Breaking the Law

For the first time in many years I feel that there is some potential uncertainty in the results Apple will announce. After a period of excellent accuracy (shown in graph below), the company’s guidance has begun to diverge dramatically from reality and the trend might continue this quarter. The cause might be unanticipated demand for the iPhone 6/6 Plus. The growth rate for the product was 46% in Q4 and 40% in Q1. This is unanticipated because growth rates have been below 20% for five quarters and below 50% for eight.

Screen Shot 2015-07-13 at 12.21.00 PM

This slowing of growth was explainable given the rate of diffusion of smartphones in the global population. Within the US and some other early adopting economies the market is reaching late stages where most people have switched to smartphones. Globally we are at a more modest 30% or so but in many of the late adopting economies Apple does not have wide distribution.

Of course this thesis is thinly supported. There are many reasons to think that late adopters would still start with iPhone and that earlier adopters of Android would upgrade to iPhone after a few purchase cycles. Thus, the iPhone could prosper in later-adoption or even in post-saturation states of the market.

Indeed, in the post-saturation PC market, Apple is doing very well with the Mac and in the late to post-saturation MP3 player market the iPod did extremely well. This suggests that when it comes to value capture brand, experience and satisfaction trump function, price and share considerations in almost all consumer markets[1]

With so many assumptions put asunder the iPhone business suddenly looks downright lively. I adjusted my own growth assumptions and the resulting figures are shown below.


F3Q15 Daniel Tello Horace Dediu
iPhone Units









iPad Units









Mac Units









Services Revenues



Other Revenues



Total Revenues


































I include for comparison Daniel Tello’s forecast as his work carries quite a bit of thoughtful analysis.

The upshot of this is that the company is poised to grow earnings per share at a rate of at least 50%!

That growth rate is astronomical, especially for what is already, by far, the world’s biggest company by market capitalization.

This was not supposed to happen because of a so-called “law of large numbers.” The “law” is actually a probability theorem which states that the average of experimental results should be close to the expected value given sufficiently large number of experiments. The way it’s applied in market analysis (I assume) is that “no company can perform above market average performance for a sufficiently long time”.

It implies that there can be no outliers and that all companies “revert to the mean because …”

Actually, I don’t have any idea why they might. The premise that all companies are the same must play into this but companies can only be alike if they have the same processes, priorities and resources. As long as I’ve been able to observe and as much as I’ve ever read on the subject I have never encountered any two which had anything in common.

And so the law of large numbers, as applied to market performance is a myth. It is easily disproved with a simple deconstruction into the causes of firm performance, but the empirical data from Apple alone shows how foolish it is to believe it.

  1. Enabled by design for jobs to be done. See non-technology markets for abundant evidence of this. []
  • Wow. Thank you.

  • Actually, The Law of Large Numbers used in business is different from the probability theorem.
    Simply put, a company cannot maintain growth because it will eventually reach the economic ceiling of the market itself. Apple doesn’t get around this; analysts just underestimate where the ceiling is.

    • That’s even worse! There is no “economic ceiling” to a market. Markets are created, grow and die. Their size ranges from zero to undefined.

      • Well, undefined does not mean it’s not there somewhere. One can estimate the reasonable upper limits of a market based on sales growth, audience, etc. The problem is no one knows how to do this for the iPhone, likely because they keep looking at precedent from other vendors. Samsung in particular was a terrible indicator because they served every location in every screen size when the “Law” caught up with them. Samsung expanded rapidly but then had nowhere left to grow.

        On the other hand, Apple is still expanding into more markets and just added different sizes. They are also showing new interest in eating Android’s market share (new ads, switching tool, Apple Music for Android), which I take to mean they are anticipating a slowdown, which they actively seek to delay.

      • mithlond

        We might reasonably define the ceiling as the intersection of the total value humanity is able to assign to the jobs they need done and the total ability of humanity to assign value to products that are hired for those jobs (all the money in the world). If the market we’re speaking of is the world’s economy, then there is a limit.

        I do not say this to be snarky. I believe this is the very reason why Apple has no fear of slowing down or running out of product ideas that would do remarkably well. All they have to do is ask their standard question: “where can we make a substantial contribution?”

        The real challenge for them (which they seem to be doing well with so far) is how to scale their processes.

      • The world’s economy is no limit. The economy is the sum of all markets and markets are born, grow, decline and die. The sum of all markets has gown exponentially since the beginning of the 1820s. The number and extent of markets has varied and continues to vary at increasing rates.

      • normm

        Excellent point! As long as the world economy is growing exponentially, it’s hard to set a ceiling on Apple’s growth. All you can say for sure is that it can’t grow faster than the world economy indefinitely.

      • Accent_Sweden

        I’ve argued before, market saturation of the world population or the entire global economy should not be viewed as a limiting factor. It’s also a silly idea. Markets are what we make of them, not what defines our limits.

      • I didn’t see any snark and mostly agree. However, I believe Apple has a lower limit than the world as a whole, but their limits are mostly self-imposed. Apple has thus far paced their growth to avoid a balloon. The strategy shift I described earlier would be more akin to running harder up a steeper hill to maintain pace.
        I also believe scale is not just the real challenge for Apple but their only challenge. Apple could easily surpass all their competitors if they didn’t have to source and support tens of millions of flagship iPhones at each launch. (Samsung choked sourcing a fraction with the S6 Edge.) That growth is truly baffling.

