Category Archives: Publishing

How to Make Figures for Formal Articles

Posted on August 10, 2020 | Leave a comment

My last post on how I write formal articles stressed the importance of figures. I thought it might be helpful to expand on that idea. In short, figures are a critical part of the communication process. Good figures separate the well-executed papers from the just good ones. They will reinforce your key points, allow you to write about your results in a more engaging manner, and help you learn more about your model in the process.

Put differently, you need figures in your paper. And the better they are, the better it is for you. These are my thoughts on them.

Why Should I Have Figures?
There are two connected reasons to have figures in your papers: clarity and readability. The majority of formal papers attempt to convince the reader that something that is not obviously true is, in fact, true. We jump through all sorts of hoops to accomplish this. Unfortunately, those hoops are often dense or dull (inclusive or). A picture is worth a thousand words, and replacing a thousand words of abstract mathematics is a win.

Regardless of the mathematics, you want to invite your readers to actually read your manuscript. If someone is skimming through articles, a 10,000 word wall of text is not going to stop them. It also will not stop someone who has read the first five pages and getting bored from closing the window.

But imagine instead one of these readers encounters a figure that shows them something really strange. Someone who was not planning to read your paper might want to learn how the figure came to be. And it might also convince your slipping reader that the ride is worth continuing.

What Should Be Made into a Figure?
My rule of thumb when making figures is to pretend that I am doing an invited talk for the paper I am writing. What do I want to put in the slides to illustrate all my main points? I do not want a slide that says “Proposition 3: The probability of war is nonmonotonic in its costs.” That is boring. I should instead have a plot that illustrates the point. After thinking about all of those slides I would want to make, I will then put almost all of them in the paper itself.

More concretely, I almost always want an equilibrium plot that varies a parameter of interest and shows how the equilibrium changes. These come in two forms. The first is one dimensional. If the narrative you are telling only focuses on one variable, then put that variable on a number line. Add some cutpoints on that number line, and describe the equilibrium behavior associated with it.

Here is an example from my Doubling Down paper:

We are varying the quantity of a CDF evaluated at a particular value. Because it is a CDF, we have bounds on 0 and 1. There are two cutpoints also labeled along the axis that separate the three equilibrium parameter spaces. The top part gives a little context of what is happening in the equilibrium and matches that description to the corresponding proposition in the text. Keep in mind that these are not hard rules about what should be in the figure—what you ultimately put into it depends on what you think is important to communicate with the reader.

The second type figure is two dimensional. These are more complicated to build but are necessary if the narrative is on how large some quantity is related to another. The first step is to put all of the cutpoints in terms of one parameter. This becomes your vertical axis. Your horizontal axis is the other variable of interest. The equilibrium regions of the corresponding figure are now shapes that you can fill in with the critical information.

Here is an example from my Bad-Faith Cooperation paper:

The two key parameters we vary in this figure are the cost and effectiveness of resistance. The labels tell the reader what type of signaling strategy the types adopt for each parameter space and how much resistance the actor chooses within the equilibrium space.

To actually draw two dimensional figures correctly, you need to use realized values of the parameters. It will often take some finagling to get the ideal spacing for each region and to make sure that the each parameter space you want to cover exists for those realized values. As a result, there are usually a lot of moving parts in the final figure you draw. I try to compensate for that by removing any extras that do not absolutely need to be in the figure. This is why the two dimensional figure does not have axis labels for the cutpoints, unlike the one dimensional figure.

Outside of equilibrium plots, you should consider drawing figures for any comparative statics of interest. Any nonmonotonicities or discontinuities always make the cut. Here is an example of that from my Credible Commitment in Covert Affairs paper:

The horizontal axis varies how much trouble an executive gets in if a covert action is exposed. Even if I have lost a reader during the modeling section, there is a good chance that this figure will pull them back in. The executive would seem to be hurt by the potential to get into trouble. The black line on the figure would appear to confirm that. But why does it suddenly go up (red) and then level off (gray)? That is puzzling. I may just have pulled the reader back into the text to find out the answer.

For the most part, the only comparative statics do not receive corresponding figures are basic monotonic relationships, especially if the plot would be just a straight line. Even then, if something strictly increases before becoming flat, I may still want to include that.

How Do I Make Better Looking Figures?
Now that we have established why you should have figures and what is worth figuring, you may want to spend some time making those figure look more attractive. I have two tips here.

First, I strongly recommend TikZ. It integrates seamlessly with TeX, so you can insert math expressions at the proper cut points. It offers precision in what you draw that you cannot obtain from computer-assisted hand drawing. You can even use functions to draw your lines, meaning that you are visualizing exactly what the value is and not some approximation. And it is rendering all of this as a PDF, so your figures will scale nicely with the rest of your document.

The other major recommendation I have is to use color. Oftentimes, adding color will reduce the complexity of the figure, and it also helps make the figure pop out of the document. For equilibrium plots, this means giving each region its own color. Narrating the figure becomes easier, now that you can describe regions by color and not by location.

For estimated quantities, this means giving each value drawn its own color. Actor A’s utility could be black, while Actor B’s utility could be red. If there is only one line to be drawn, then sticking with black and white is fine. Sometimes, though, you will still want to use multiple colors for the same line. This can help distinguish between two regions of the figure as you are narrating it in the text. The utility plot above is an example of that.

The one word of caution I have here is that you are a researcher and probably not a graphic designer. When you start adding a ton of different colors, it is easy to inadvertently create clashing palette. The simple solution to this is to rely on preexisting sets of colors.

