The Bass Diffusion Model…Explained! The Most Important Shape of the Streaming Wars

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(Before we start, I launched a newsletter! It’s weekly and it’s short, and I explain my logic here. In today’s social media age, it can be hard to keep up with independent writers like myself so my newsletter will link to all my writings at every outlet and the best stories I read on entertainment strategy each week. Sign up here.)

Here’s three articles. See if you can spot the underlying mistake. An implicit prediction about the future given the facts…

From Variety about CBS All-Access:

IMAGE 1 - CBSAA 50 percent

From Fierce Video about Roku:

IMAGE 2 - Fierce Video Roku

From Decider about Hulu:

IMAGE 3 - Hulu Decider

In each case, a new company is growing wildly. Not just wildly, but 40-50% growth. Which is excellent growth if you can get it.

Implicit, though, is optimism about this growth. This high growth will continue. And the growth is specifically compared to Netflix—entertainment’s boogey man—usually to (again) imply that these companies will overtake or match the streaming giant because of the double digit growth.

This is wrong!

But it isn’t unusual. Frankly, as humans, we tend to believe that patterns continue at their current rate. We like our trend lines to be linear. Stated in layman’s terms, we like straight lines on graphs. Unfortunately, reality is often curved.

Fortunately, though, we know what the curve should look like. One key shape shows not how unique those three companies mentioned above are, but how very, very ordinary that type of growth is. That shape, though, isn’t linear. It’s a double curve and it is one of the most well studied models in marketing and business.

It’s called the Bass Diffusion Model. Today, I’m going to explain what it is, how it works and show a few examples. My goals isn’t to teach you how to use it (we don’t have that type of time), but to recognize it when you see it. Then, over the next week or so, on other outlets and social, I’m going to release some examples. 

To start, though, let’s dig deeper into the problem above.

The Problem – Growth Doesn’t Work This Way

A few years back, I sat in a company-wide “all hands” meeting, and I saw the head of our entertainment group roll out a slide. Our streaming venture was pretty new overall. But we’d had fairly strong growth in the last year, building off growth the year before. Our growth was growing! Here’s a version of the graph he showed, and the numbers have been changed to protect the innocent. 

Image 4 - The Hypothetical

The key numbers are the growth rates between periods 4 & 5, and 5 & 6. Initially, customers are growing slowing. But then the numbers double in year 5. That’s great. And then they increase by 15 units in period six. Again, sixty percent growth, which is even better. The next part stunned me. The executive literally added a dashed line into the future which looked like this.

IMAGE 5 - Exec Projection

That’s pretty incredible, isn’t it? Your growth isn’t just growing, but accelerating as your business matures. To emphasize—because as I type this I shake my head so hard in disbelief I may throw my neck out—this was an executive setting expectations for his entire company/business division, and he expected his subscriber base to double and then triple in the next few years.

As soon as I saw his graph, though, I drew my own chart mentally in my head. I’d seen that sort of growth before in text books and business case studies and in the press, and far from watching growth accelerate further, I thought it would slow down…

IMAGE 6 - Bass Diffusion Growth

Does this matter? Heck yes. Look at the delta (change/difference, in case I dropped in too jargony of a term) between the different estimates, using my model with the executive’s aggressive predictions, my model and a linear growth model.

IMAGE 7 - Reality vs Exec

By “period” 11, that’s a difference of 200 million customers. Or 40 million if you assumed linear growth continued. That’s huge! If you’re planning for the future, that difference is life or death.

For a huge number of early stage companies, I see subscriber numbers mentioned in these breathless terms. The double digit growth is rightly applauded, but then the implications are always that these double digit growth percentages can be sustained indefinitely. 

The vast majority of the time, they can’t be. And one model explain that.

The Bass Diffusion Model…Explained

Basically, it’s this chart, which I’ve borrowed from Wikipedia:

IMAGE 8 - Wiki Bass

What is the chart?

Explaining the pieces will help set up the model. First, this is a “time-series” graph, meaning the “x values” are dates. (X values, being the axis on the bottom.) These can be months, quarters or years. But the result is how a given value is changing over time. That value is the y-value or dependent variable. The “thing” you’re measuring.

Second, this is a “cumulative distribution function”. That means it adds up all the numbers over time. And shows the total percentage at any given time. So if you have 100 million total customers, the cumulative distribution function shows the total customers by time period, until you get to 100. It is often in terms of 0-1, or 0 to 100% (which mathematically is the same thing). 

Third, the “thing” being measured here is customer or subscriber numbers. Meaning, it shows the number of users of a product in total over time. This is different than the revenue of a product or its total contribution profit or even the number of units sold. Again, the model I’m about to explain and describe is about customer adoption of a given product or technology. So the “unit” is “people who adopt” a technology, which in business terms is subscribers or users or customers.

The Bass Diffusion Model

That’s what the chart is made up with, but where does it come from? A differential equation. Or the difference over time between adopters and non adopters. Frank Bass developed this model while working with Everett Rogers on his wildly influential book Diffusion of Innovation. The model is predicting when customers will adopt a given innovation.

