Lady_with_unicorn_by_Leonardo_da_VinciThere are three kinds of blockbuster markets – which is yours?

Comparing revenue spreads among films, books, and other cultural products offers lessons for other blockbuster markets, too.

Financial backers need to know that on average they’ll make money. But it’s a scientific fact that the true average is unknowable in some blockbuster markets. Does that apply to your market?

Blockbuster markets range from business start-ups and venture capital to media and entertainment, and various other “super-star” and “category killer” kinds of businesses. I’m going to discuss the technical statistical distribution in these markets, and its implications.

In a blockbuster market, it’s winner-takes-most. There can be multiple winners, but you know what I mean. The majority of new entrants fizzle out; a few generate modest returns; and one or two knocks it out of the park and everybody goes home in limousines. That’s the unicorn, of course.

The media/entertainment field is the classic example, and I’ll have more to say about that in a moment, but venture capitalists and start-ups live in this world as well. So do others, including Big Pharma and other discovery-led businesses. It’s debatable how broad this market feature is. For example, many consumer markets feature a Coke-vs.-Pepsi dominant core – but that’s talking brands and I’m talking specific product entries, a different focus.

So the general idea is obvious, right? First, there are plenty of underemployed actors and few superstars. And second, almost no one claims the ability to pick the winner in advance. Welcome to the casino, roll the dice, and then go home, by limo or maybe by bus.


The financial backer should know the exact revenue shape and its implications 

Actually there is more to it. I read academic research so you don’t have to. What I offer below is basically my real-world interpretation of academic research. I’ll focus on the academic literature on similar revenue distributions for “cultural products.” These include Hollywood domestic revenues and book sales (unfortunately restricted to Italy). If you will, I’m advancing a series of hypotheses about what it all means, and I’d welcome your own thoughts. While each market is in some respects unique, we’re going for the similarities here.

Here’s the investor’s dilemma in a blockbuster market: The typical new entrant will fail to make a return on investment. But the investor also needs to make money overall.

Another way of saying this, from a statistician’s point of view is this:

  • The median entrant earns little at best, or fails big or fails small.
  • None the less, the average or mean over all entrants had better be positive.

This must be so, because total returns over all entrants must be solid, so the average (the total divided by the number of new entrants) must be positive. That positive average is what funds the financial backer.

This is a more precise way of looking at the received wisdom about Blockbuster markets. Drilling down into the implications, here’s the good and bad news:

  • In Good blockbuster markets, the investor can count on past results as a guide to the future.
  • In Bad blockbuster markets, the investor can still use the past if s/he accounts for change.
  • In Ugly blockbuster markets, past results cannot – even in theory – guide expectations about the future value of the mean and total. Even if there’s no change in the market.

Please note: In an Ugly market, this is not just a case of “past results don’t guarantee future results,” as fund managers like to say. It’s worse than that. It’s baked into the mathematics. It’s baked into the blockbuster phenomenon itself.

Well that really puts the limbo in the limo, doesn’t it? Don’t despair yet. Wouldn’t it be a fine idea to know which of these types of markets you’re operating in? In that regard, statistical science offers some help. And with that, we now move on to the part of this post that really does read like a faculty blog.


The shape of the revenue distribution tells you which type of market you are in

In a blockbuster market, the spread of total revenues across multiple offerings generally follows the shape of a Pareto distribution. A Pareto distribution is a special type of power function. The cumulative probability is given by the formula:

F(x) = Pr(X≤x) = 1 – ((Xmin-x)/x)α with x ≥Xmin; Xmin>0; α > 0

If you think that’s the funniest thing I’ve said in this blog, we should talk. Everyone else: never mind, let me draw you a picture:blockbuster revenues


Hollywood has the steepest shape, which in a way is good. Typical revenues are relatively uniform. Unfortunately, Hollywood also has high fixed costs, so it’s that long tail that makes a difference. (Technically, this is Hollywood domestic box office – that’s the underlying data.) Concerts are the most democratic offering. The Broadway estimate is based on research in progress and subject to on-going refinement.

All of these estimates should be considered purely illustrative – I’ve simply charted the mathematical curves using hypothetical “revenue” levels, so you can compare the general distribution shapes. This is so-called “normalized” revenue levels, so we can compare the shapes. Obviously in the real world the scale on revenues varies from one market to another.

All of these are Ugly markets as I use that term. Alpha is less than two, which means the distribution has infinite variance. Moreover, Broadway and concerts also have means (mathematical averages) that cannot be reliably measured. In other words, they are mathematically equivalent to “infinite” – suggesting there’s always a non-zero chance one or more offerings will go almost inconceivably big. Now that would be a nice problem to have, but going back to my original point, forecasting average sales is not improved by collecting more data or doing more analysis. That must be so because with infinite variance, no calculation of averages is reliable.

And here’s a related thought: Product/portfolio diversification doesn’t reduce risk in an Ugly market. For example, a publisher can’t dodge this distribution by saying: “Hey! Let’s do a mix of Celebrity Cookbooks, Young Adult, and Detective stories!”

Let me reiterate that these are pro forma charts based on published alpha estimates, but they’re just illustrations. And if your field is, say, smart phone apps, your alpha could be different.


What drives a blockbuster distribution?

The usual suspects are three kinds of contagion among buyers. Or if you prefer, “social learning,” in which other consumer’s purchases influence the next consumer’s purchases.

  • The “information cascade” is a model of fads. This arises where a given consumer allows the buzz to overwhelm his/her own estimation of value. When it works, this is great; but cascades are regarded as fragile and subject to quick reversal.
  • “Word of mouth” – where the consumer’s awareness is piqued by the earlier purchasers, but ultimately the consumer’s preference is set by him or herself.
  • True “network effects” – where the product’s utility increases for each prospective buyer to the extent that others have already purchased it. No point in downloading Snapchat if nobody you know uses it.

Add to that the supply response – early promise means bigger marketing budgets, better distribution, and so on. Nothing succeeds like success.

How do you manage in a blockbuster market? That’s a subject in its own right. The point of this post is simply that there’s more than one shape to a blockbuster market, and you should know which shape you’re working with.

The Broadway estimate (the alpha value) is preliminary and tentative, and subject to change. The other results are final.

A good entry point into this research is the 1999 paper by Arthur De Vany and W. David Walls:

My thanks to doctoral student Kyle Maclean and Professor Srini Krishnamoorthy for sharing their working paper on Broadway revenues. You can find it here:

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