These are easy to find online, and universities conveniently give all of the information you need. A simple Google search consisting of the university name + identity (e.g., University of Pittsburgh identity) usually gives you what you need. The key piece of information is the RGB values for the brand colors. You can then define those colors in the preamble of your TeX file (e.g., \definecolor{cardinal}{RGB}{140,21,21}), and use the newly named color in the TikZ commands. I think that Stanford and University of North Carolina are particularly good for these purposes.

One thing to be mindful of is whether the colors are distinguishable in grayscale. Publishers now commonly allow for colored images appear in the online version of articles, but whatever goes to the printer needs to be black and white. Moreover, a peer reviewer may use an office printer to print your color PDF before reading it. Verifying that every color is distinct in grayscale will reduce that reviewer’s frustration.

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Tagged figures, Publishing, tikz, writing

How I Write Formal Articles

Posted on May 25, 2020 | 1 comment

Suppose you want to write a formal theory paper. Below is the template I use to do this. I do not always follow these rules. But whenever I break them, I usually justify to myself first why it is a good idea to sidestep the norm.

The Introduction
My introductions usually have a set formula:

Begin with an anecdote that motivates the main point of the paper.
Generalize that main point.
Pivot to how existing work does not address that main point.
Describe the model setup.
Give the results and basic intuition.
Explain empirical content, if there is any. For quantitative work, this means describing the type of regression you are doing and one or two key substantive effects. For qualitative work, this means describing the case, how the central issues of the model were in effect, and how the outcome fits expectations.
A paragraph or two of related work. Note that this may not be necessary depending on the extent of the comparison in (3) and whether there is a motivation section below.

Of these, I think (5) is the biggest problem I see as a peer reviewer. There are way, way too many papers that will say things along the lines of “increases in income decrease the probability of terrorist attacks” full stop. The intuition explaining the connection will not appear for the first time until page 18 or so. This fundamentally misses the point of doing formal theory. We are not interested in the what. We are interested in the why. Formal theory helps elucidate mechanisms. If you are not elucidating the mechanisms in the introduction, you are not writing an effective paper.

To that point, I find it helpful as a reader (and a reviewer) when this part begins with “The model produces x main results. First, …” Then each subsequent x – 1 paragraphs then explains the other results. This gives a good benchmark to the reader of what to expect in the paper and think about what a model look like that would be good for addressing those issues.

Motivation, Sometimes
I have the most variance in what comes next. Sometimes, it is straight to the model. Other times, I give a deeper explanation for why I am building the model that I am.

An underappreciated aspect of formal theory is that it just an exercise in mapping assumptions to conclusions. As the saying goes “garbage in, garbage out.” If the assumptions you put into a model make little sense, then there is no reason to pay attention to whatever the model outputs. Thus, if readers may view the assumptions your model makes as controversial, this is the time to defend them.

Sometimes, this is unnecessary. For example, if the model takes an existing approach and adds uncertainty, then you probably only need a couple of citations in (3) from the introduction to take care of it. Otherwise, I think through the main critical assumptions from the model. I then begin the second section by listing them. The following paragraphs take each assumption and motivate them. Basically, this is an exercise in going through the existing literature to demonstrate that your assumptions have merit. Key places to draw from are:

existing models that use the assumption in a different context (e.g., models of war have uncertainty over resolve, but the standard models of terrorism do not)
quantitative literatures that establish stylized facts that the theoretical literature has not yet developed
qualitative studies that devote the entire work to motivating the same point you want to make

Of these, (3) is the most useful and the type I try to emphasize.

There are two important notes to this section. First, it is not a literature review. You are not just rehashing what the literature says about a particular subject. You are motivating assumptions. Everything you write should be geared toward that.

Second, this is a good way to come up with research ideas in the first place. As a general exercise, whenever I read through the literature, I think about what assumptions are out there and whether they appear in the more specific areas I work in. When there is a mismatch, it is worth spending some time to think about whether those alternative assumptions fundamentally alter existing ideas.

The Model
My modeling sections usually follow a basic formula:

Introduce the players, moves, and payoffs in that order. For most models worth exploring, drawing a game tree is often more cumbersome than it is helpful to the reader. Bulletpoint lists are often more useful for illustrating this.
Describe any conditions on parameter spaces. For example, corner solutions often complicate the math without providing any extra insight. If that is the case, describe what you are assuming, give the explicit mathematical expression (perhaps in a footnote), and explain why the reader should not care about this.
Give any baseline results that are necessary to understand what is to come. For example, if you are working on an incomplete information game, explain the results of the complete information game first. Sometimes, these will be so straightforward that you can do this in a couple of paragraphs without the need to have formal propositions. Do this if you can. Other times, the baseline results are themselves of theoretical interest. In this case, use the formula below.
Give a proposition. Propositions are usually if-then statements. The “if” part should be an intuitive meaning and parameter space. For example, “Suppose costs are sufficiently high (i.e., c > mk – d).” The “then” part is the strategy or outcome that is worth exploring.
Explain the intuition of the proposition. Do not get bogged down in the calculations. But at the same time, do not be afraid to explain the derivation of cutpoints. Some cutpoints appear to be incredibly complicated but are in fact straightforward comparisons. This can give the reader greater insight as to where the relationships are coming from.
Repeat (4) and (5) until equilibrium is exhausted.
Recap using an equilibrium plot. Almost every paper benefits from one of these.
Give the interesting comparative statics, either as propositions or remarks. Provide the intuition just as you would with the equilibrium. Plot the comparative static.

