!).

One final factor is that book printing is a scale game: the more you print, the cheaper the cost per copy. The reason is that setting up the print run carries a high cost, which gets amortized across all the books in the run. Unfortunately, this effect is strongest at small print runs; once you get out to 20,000 copies, the incremental price drop becomes small for the next 5,000.

If anybody has thoughtful suggestions about many copies we should print, I’d be happy to take them. Just post them as comments here.