      • Jacob Williams

        How I explain this to friends: The economy is a bakery not a pie.

      • GlennC777


    • DarwinPhish

      There is a difference between earnings growth and market cap growth. The Investopedia Law of Large Numbers iapplies to market cap. Its corollary is that given two companies with equivalent earnings growth, the market will assign a higher multiple to the smaller company. But no one should think that a public company’s market cap should somehow limit its earnings growth potential.

      • The Law applies to both; growth in either slows as the respective economic ceiling is reached. Apple cannot earn more money than is available, nor be valued higher than the total value in the market. Also, market cap is, in part, judged by the perception of earnings growth potential, not vice versa. Certainly with Apple, we see record-setting earnings driving their record-setting market cap. There is fear they will hit the ceiling on both, but as I said, no one seems to be adequately estimating the height of the ceiling.

  • Try Business Physics, probabilistic-theory-misapplier-people.

    At least it makes more sense when contemplating a $225B+ per year Apple flying in revenue ionosphere that no consumer tech company – heck, no TECH company, even Samsung Electronics – has ever seen.

    Apple growth “has to” slow down (YOY growth percentage terms) sometime, but it won’t be due to a “Law of Large Numbers”, and it won’t necessarily be a Bad Thing(tm) either.

  • aPunter

    “And so the law of large numbers, as applied to market performance is a myth.”
    The last time I heard things like that was 15 years ago. Apple will probably continue to do well for the forseeable future, but if you really believe that you are smoking too much of your own ganja

  • I’ll take a hit off that: Maybe if Apple were to drive all its competitors out of business (or into very small share), then Apple would *be* the mean, and so the law of large numbers would come true that way.

  • Sacto_Joe

    I think Apple is expanding investor’s awareness of how big a business can grow. I see the continued growth of other stock’s market caps (Microsoft comes to mind) as a function of this changed perception.

  • Martin

    The irony here is that the economic value for smartphones is being made almost entirely by Android. Google is growing the pie by pushing smartphones into every last corner of the planet, and Apple follows on their heels with the device that everyone aspires to buy once they’ve made enough money thanks to owning a smartphone. Google wins either way, at least toward the goals that they’ve set for themselves.

    • dajhilton

      How does Google ‘win’ from Samsung selling android phones around the world? It seems to me that that loss leader for Google (the whole expensive android development and deployment) is only a winner if it brings some monumental market advantage to Google, such as by critically hobbling Apple. And it hasn’t done that.

      • Martin

        Even if Android doesn’t deliver profits directly it does get people online which previously were not, which creates a larger addressable market for Google. That may result in new ad markets, new analytic data, and inevitably will result in some ad growth. Google is, if nothing else, confident that they would/should get some piece of every connected user. Whether that is realized is a different matter, but Google believes that they will succeed at it, therefore they see it as a win.

      • jimble

        The problem is that while that may be google’s plan, it kinda invalidates itself based on the logic of your first comment. The fact is that Apple is owning more and more of the high end smartphone market. They essentially have no real competition. Samsung is a blip in that market and, while android users may not want to admit it, the vast majority of people with money want nothing other than the iPhone. So Google is basically investing in creating a market for Apple by selling ads to the poor. That’s simplistic, I know, but assuming China’s middle class continues to expand rapidly over the next 20 years google’s potential market there will shrink and apple’s will grow. The Chinese market is less likely to experiment with 3rd party American services so ultimately they’ll also stay inside apple’s Eco system once they get those phones. Meaning no money for Google. So google’s basically investing big in a medium term strategy which will give the world’s poor access to the Internet and eventually make apple even bigger and more free to invest in things like search and ads that can damage Google in the long term. Ads are profitable for Google, sure, but they won’t be so profitable when the platform that the people with money use starts making it more and more difficult for users to see those ads.

        Even after saying allllll of that, I don’t actually think what you said is correct. It’s western superiority complexes that make us think the poor need to be taught to rely on smartphones. They don’t. Smartphones are immediately appealing to everyone. The reason for that is that Apple set the bar for usability. Android would not exist today without the iPhone and the iPhone would not be the amazing tool it is today without Android’s competition. But I think you’re confusing the idea of the rural Indian farmer who gets a cheap android smartphone to use banking with the urban poor in China who use android because it’s all they can afford. Those people would have bought smartphones no matter who made them. Google isn’t doing anything there. They didn’t need to create a use case for that market, the appeal of the iPhone did. The farmer, sure, needed android in order to see the value in the smartphone but he’s valueless to Google. Ads don’t apply to him.

        So if what you say about google’s strategy is true, it isn’t a very good strategy. Google can clearly manage a market occupied by the working class and make money but it seems like such a pointless exercise when that plan will ultimately result in the company getting by on razor thin margins when Google could be eating premium high margin pie like Apple and Microsoft. Android may well be the next Windows but Windows added value to products. It didn’t create a lowest common denominator. It built upon its brand and made “Windows” a valuable name and maintained that for as long as it could. Google seems to be taking a brand that peaked in value in 2013 and is now slowly devaluing itself for no good reason.

        Good quarter or no good quarter, Google is behaving like a VC startup in all the wrong ways.

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