The plot part is the thing I see as the easiest way to improve papers. A good rule of thumb is to pretend every paper you are writing is going to be used as a job talk paper. Then think about what slides you would want to present to illustrate the key points. For example, if you had a slide that said “the probability of war increases in the cost of fighting,” you would not want to leave it as just that. You would want the next slide to show a plot with cost on the x-axis and the probability of war on the y-axis. After going through this mental exercise, every visualization of the results should go in the paper.

Empirical Evaluation
This section may or may not exist. Some models require so much space that doing any sort of empirical evaluation is not impossible given the 10,000 word limit you have to aim for to fit most outlets. Otherwise, there are two ways to go here.

Option 1 is to do some sort of qualitative examination. Hein Goemans and I have written about this in Security Studies. If you want to go down this route, you should read that.

The main trap I see when papers take qualitative approach is matching outcome to outcome. For example, the model might predict that poor people commit terrorism, and then the case study talks about how poor people commit terrorism in a certain country.

This misses the point of doing formal theory. As I described above, models map assumptions to conclusions. Case studies should do the same. In other words, I take the three or so assumptions that are key to the model’s mechanism. I then motivate why those assumptions held in the particular case. Only then is the outcome variable worth mentioning. But the key here is to establish that the incentives that the model describes was key to the actors’ reasoning. (Or at least those incentives plausibly drove it. There are many cases where finding a smoking gun would be a ridiculous expectation. If that is the case, then you should make an argument about why it is ridiculous.)

Option 2 is a quantitative examination of a comparative static. Most of this follows the basic quantitative paper template, so there is not much more to say here. The only thing worth adding is that you need a subsection that pivots the comparative static to a hypothesis that you can test. (Comparative statics are true statements. Hypotheses are things that may or may not be true of data.)

Conclusion
I think conclusions are overrated, so I have a simple formula for this:

Recap the main findings.
Describe takeaways for policymakers.
Consider what extensions to the model might be interesting for future theoretical research.
Explain how empirical scholars might wish to address the findings.

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Tagged article, formal theory, how to, Publishing, writing

How Long Does It Take to Publish an Academic Book?

Posted on April 8, 2019 | 1 comment

My first book with original research just came out. (Amazon even has proof!) This excites me, as you can see from this picture from a couple of weeks ago, when I held it it my hands for the first time:

Part of my elation came from reflecting on just how long I had been working on the project. I thought it might be interesting for younger scholars to get a full perspective, so I am writing out a brief timeline of book-related events here. It might also give a better overview on the origins, thought process, and evolution of a long-form project. There is also going to be a healthy dose of luck. And regardless of utility to others, it’s going to be cathartic for me.

Here goes:

9/25/2009: Yes, we are starting almost ten years ago. I was in my gap year between undergrad and grad school. Applications were not yet due, but I was set on getting into a program and making international relations research into a career.

Globally, Iran was getting bolder with its nuclear program. President Obama, at a G20 summit, issued a warning:

Iran must comply with U.N. Security Council resolutions and make clear it is willing to meet its responsibilities as a member of the community of nations. We have offered Iran a clear path toward greater international integration if it lives up to its obligations, and that offer stands. But the Iranian government must now demonstrate through deeds its peaceful intentions or be held accountable to international standards and international law.

I remember watching Obama make that speech (which YouTube has preserved for posterity) and thinking that such a bargain would not work. Everything I had read at that point about credibility and commitment problems would suggest so. Why wouldn’t Iran simply take the short-term concessions and continue building a weapon anyway? No paper had constructed that exact expectation yet, and so I thought it would be a straightforward project.

Nevertheless, it would have to go on the backburner. I still needed to revise my existing writing sample and do grad applications.

4/2010: By this point, I had accepted an offer from the University of Rochester. I started fiddling around with modeling Obama’s deal and came to an interesting conclusion. It seemed that compliance was not only reasonable, it was rather easy to obtain. All the proposing country had to do was give concessions commensurate with what the potential proliferator would receive if it had nuclear weapons. The potential proliferator could not profit by breaking the agreement, as doing so would barely change what it was receiving but would cost all of the investment in proliferation. Meanwhile, as long as the potential proliferator could keep threatening to build weapons in the future, the proposer would not have incentive to cut the concessions either.

This project was a lot more interesting than I thought it would be!

8/8/2010: I moved to Rochester and got serious about trying to formalize the idea. The problem was that I had only taken a quarter of game theory before. So the process was … painful, especially in retrospect. I still have an image of my work from way back when:

I can make out some of what I was trying to do there. It is ugly. But I also think this is useful advice for new students. As a first year grad, you are in a very low stakes environment. Trying to do something and doing it poorly still gets you a foothold for later.

In any case, active progress on this was slow for the next couple of years. I had to take some classes to actually figure out what I was doing.

3/9/2012: I watched the previous night’s episode of The Daily Show for no real reason. In a remarkable stroke of luck, it featured an interview with Trita Parsi, an expert on U.S.-Iranian relations. He made some off-the-cuff remarks about Iran’s concerns of future U.S. preventive action. Fleshing out the logic further gave me the basis of Chapter 6 of my book, with an application to the Soviet Union.

9/2012: I made “The Invisible Fist” my second year paper. At the time, this was the biggest barrier for Rochester graduate students, but the idea from three years earlier got me through it.

