*(Before we start, **I **launched a newsletter!** It’s weekly and it’s short, and **I **explained my logic here**. **Sign up here.**)*

My goal is to try, as best I can, to explain the complicated parts of the entertainment biz, trying to walk readers through what I’m doing and how I’m doing it. Unfortunately, even when I’ve tried to simplify things, I’ve gotten comments that my articles are pretty dense. That’s what happens when you don’t have an editor.

With that preamble, today’s article is math-y.

This is about as math-y as I can get. I’ll be slinging terms like linear programming and mean absolute percentage error. To help out, I’m going to start with a BLUF (bottom line up front) so you can read my findings even if you don’t want to read my process to learn how I pulled it off.

Today is the “Bass Diffusion Model” in action. In layman’s terms, the Bass Diffusion Model is a way to calculate a “total addressable market” (TAM or “market size” in non-jargon terms) for various new products or innovations. As the headline suggests, today we’re turning our gaze towards Netflix as a stand-in for the streaming world.

**BLUF – Netflix’s Market Size in the US is closer to 70 million than 90 million**

When you apply the Bass Diffusion Model to Netflix’s US operations, the model which fits best has a market size in the United States of around 70-72 million subscribers. In other words, a saturated US market is much closer to the low end of Netflix’s projected outcome (60 million) than the high end (90 million).

The Bass Diffusion model fits the data pretty well. My average “error” fitting the Bass Model to Netflix is 1 million for streaming only and 600K for all subscribers.

That said, applying the Bass model to Netflix isn’t perfect. First, Netflix transitioned from a DVD company to a streaming company, which is arguably two different product innovations. Second, Netflix isn’t alone in the streaming world, and we only have current Netflix subscribers in any period, and don’t know how many folks are still streaming, but no longer Netflix subscribers. Third, this is a US only model. In the future, I plan to apply the projections to the international markets (which has its own problems) and for all streamers.

**The Origin Story – Seeing Bass Diffusion Applied in the early 2010s.**

Going to b-school during the Qwikster debacle of 2013 made for interesting class discussions. Overnight, Netflix became a laughing stock. Yet, even with that debacle the year before, they had kept adding streaming customers. They were the growth story already—23%!—leading some early analysts to throw out huge potential market sizes. How long would this double digit growth continue for?

That’s when my professor—a marketing professor, naturally—trotted out the Bass Diffusion Model. We’d all learned this model in marketing the year before; I’d never considered applying it here. He did, and out popped a total market size: about 60 million US subscribers. The model fit really well.

That 60 million has stuck in my head and influenced my thinking ever since. It’s why I launched this series and why I kept my annual subscriber projections a bit lower than most observers last January. Seriously, look at this chart I made back for an article on Hulu at Decider. Bass doesn’t leap off as strongly as it did for Fortnite, but you can see it for Netflix and especially see it for Hulu.

Frankly, because of that one application, the 60 million subscribers point in the US felt like the point where we’d see Netflix slow down. Then, in Q2 of this year…that reality finally happened.

The good news for Netflix is the last few years have had better subscriber growth for Netflix than that old Bass model. (For those keeping score, my projection last year was probably too low.) The bad news? Well, 90 million subscribers is looking MUCH harder to reach. But instead of relying on old estimates, today is about making new ones.

**The Task – Forecast Netflix Subscriber Growth in the United States**

Just to be clear, my goal today is to apply the Bass Diffusion Model to Netflix’s US subscriber count. Why US only? Well, it has a few more data points which will make it a bit more accurate. More over, the recent slow down point gives me a bit more confidence that we’re seeing the inflection, which I’m not sure we’ve seen internationally yet.

I’ll be building two models, though, because Netflix has actually had two products: the DVD delivery and streaming video. Unfortunately, Netflix has been a bit tricky when it releases subscriber counts, which means I needed to make some assumptions. Let’s explain those.

**The Data – Netflix Subscriber Counts Over Time**

To really make the Bass model work, I needed to do a lot of cleaning of my Netflix subscriber data to make sure everything I was calculating was apples-to-apples. Wait, doesn’t Netflix provide this? They do, every year. Here’s a Statista table summarizing that. Can’t we just use that?