Bass, basically, created the mathematical model that explains the “s-curve” (which I learned today is technically a “sigmoid function”) of adoption of innovations. In Bass’s case, he applied this to consumer goods. His model as he developed it contains three key inputs:

M – Total market size
P – Coefficient of Innovation
Q – Coeffecient of Imitation

And from those spit out this equation. I’m not a mathematician or economist, so I won’t explain it to you, but here it is:

IMAGE 10 - Equation

This equation can then forecast new adopters by time period. That’s what makes it so useful for marketers, as it allows them to accurately predict future sales. Even for new products, you can use comparisons to previously launched products with similar profiles.

Does it Work?

The Bass Diffusion Model is basically how customer acquisition works for new technologies and new products. Don’t take my word for it. Here’s from one of my teaching notes:

IMAGE 11 - Bass Quote

Let’s emphasize that this isn’t some random model I’ve made. It’s one of the most widely cited papers in economics/business. It’s taught in Introductory Marketing at Harvard Business School (and most other b-schools who copy their curriculum from there). It’s a foundational model customer adoption. Here’s another quote from Wikipedia:

Screen Shot 2019-09-11 at 12.55.35 PM


And like any good model, it’s been improved on. There are models for successive generations of innovation (which tend to have the same innovation and imitation rates), incorporating the marketing mix framework and more. There are similar looking (but differently derived) models for other technology, but Bass gets you almost all the way there most of the time.

The Cautions

Over the next week or so, I’m going to trot out a bunch of examples of this shape in action. The caution is that most of my models are about individual companies. (Take my three examples at the start.) But the Bass Diffusion model is NOT about individual product sales. It’s about customer adoption of an innovation.

That said, if customers adopt a technology, and firms have roughly the same market share, the Bass curve tends to show up in those sales. As an example, if Apple routinely sells 20% of cell phones in a given year, and it rolls out a new generation of phone at the same time as competitors, it can assume 20% of that new generation’s sales. That’s a safe assumption, and I’ve seen Bass replicated on lots of phone sales.

In some cases, too, the products will be so innovative that one or two companies could stand in for the industry as a whole. So I’ll use some examples where a new product basically created a new industry.

Oh, and a lot of getting the forecasts to be accurate with Bass requires understanding the potential market size. So if you get that wrong, then it’s hard to forecast accurately what the model for a new product would look like. This is easier for some industries than other. Like pharmaceuticals where companies tend to know the prevalence of a disease in a population. Or some technology innovations, where the DVD players could have rightly been forecast to replace VHS players. Other market sizing can be more difficult or unprecedented, like social media adoption.

The lesson in either case is to be ready. If your sales start slowing down, this can also be a strong signal that your market sizing estimates were too high, which I’ll show.


You’re ready for some examples, right? Today I’m going to trot out some examples I found across the inter webs for various technologies. First, if this model looks vaguely familiar, even if you aren’t familiar with Bass, you’ve probably seen this table from Rogers’ seminal work:

IMAGE 9 - Rogers Diffusion of Innovation

This is probably my favorite look at the shape and really shows how technology adoption can start very slow, accelerate quickly, then slow down rapidly as it matures. Here’s an example on PCs and Cassette tapes, comparing to a current company’s product.

Image 13 - PC and Cassettes

Here’s a very cool version (not cumulative distribution, but sales over time) from Bass on PC adoption growing over time. (These are the adoption curves from Roger’s graph.)

IMAGE 14 - Bass PC Adoption

Finally, this webpage has a brilliant example of broadband penetration in Australia:

IMAGE 15 - Broadband Australia

Once you understand what the Bass Diffusion model looks like, well, you tend to see it everywhere.

Conclusion: Beware Those Bearing Double Digit Growth Projections

Let me go over the takeaways for this article, so if you made it this far you will have a handful of “tools” to make you smarter when reading the news.

To start, understand that it is extremely common for a product to launch slowly, then accelerate by double-digit percentage (10-99%) growth for 2-3 years. Then it slows down rapidly. Again. Let’s focus on that first part, though. The more disruption and expense involved in an innovation, the longer it can take to catch on. Which doesn’t mean it failed, just has a very slow adoption curve. (One technology in particular has this characteristic.) That’s lesson/tool one.

Next, double digit growth is normal in adoption of new technologies. The conclusion from this—which could change how you read TONS of media coverage going forward—is to immediately view any growth rates viewed as extraordinary (Hulu, Roku, CBS All-Access from the introduction) as ordinary in the lifecycle. Don’t overreact to these types of extraordinary numbers. If it’s a new product/innovation, we should expect that growth. That’s lesson/tool two.

Even better, we can understand that double digit growth is not perpetual. When a company grows rapidly very quickly, it can be tempting to assume that growth will continue and eventually we will all be SnapChatting, Fortniteing, Ubering, VRing and Scootering. Very few companies continue growing until they suck up all the oxygen in the media universe. Instead, growth inevitably and quickly slows. So watch for that growth slowdown. That’s lesson/tool three.

Pushing this further, when the growth inevitably slows rapidly—and the model shows it will—we shouldn’t overreact. This isn’t a sign of management failure, though we often phrase it that way, but simply a market becoming saturated. That’s lesson/tool four.

The Entertainment Strategy Guy

The Entertainment Strategy Guy

Former strategy and business development guy at a major streaming company. But I like writing more than sending email, so I launched this website to share what I know.


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