The major criticism as I circulated the paper was that the model only explained why states should reach an agreement. And while nonproliferation agreements are fairly commonplace, so too are instances of countries developing nuclear weapons. Trying to simultaneously demonstrate that (1) agreements are credible and (2) other bargaining frictions might make states fail to reach a deal anyway was too much for a single article. I began looking for more explanations for bargaining failure beyond the one I had encountered for the Soviet Union.

5/17/2013: My dissertation committee felt that I had found enough other explanations, as I passed my prospectus defense. This was the first time I produced an outline that (more or less) matches what the book would ultimately look like.

12/2014: International Interactions R&R’d an article version of Chapter 6. It would later be published there. Tangible progress!

5/2015: Reading through the quantitative empirics of my book, Brad Smith suggested a better way to estimate nuclear proficiency. This eventually became our 𝜈-CLEAR paper. I would later replace the other measures of nuclear proficiency in the book with 𝜈.

6/10/2015: After two years of grinding through lots of math and writing, I defended my dissertation. Hooray, I became a doctor!

7/14/2015: The Joint Comprehensive Plan of Action—a.k.a. the Iran Deal—is announced. This was could not have been timed any better. Chapter 7 of my book was a theory without a case, only a roundabout discussion of the Iraq War. But the JCPOA nailed everything that the chapter’s theory predicted. I began revising that chapter.

8/2015: I began a postdoc at Stanford. My intention was to use the year to get the dissertation into a book manuscript and talk to publishers. But after six years of thinking about nuclear negotiations and not much else, I was really burned out. I still received excellent feedback on the project during the postdoc, but I set aside almost all of it. The year was productive for me overall, just not on the one dimension I had intended.

10/2015: The JCPOA went into effect. With nuclear negotiations all over the news, I hit the job market at exactly the right time.

7/2016: I moved to Pittsburgh. Remember that Obama speech in front of the G20? In what is a remarkable coincidence that bookends my journey, that summit was just a couple of miles away from where my office is now.

1/2017: I was still burned out. This became a moment of reflection, where I realized that 20 months had passed without making any progress on the manuscript. I convinced myself that if I didn’t get moving, the thing would hang over my head forever and not provide me any value toward a tenure case. So I cracked down and got to work.

3/2017: I sent an email to an editor at Cambridge. He quickly replied, and we set up a meeting at MPSA. Once in Chicago, he liked my pitch and asked to see a draft when I was ready.

5/22/2017: After making some final changes to the manuscript, I sent off a proposal, the introductory chapter, and the main theory chapter to Cambridge.

6/6/2017: My editor wrote back asking for the full manuscript to look over. I did so the next day. One day later, I saw an email notification on my phone that he had responded. I panicked—there is no way that a one-day response could be good news, right? But it was!

You may notice a theme developing here: my editor was fast.

9/6/2017: After three months, the reviewers come back with an R&R. Hooray!

Having published a few articles beforehand, the R&R process was not new to me. But it is an order of magnitude more complicated for book manuscripts. Article reviews are rarely more than a couple of pages. In contrast, I had twelve pages of comments to wade through for the book. This was daunting: a mountain of work and a lengthy road before any of it actually makes noticeable progress to any outside observer. After having gone through almost two years of burn out on the project, this had me slightly worried.

9/12/2017: I developed a solution to the problem that would work. The key for me to maintain focus and appreciate progress was to create a loooooong list of all the practical steps I had to take in revising the manuscript. By the end, I had a catalog of 70 things to do. I put that number on my whiteboard:

I dedicated at least a couple of hours every day to working on the book. Whenever I finished an item, I would go to the whiteboard and knock the number down by one. This gave me some tangible sense of progress even when the work ahead still seemed enormous. It also kept me focused on this project and resist the temptation to work on lower-priority projects that I could finish sooner.

11/28/2017: I sent the revised manuscript back.

1/28/2018: The remaining referee cleared the book. All the hard steps were over!

3/28/2019: I held the real thing in my hand for the first time.

So almost ten years later, I am all done with the project. I cannot describe how satisfying it was to move the book’s computer documents out of the active folder and into the archived folder. I can now finally put all of my effort into the other projects that have been pushed to the sidelines.

But with all of that said, ten years feels like a bargain. Some of that time was pure circumstances: I had to actually learn how to be a political scientist for a good portion of it. I was also an okay writer at the beginning of this, but now I feel that I have a much better grasp of how to communicate ideas.

Nevertheless, some portion of it was my own fault. I could have not put the project on the back burner for more than a year. I suppose if that was the price I had to pay to maintain my own sanity and happiness (and not work on something I was not into at the time), it was a deal well-worth taking.

I was also really, really fortunate with the review process. The first editor I spoke to was receptive of the project, and the reviewers I pulled liked it. Had that not been the case, it is easy to see how a ten year project could have turned into a twelve or thirteen year project. While I hope that future book projects will not last as long, I doubt this part will be as simple the next time around.

In any case, it feels great to finally be done!

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Posted in nuclear weapons, Political Science, Publishing

Amazon’s Clever Price Discrimination Strategy

Posted on March 9, 2015 | 2 comments

Amazon likes to discount books. Here are some examples, starting with Game Theory 101: The Complete Textbook:

We are only looking at the print prices in this blog post. Originally $13.99, Game Theory 101 is yours for only $11.75.

It’s a similar story for The Rationality of War:

Down from $10.54, you can buy The Rationality of War for $9.30.

And finally, here’s Game Theory 101: Bargaining:

Originally $11.09, Bargaining now sits just under $10.