Unfortunately, it’s a bit unreliable. When I use data, I pull it myself so I can vet it. For example, with those Statista numbers, are those numbers paid subscribers or free? Streaming only? Or all subscribers? Many tables and charts for Netflix actually mix up those categories in the same chart.

In fact, even in my chart above—the one for Decider—I did a bit of that.

So I updated all my Netflix subscriber numbers, calculating streaming and all subscribers for Netflix from the beginning of time. This took me SO long—and I had some insights into Netflix’s history from it—that I’m going to write it up as its own, probably too-in-the-weeds, article. In the meantime, just know these colors are the six different ways Netflix has revealed subscribers to investors:

Also, I assumed this year’s growth doubles from the current 3% to 6%. If it goes up or down significantly by the end of Q4, that could change this model. Also, I made assumptions about percent of streamers and percent of “DVD-only” customers that I’ll explain in that future article.

**The Graph – Eyeballing It**

Now that we have the data, we can try to fit Bass to it. After I refreshed myself on the Bass model two weeks ago, one of the first things I did was apply the model to the Netflix data to see if it still fit my professor’s prediction.

Guess what? It did. Here’s my initial take for all Netflix subscribers going back to launch. I ended up with about a total market size of 64 million.

The question is, how accurate is that? Glad you asked. When it comes to values versus actuals, I’ve always liked “mean absolute percentage error” (MAPE). This is basically the mean average for the percentage that the actuals are off of the predicted result. (See, this is math-y.) In this case, the average error was off about 14.3% by eyeballing the Bass Diffusion model.

But I’ll be honest, when I remembered to calculate the MAPE, a light bulb went off. This was my “a ha” moment from two weeks back. If I had the MAPE, I could use an Excel tool to make calculate the Bass curves for me, instead of me playing around with the numbers.

**The Math – Non-Linear Programming**

One of the core tools of “operations research” (sometimes called “management science”), is (second math alert!) linear programming. This is, I’ll concede, complex stuff. But basically, a linear programming model is a set of equations that the computer can solve to optimize (maximize or minimize) for a given value.

You probably know it by it’s Excel name, Solver!

That’s basically what I did here. I took the Bass Diffusion model, and put it into Solver. I optimized for the MAPE, trying to minimize the error. This is what Solver was built for. I couldn’t get the “Simplex LP” to work and had to use “GRG Non-Linear”. I’m not a math PhD, but I think the fact I’m working with a differential equation invalidates the linear programming. For our purposes today, we should be fine.

The next challenge is figuring out the total market size. To use Bass, you need to know the eventual market size, and find the p and q from that. We’re going a bit backwards here. In the eyeball case, I played with numbers and 64 million seemed to fit. To be more rigorous, though, I’ll run through the all the numbers between 60-90 million subscriber, in intervals of 5 million, and see which model fits the data best. Here’s the type of output I got using non-linear programming, with 65 million as the market size.

(Black line is model; blue line is real life Netflix data.)

You can likely see the same problem I do. Basically, the lines at the very end now trending in different directions. As I looked at the error rates, the problem is that early errors are weighted the same as later errors, even though the magnitude in actual numbers are much smaller earlier on. So I tossed the “percentage” and just optimized for the “Mean Absolute Error” in real terms. Here’s what that looks like for 70 million subscribers:

Wow, that looks pretty nice! The MAE is about 600K subscriber misses. As I ran these scenarios, with the MAE, 70 million subscribers ended up the best fitting model. Here’s a table showing that:

On to streaming subscribers. (Not streaming “only” but subscribers who used streaming and/or DVDs.) I made some assumptions about early streaming adoption, then put those same numbers into the Solver model. Here’s how that looks at 70 million subscribers:

And now the table of results for Mean Absolute Error. I tried MAPE, but ran into the same issue where the early errors pulled the table down too much. So I didn’t pull those numebrs.

I highlighted 72 million because I drilled into that specific range and that’s the model that gets the absolute best fit. This means that ultimately I see Netflix total market for streamers at about 72 million in the United States for streaming subscribers.