I suspect the average consumer is pleased to see these discounts. For authors who publish through CreateSpace, however, these discounts are incredibly confusing. We can set the original price. No matter how much Amazon discounts it, they pay us a set amount of money per sale. As such, we also like Amazon’s discounts. In fact, the larger discount is, the happier we are.

The problem is, the discounts are inconsistent. When you initially publish a book, Amazon will always tag it with the list price. Then, after some time and without any warning, Amazon might reduce the price. Or they might not. I have discussed this problem with other authors, and there doesn’t seem to be any explanation for what’s going on.

That said, I now have a theory. Amazon has found a clever form of price discrimination.

What Is Price Discrimination?
The maximum price any of us is willing to pay for a good or service can vary heavily. A lot of Americans will pay $10 or more to see Fifty Shades of Grey. Meanwhile, others may only be willing to pay $1 to see such a movie. We call such a maximum price an individual’s reservation value.

As a business owner, your dream is to charge everyone their reservation value. For example, suppose Fifty Shades’ potential audience consists of two people, one who is willing to pay $10 to see the film and the other who is willing to pay $1. If you could somehow charge the $10 person $10 and the $1 person $1, you would make $11. This makes you the most amount of money possible.

Of course, movie theaters cannot easily distinguish between those high value and low value types. As such, like most businesses, they offer a single blanket price of $10. The $10 person sees the film but the $1 person does not.

Despite the difficulty in price discriminating, businesses try it to varying degrees of success. Student and senior citizen discounts are perfect examples. Both of these groups live off of fixed (and small) incomes. Consequently, as a whole, they are less willing to pay high prices for entertainment. Businesses like movie theaters therefore offer cheaper prices to these groups than to people who tend to have larger disposable incomes.

Airplane flight prices work in a similar way. Vacation travelers are unwilling to pay $1000 for a flight across the United States. In contrast, many business travelers who need to get to New York on short notice are willing. Airlines thus charge relatively cheap prices on flights booked well in advance and massively jack up the prices on the days before takeoff.

Don’t let these discounts fool you. Although they may make it seem like the businesses are acting generously, the discounts exist to maximize profits.

Price Discrimination on Amazon
Broadly, people who publish through CreateSpace fall into one of two categories: vanity authors and what I will call profit makers. Vanity authors write books without the intention to make money. They simply want to “publish” a book so they can say they have. These authors will sell tens of books to friends and family, but their work will never catch on with a larger audience. They give self-publishing a bad name.

Profit makers use CreateSpace because they do not want to hand over a large share of revenue to a traditional publishing house. Vanity is not a concern here. They invest time in writing books and publishing through CreateSpace because they know their works will make a substantial amount of money.

Unfortunately for Amazon, it is very difficult to differentiate between vanity authors and profit makers. Further, there are substantially more vanity authors than profit makers out there. As such, Amazon’s best guess for any new book coming from CreateSpace is that the work is from a vanity author.

This is where I think Amazon’s price discrimination comes into play. Amazon suspects that every new book is vanity. Sales of vanity books do not operate like a normal market. Vanity authors are selling virtually all of their books friends and family. These individuals are willing to spend more money on these books because they know the author. Their reservation price is consequently higher than your average individual. In many cases, it may be substantially higher—a poorly edited vanity book is essentially worthless to the average consumer, but friends and family might be willing to spend $10 or $20 on the book.

If you are Amazon, what incentive do you have to cut the price? Any discount you offer directly hurts your bottom line, and these vanity books are not responding to standard supply and demand factors. Consequently, you don’t have any incentive to discount. The vanity books will be sold to the friends and family and no one else. No discount maximizes your profit.

Of course, Amazon suffers when the book is from a profit maker, not a vanity author. These books respond to supply and demand, so cutting prices by 10% can actually cause more people to buy them. So Amazon might want to reduce the price in these circumstances.

Put yourself in Amazon’s shoes for a moment. You want to discriminate here to maximize your profit. But how?

From my personal experience and discussion with other authors, I think Amazon has figured out a way. They start by offering no discount, under the assumption that the book is from a vanity author. They then wait. And wait and wait and wait. Vanity books will see their sales fall off a cliff after a month or two. Profit making books will see continued sales over the long term. This differentiates the type of book. Amazon thus cuts the price of books that sell, knowing that doing so will lead to even more sales.

To be clear, this is speculation backed up with some non-random observations. Still, I think there is a good chance that price discrimination explains Amazon’s strategy. Although the discounts may seem to be applied randomly, I can’t imagine a company with $88 billion in revenue is doing this without purpose. Price discrimination explains it.

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Tagged Publishing

Kindle Unlimited and the Economics of Bundling

Posted on July 18, 2014 | 1 comment

Today, Amazon announced Kindle Unlimited, a subscription service for $9.99 per month that gives buyers all-you-can-read access to more than 600,000 books. And it took, oh, five minutes before someone called this the death of publishing.

Calm down. This isn’t the end of publishing—it is a natural extension of market forces and is potentially good for everyone.

Amazon is taking advantage of the economics of bundling—selling multiple products at an identical price regardless of how much the consumer uses each component. Bundles are all over the place; cable TV, Netflix, Spotify, and Microsoft Office are all examples of bundles. These business plans are pervasive because they work, they bring in a lot of money for their providers, and they leave consumers better off as well.

Wait, what!? How is it possible that both providers and consumers are better off by bundling? A while back, I too believed that this was insane and that bundles were a scam to get me to pay more money than I wanted to. (Why should I pay $1 for Home and Gardening when all I want is ESPN?) But then I read up on bundling and understood my folly.

An example will clarify things (and potentially amaze you, as it did for me not too long ago). As usual, I will keep thing simple to illustrate the fundamental logic without getting us bogged down in unnecessarily complicated math. Imagine a world with only two books available for purchase:

Further, let’s assume that there are only two customers in the world. Let’s call them Albert and Barbara. Albert and Barbara have different tastes in books. Albert prefers Hunger Games to Game Theory 101; he would pay at most $4.99 to read Hunger Games but only $1.50 at most for Game Theory 101. Barbara has the opposite preference; she would pay at most $2.25 to read Hunger Games and $3.99 to read Game Theory 101. You might find the following graphical representation more digestible:

Finally, assume that the marginal cost of each book is $0.00. That is, once the book has been written, it costs $0.00 to distribute each book. This is a bit of an exaggeration, but it is close to reality for electronic books. However, it is definitely not true for physical books (printing, shipping, etc.). This distinction will be important later.

With all those preliminaries out of the way, consider how a seller should price those books in a world without bundling. There are two options. First, you can price a book at a low price to capture the entire market share. Second, you can publish the book at a high price; it will sell fewer copies but make more money per unit.

Let’s apply that decision to Hunger Games. Selling at the low price means a cost of $2.25 so that both Albert and Barbara purchase it. (This is because Barbara’s maximum price for it is $2.25). That brings in $4.50 of revenue. Alternatively, you could sell at a high price of $4.99. This ensures that only Albert will buy. But it also brings in $4.99 in revenue, which is more than if you had set a low price. So you would sell Hunger Games for $4.99.

Now consider the price for Game Theory 101. Selling at the low price requires a cost of $1.50 so that both Albert and Barbara purchase it. (This is because Albert’s maximum price for it is $1.50.) That brings in $3.00 of revenue. Alternatively, you could sell at a price of $3.99. Only Barbara would buy it at this price. But it also nets $3.99 in revenue, which is more than if you had set a low price. So you would sell Game Theory 101 for $3.99. (Not coincidentally, if you click on the books above, you will find that they are priced like that in real life.)

Let’s recap the world without bundling. Hunger Games costs $4.99 and Game Theory 101 costs $3.99. The seller brings in $7.98 in revenue. Neither Albert nor Barbara benefit from this arrangement; Albert is paying $4.99 for a book that he values at $4.99, while Barbara is paying $3.99 for a book she values at $3.99.

Now for the magic of bundling. Suppose the seller bundle of both books for $5.99. Who is willing to buy here? Albert values Hunger Games and Game Theory 101 at $4.99 and $1.50 respectively. Thus, he is willing to pay up to $6.49 for the pair. So he will definitely purchase the bundle for $5.99. In fact, he’s much happier than he was before because he internalizing a net gain of $0.50 whereas he had no gain before.

What about Barbara? She was willing to pay respective prices of $2.25 and $3.99. Consequently, she is willing to pay up to $6.24 for the pair. So she will also definitely purchase the bundle for $5.99. And similar to Albert, she is internalizing a net gain of $0.25, up from no gain before.

So Albert and Barbara both win. But so do the producers—rather than bringing in a total of $7.98, the producers now earn $11.98. Every. Body. Wins. (!)

(Yes, I know that Kindle Unlimited costs $9.99 per month. If we added another book to this puzzle, we could get Albert and Barbara to want to pay that price. But that would require more math, and we don’t want more math.)

Why does this work? Bundling has two keys. First, as previewed earlier, the marginal cost of the products must be very small. If they were larger, those costs would make distributing more goods look comparatively less attractive. This would drive up the cost of the bundle and make it less attractive for the consumers, perhaps forcing them to prefer the a la carte pricing. That helps explain why book bundling is just now catching on; electronic books only cost server space whereas physical copies involve UPS.

Second, it helps when customer preferences are negatively correlated. This pushes everyone’s reservation price for the bundle closer together, which in turn makes the producer more likely to want to sell at the bundled price.

Before wrapping up, bundling has an important secondary effect for authors. The main takeaway here is that producers of the materials can make more money through bundling. This gives authors more incentive to create additional materials—an author who would otherwise only make $10,000 from a novel could now make, say, $15,000 instead. So an author on the fence whether to produce the book is more likely to follow through. This further enhances consumer welfare because those buyers can now read a book that would otherwise not exist.

Finally, “producers” here has meant a combination of authors and Amazon. A skeptic might worry that Amazon will end up taking away all of the revenues. That may be an issue in the long run if Amazon becomes a monopoly, but the revenue share is more than fair for now. Indeed, Amazon is giving authors roughly $2 every time a Kindle Unlimited subscriber reads 10% of a book, which is substantial. And with Kindle Unlimited reaching more consumers than a la carte pricing would, writers can earn revenue from a larger share of readers.

If you want to know more about bundling, I highly recommend you read the Marginal Revolution post on the subject.

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Calculate Day-of-Week Sales Averages on KDP

Posted on July 11, 2014 | Leave a comment

For the longest time, KDP aggregated all sales information by week. Now KDP has nice graphical breakdowns of daily sales. Naturally, I wondered if my sales averages differed significantly by the day of the week. I compiled an Excel spreadsheet to give me a quick answer. Apparently the day of the week does not an impact for me, at least not in any significant way.