**Caveats & Self-Criticism**

Listen, I really like the above fit, but no model is perfect. Here are the critiques I would level at myself:

– First, the sample size is pretty small. We only used annual data points which means we have sample sizes of 21 and 13 respectively.

– Second, this model has a “margin of error”, but using this method I couldn’t really tell you what it is in a rigorous fashion. Netflix won’t end up with precisely 72 million subscribers, so the eventual numbers will be off in some fashion. That’s forecasting.

– Third, I had to make assumptions about the streaming adoption in the early time period and DVD-only customers in the later period. Assumptions are always a source of risk/error. I’d add that in the streaming only model, my initial assumptions seem a bit low and likely Netflix had some more early adoption than I assume. (They had a large installed base of customers to quickly adopt is my explanation.)

– Fourth, this year really is critical. And hence will impact the model. If the content works and Netflix adds 8% subscribers from last year’s end, 75 million looks more likely. If they end at 4%, 70 million is more likely.

– Fifth, and most importantly, using “current subscribers” versus “total subscribers” really is a problem here. It’s huge. Frankly, Netflix used to report gross versus net subscribers, and when you see those numbers (you will), you forget how many people churned in and out of Netflix every year. In short, there’s a chance Netflix has actually had a much higher total streamer adoption than these numbers, they just haven’t shared that.

– I’d add, this is one of those times I wish I had peer review. So I welcome feedback. One of the joys of writing is that the inter webs have way more eyes than I do, so I get tons of great recommendations/feedback.

**Implications – Why This Matters & How You Can Use This**

Despite those caveats—and honestly, how few prediction brokers are willing to tell you why their model may be wrong?—I think we can learn a few crucial insights from this data.

In particular, the idea that Netflix will grow until it sucks up all the oxygen in the media universe doesn’t hold up to this scrutiny. If there are 120 million households in the US, well, Netflix is going to miss about 48 million of them unless it changes its business model.

Specifically too, Netflix won’t hit the high end of Reed Hasting’s forecast unless growth rapidly reaccelerates. Netflix has previously forecast 60-90 million total US subscribers. But that’s the thing with innovative product diffusion: growth hardly ever just “pick ups” to mid-to-high double digit growth after it slows. Especially as a stream of streaming competitors enters the market. And as cash flow pressures force price increases. (Which is another caveat I’d love to know: how did artificially low prices impact growth rates? There’s a Bass Model for that, but I’m not skilled enough to deploy it.)

Other streamers can learn something too. If you built your model for 120 million US customers, I’d seriously reconsider that. For a low end, consider using Netflix as a stand-in for all streamers. That’s probably more accurate, honestly. So for Disney+, if it is a “family-focused” brand, and 40% of households are families, well Disney+ nets out to 28 million subscribers in the US. That would mean it won’t catch Netflix anytime soon.

After I finish a model like this, I try to find other estimates. I couldn’t find any Netflix-specific estimates in academic articles but just last week, I found *The Hollywood Reporter* published an article by Simon Murray that forecasts that Netflix will add 10 million subscribers in the next five years. Hey, that matches my estimate too! (I’ve seen other Netflix forecasts predicting similar slow downs too.) Then today, I saw an article that is way back at the high end, with *THR* reporting the investment company is forecasting 90 million subscribers in the next ten years. Honestly, I’d take this model built on data over subscriber survey results.

**Future Work**

Three specific projects leap off the page for me. First, if I used the quarterly data in the model developed, we’d essentially quadruple our data set. Which would add some noise to the data, but again more data points.

Second, international, right? Of course, we’re much farther from the inflection point for growth and we have even fewer data points to choose from. Plus, you could do both “global” penetration and “international” (everything not US), so I’ll have to play with that model.

Third, attempt to do all “streamer” adoption versus “Netflix only”. Similarly, I could run the analysis to “cord cutting”, which I’ve been mulling. Or to focus on Hulu or another streamer, if we have enough data to do it. (Right now we don’t for any other streamer besides Netflix.)

[…] so often they change their definitions, and stop reporting old numbers. Which makes an enterprise like the one I pursued last week much more fraught. To help build the table with subscriber numbers, I had to go through essentially […]

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