Still, I figured others would want to know the same information. As such, I did a little bit of extra work on the spreadsheet to make it usable for others. You can download it here. It is very simple to use. Just follow these four steps:

1) Select the tab in Excel that corresponds to the current day of the week. (For example, if today is Tuesday, use the Tuesday tab.)

2) Go to KDP’s sales dashboard. Use one of the pull down menus to open the last 90 days of sales. This will give you the most days to average over.

3) Copy each day of sales from the graph to the spreadsheet. This will require some work because you have to do it manually and need to pay close attention to graph to make sure you are copying down the correct number.

4) Excel will automatically calculate each day of the week’s average sales.

Again, you can download it here. Let me know what you think.

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“I Was a Digital Best Seller!”: NY Times’ Bizarrely Misleading Op-Ed

Posted on June 21, 2014 | Leave a comment

A couple days ago, the New York Times published an op-ed from Tony Horwitz, a Pulitzer Prize winner, chronicling his publishing of BOOM: Oil, Money, Cowboys, Strippers, and the Energy Rush That Could Change America Forever. A Long, Strange Journey Along the Keystone XL Pipeline. Ostensibly, it is the story of how online publishing does not live up to its hype. In reality, it is a parable of someone without good strategic or business sense committing a bunch of mistakes. And the best part: despite a lack of self-awareness, he gets paid off anyway.

To recap the important points from the op-ed, The Global Mail offered Horwitz $15,000 (plus $5,000 for expenses) to write a long-form piece on the Keystone XL pipeline. By the time Horwitz finished, The Global Mail had folded. He thus approached Byliner, who offered to publish the story as a digital book for 33% of the profits and a $2,000 advance. After a month, his book had only sold 800 copies, not enough to pay through the advance. This leads Horwitz to conclude that digital publishing is a failing enterprise.

However, the op-ed is actually a story of Horwitz making a bunch of mistakes and not realizing it. To wit:

1) As far as I can tell, he never signed a contract with The Global Mail. If I were going to spend a large percentage of my year writing a single story with the promise of $15,000 at the end, I would want a legal guarantee to that money precisely because of the issues he encountered.

2) He had a publisher (Byliner) that apparently did nothing for him. With digital publishing so easy now, the only reason to use a publisher is because they will actually do something for you. After all, Amazon will give you 2/3rds of the purchase price if you go it alone. If you are giving half of that to your publisher, you had better be getting a lot back. Instead, the publisher gave him a cover and siphoned off a large chunk of money.

3) He used an incompetent agent to sign the deal with Byliner. A good agent here would make sure the contract forces Byliner to do its job by publicizing the book to warrant its share of the revenue. Apparently there is no such language in the contract. If you are planning on signing a contract without giving it much forethought, why let the agent steal a percentage of your money as well?

4) Okay, #3 is not completely true—Byliner’s publicist “wrote a glowing review of “Boom” on Amazon, the main retailer of Byliner titles.” Amazon’s review policies make it clear that this is a flagrant violation: “Sentiments by or on behalf of a person or company with a financial interest in the product or a directly competing product (including reviews by publishers…)” are not allowed. So Horwitz is openly admitting that he has used false reviews. In the process, he implicates his publisher as well.

5) He thinks that being on the best sellers list for a particular subcategory means that he was selling a lot of copies. For someone with an extensive publishing history, this is remarkably naive. In fact, you can sell a handful of copies and get on these lists; you should not expect to make it rich unless you are on the overall best sellers list.

So we have a publisher that is completely unhelpful and an author who lacks business and strategic sense who are not making much money on a book venture. Does this warrant a New York Times op-ed on how digital publishing is full of false promises? Hardly.

The irony? The New York Times provides great publicity, even if your op-ed is completely wrong. As it stands, the book is #445 on Amazon’s best sellers list and was probably higher a couple of days ago when the story was first published. The real lesson here is that you can be horribly incompetent and still make a lot of money by writing about all of the mistakes you make—as long as you can convince the New York Times that it is the system’s fault, not yours.

This post has been very negative overall, so I feel like I should end on a kinder note. Tony Horwitz may be a fantastic writer. (I don’t know—I’ve never read anything of his. But a Pulitzer is a good indication.) His book on the Keystone pipeline might be great too. (The reviews on Amazon are good, likely even if you take out the fake review(s).) The takeaway point is that you need more than just good writing to succeed in the publishing world. Horwitz showed a lack of good sense here, and these are mistakes that you should avoid making yourself.

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Do Book Sales Determine Number of Book Reviews?

Posted on March 23, 2014 | 1 comment

In a word, yes.

That is not what I thought I would say when I first considered writing this blog post. Authors frequently complain that a book of theirs has sold very well and yet does not have very many reviews over on Amazon. And, in fact, that is what inspired me to look into this–my Rationality of War has sold better than I expected it to for the past two years or so, yet it still has zero reviews. Perhaps stranger, Game Theory 101: The Basics is by far my best seller, yet Game Theory 101: The Complete Textbook has the most reviews despite selling only a fraction of the copies.

Aside: I’m being intentionally vague about the exact number of sales any particular book has made because that is a part of my contract with Amazon. The graphs that follow will also be unlabeled. Apologies.

I understand that readers choose to review books for different reasons, so we should not expect reviews to be consistent across genres or even otherwise very similar books. But it seems weird that the difference is so big. Right?

Well, I figured doing some math could help out here. One obstacle to doing a large study on this is having data on a large number of books. Outside of New York Times best sellers, we simply do not know much about sales figures. And looking only at NYT best sellers is problematic since they are all very similar–they have all sold a tremendous number of books.

I can provide a partial solution. I have twelve books up on Amazon and have kept extensive sales records on all of them. While twelve is not a huge number, it will still provide a useful picture on the connection between sales and reviews.

My first thought was to plot the number of sales and the number of reviews each book had. This was not particularly helpful:

The diagonal line is the OLS “best-fit” line. Sales do increase the number of reviews, but the graph is not particularly meaningful because of the bunching on the left side of the graph. This is common for data of this type. Book sales have an exponential distribution–many, many books only sell a handful of copies while very few sell a substantial amount. My library also follows this distribution.

To solve this problem, I logged my sales figures and recreated the same graph:

Ah, much better. We now see a clear trend: more sales lead to more book reviews, though the expectation becomes murkier for the best selling of books.

It shouldn’t be surprising that more sales lead to more books–more people reading increases the number of potential reviewers, after all. However, I was surprised by just how strong the relationship is: the correlation between logged sales and reviews is .896! (Positive correlation ranges between 0 and 1, so it is difficult to get much higher than this.) Even the unlogged data have a strong correlation of .757. The number of sales really is determining the number of reviews.

TL;DR

Book sales are extremely correlated with book reviews.
Variance in the number of reviews increases as books become better sellers.

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Game Theory 101: The Complete Textbook Update

Posted on July 18, 2013 | Leave a comment

Two years ago today, I published the first incarnation of Game Theory 101: The Complete Textbook. (It was incomplete back then, heh.) Every summer, I like to go through it and make changes where I can. This time around, I decided to add a new lesson on games with infinite strategy spaces, like Hotelling’s game, second price auctions, and Cournot competition. I have correspondingly added some content to the MOOC version. Videos below.

Initially, I was hesitant to add more material to the textbook because Amazon’s fee increases as the file size of the book increases. Yet, the size of the textbook shrunk because I cut down on unnecessarily wordy sentences. (Switching “is greater than” to “beats” probably chopped off 300 words from the book.)

The optimistic interpretation: Readers now learn more while reading less!

The pessimistic interpretation: I really, really need to work on writing shorter sentences.

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How to Format Images for Kindle

Posted on September 22, 2012 | 30 comments

Formatting images for Kindle is a huge drag. The official KDP FAQs are laughably underdeveloped here, basically telling you that the four most common image types are supported (gee, thanks!) and not much else. Personally, I have completely redone the images in my textbook Game Theory 101: The Complete Textbook at least three times now, most recently because the way Kindle compresses images changed without any notice. I am writing this post to impart my knowledge on you.

Here are the most important time/money saving tips:

This process is going to suck. You will think you are doing everything right, then the Kindle uploader will find a way to completely screw you over. An image will stop appearing. The image will appear blurry. Your document size will suddenly explode. You will become unbelievably frustrated at some point. Accept it now, and understand you will likely have to do some experimentation to fix these problems later.
Kindles (and the .mobi file extension) were created to display text. Images were very clearly an afterthought. However pretty your image looks on your computer screen, it is not going to look nearly as pretty once you have uploaded it. Sorry.
Do not use fine lines in your images. To compress file sizes, KDP evidently eliminates random lines of pixels from your images. If parts of your image contain lines that are only one or two pixels thick, those lines may magically disappear in the final version. In other words, make your images as blunt as possible. You can’t control which lines disappear, but that will not matter much if no single line is crucial to the image as a whole.
By extension, if your image contains words, be careful which font you use. I originally used Cambria in many of my game theory payoff tables, but Cambria has a lot of numbers and letters with very thin lines. (The middle part of an e has this feature, for example. Without that middle line, you are looking at a c.) I switched over to Franklin Gothic Demi. It is blocky and ugly in PDFs. But Kindle is not PDF world. Blocky texts look great in Kindle world. You can also consider bolding other fonts to manually create blockier text.
Do not create images larger than what you are using for your final product. In the normal publishing world, you should blow up all of your images, save them as large files, and shrink the dimensions once you have put them in the file. This ensures that the dpi (dots per inch) of the images remains large, which is important for printing purposes. But Kindle world is not the normal world. Following normal advice leads to two problems. (1) Kindle will randomly decide to remove lines of pixels, creating the problem described above. (2) Kindle will retain the larger file size, thus increasing the size of the document without changing the quality of the image on the screen. This means you will be unnecessarily paying greater delivery costs.
You should also compress your images. To do this, I use IrfanView, which is the greatest image cropping software ever created. Simply paste the image into IrfanView and press “s” to save. When you choose to save as a JPEG, it will give you a range of quality options from 0 to 100. I suggest selecting 50 here, which is in line with KDP file size control guidelines. If you choose a smaller amount, the colors of the image will start to bleed into one another. Anything more hardly changes the observable quality of the image in the Kindle but sucks up file space. (And we want to shrink this to save on delivery costs.)
Finally, some basic infromation: If you are writing your book on Word, you need to use the INSERT -> PICTURE command. If you copy/paste an image directly into the document, the image has a nasty tendency of disappearing when you upload the book. If you have a lot of images in your book, I suggest adding this to Word’s quick access toolbar.

Following these guidelines has decreased Game Theory 101‘s delivery costs by $0.03. While that might not seem like much, if you sell eight copies a day, that’s almost $90 over the course of the year. It has also increased the attractiveness of the book, which one would imagine correspondingly increases sales.

Let me know in the comments if you have any other tips, and I will be glad to add them here.

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