The diffusion of iPhones as a learning process

All theoretical and empirical diffusion studies agree that an innovation diffuses along a S-shaped trajectory. Indeed, the S-shaped pattern of diffusion appears to be a basic anthropologic phenomenon.

This observation dates as far back as 1895 when the French sociologist Gabriel Tarde first described the process of social change by an imitative “group-think” mechanism and a S-shaped pattern.[1] In 1983 Everett Rogers, developed a more complete four stage model of the innovation decision process consisting of: (1) knowledge, (2) persuasion, (3) decision and implementation, and (4) confirmation.

Consequently, Rogers divided the population of potential adopters according to their adoption date and categorized them in terms of their standard deviation from the mean adoption date. He presented extensive empirical evidence to suggest a symmetric bell shaped curve for the distribution of adopters over time. This curve matches in shape the first derivative of the logistic growth and substitution curve as shown below. Screen Shot 2013-11-06 at 11-6-1.51.57 PM

In the graph above I applied the Rogers adopter characterization to the data we have on the adoption of smartphones in the US. The latest data covering September is included.

The fact that smartphones in the US follow the theory is exciting, but what can we conclude about the adoption of specific platforms? There has been quite a bit of turnover in the leadership of the market in the first half of the time frame given. You can see this more clearly in the following fractional market share transformation.

Screen Shot 2013-11-06 at 11-6-2.16.03 PM

Note that, with the exception of the iPhone, if each platform is studied individually, it would not follow a logistic (i.e. linear) pattern even though, as a whole, the technology does.

This then is the big puzzle: while we might be able to predict how smartphones will diffuse into society, we can’t seem to predict how any single firm will fare. This means that an investor cannot make a credible “bet” on the technology[2]. If they choose a single company as proxy, chances are they will lose. If they bet on a basket of companies then, again, chances are they will lose. There is usually one unforeseeably clear winner.

Before we get further into the question of picking winners or predicting the future division of share among rivals, we should understand the underlying causes for this pattern of adoption.

Rogers concluded that the learning behavior of individuals is the underlying cause of the symmetry of the diffusion process.

At the beginning, when an individual is confronted with a new (learning) situation they make many mistakes. These mistakes are gradually reduced (by learning) over time because more and more information is received and acts as a stimulus. The gain in learning per trial is proportional to the product of the amount already learned and the amount remaining to be learned before the limit of learning is reached.

Arnulf Grübler[3] explains:

This is exactly equivalent to the F(1-F) transformation of the logistic curve. It should be emphasized that these properties of the learning process were found in real learning situations and are confirmed by a large number of laboratory and field experiments. Thus each adoption of an innovation in a social system is equivalent to a learning trial by an individual. Thus, the symmetric diffusion pattern results from the way messages about an innovation are emitted and processed by social learning.

So these observers of the process assign learning behavior as the cause for adoption of a technology. Can the learning behavior be applied to individual platforms? It’s tempting.

The hypothesis would go as follows: adopters are not only processing messages about the new technology but they are also trying different platforms as they enter and as they upgrade their phones. If we see platform choice as a learning process then if one platform has a natural advantage, it settles into a dominant position as users “learn” of its advantage. Conversely, if no platform has an advantage then platform “churn” repeats as rivals gain/lose positions of leverage in the market.

The pattern shown so far seems to point to Apple’s iPhone having a logistic pattern indicating that it might be benefiting from a learning pattern. The alternative platforms may simply be jockeying for temporary advantage.

It’s an interesting hypothesis. To be developed further we need to answer what any learnable advantage might be. I suspect it has to do with the ability to solve unmet and unarticulated needs. In other words, that the winning product solves a set of “jobs to be done” which are difficult to pin down and are perceived rather than defined.

  1. Tarde was probably influenced by mathematician Pierre François Verhulst who first published the logistic function in 1845 []
  2. Indeed investors often get burned when new technologies emerge. While the technology booms, individual firms supplying it often fail. See the history of transportation, communication, computing and energy. []
  3. The Rise and Fall of Infrastructures, Physica-Verlag 1990 []
  • Harry Hirsch

    Horace, this is simply the smartest thing I read this quarter. Bravo.

  • Bill Maslen

    Yo – that is one cool analysis, with some brain-blowing conclusions. I found that unexpectedly exciting!

  • Walt French

    @Asymco wrote, “If they choose a single company as proxy, chances are they will lose. If they bet on a basket of companies then, again, chances are they will lose. There is usually one unforeseeably clear winner.”

    This might be as good a place as any to lay out a non-Fama justification for indexing.

    For some of us, investing is fun speculation about the future, even a bit of a paradigm to help us understand it better. But most of the personal investments are devoted to the serious business about building, then growing, monies to put our kids thru college or ourselves thru the golden years. For the latter group, a 100% increase is very nice, but a 100% decrease is a horrific problem.* Ditto at less extreme numbers: a 50% increase, or a $500K increase makes us feel much better off, but losing half of the money we planned to live on is a deep problem.

    With that asymmetry (heh) of the “utility” of wealth in mind, it doesn’t matter if you own a couple of losers as long as you also hold the winners. Since you don’t get to go backwards in time to buy the future winners, your best hope is to build out a paper portfolio that reflects everybody else’s insights as to which will win, and then add or subtract individual companies’ weights in proportion to your proven ability to forecast winners better than the average.

    This is mathematically provable for a whole range of utility curves. Those of us who honestly haven’t done so well with all our winners vs losers will simply index; those of us who have reason to believe that by reading Asymco and other excellent analyses, our lucky streak will continue, should overweight X and underweight Z. The former group is hard to find on websites and the latter group of course has been shown to be hopelessly over-confident, and the average “above average” investor pays a couple points of growth for his dilettantism.

    * We who are still working still have our human capital and future earnings so we don’t lose everything when our investment portfolio vaporizes.

  • Walt French

    Horace, this is another of your finer pieces, and glutton that I am, I would like to see you (or other commenters) add to it along some of these lines:

    • Learning is driven by purpose which in turn is driven by benefit. It’s not just how a drop of purple dye spreads thru a dish of water. How do individual companies or industries motivate users with what benefits?

    • Christensen, as you’re very well aware, is looking intensively about the learning process for secondary and tertiary schools. Somebody recently noted that Apple’s advertising in early 2007 primarily took the form of training videos, showing how to pinch’n’zoom in Safari, tap on icons, etc. What new learning MOs are we seeing in the space, and can they speed the learning?

    • Apple recently foisted a big change in knowing how to use iPhones on its users, with iOS7. (I still have not figured out how to remove an app from my home screen that previously was done just by pressing until it wiggled and the red X afforded me the way.) Apple *knew* that would be somewhat painful for its users, but went ahead because … well, why? What benefits were worth the cost in users’ discomfit and time? Is it that Apple thinks a new look is so much more attractive to buyers in the store? Or does the iOS UX metaphor somehow make the small screen work more effectively in size and number of controls (without extraneous borders, etc)?

    Anyway, thanks again.

    • same

      “ (I still have not figured out how to remove an app from my home screen that previously was done just by pressing until it wiggled and the red X afforded me the way.)”

      It’s exactly the same, except the X isn’t red.

      • Walt French

        Ahhh, thanks. Prompted me to Google the problem, where I found that What you say IS so… once I’ve Set General Restrictions to Allow Deleting Apps.

      • marcoselmalo

        That’s weird. I didn’t need to reset that when I upgraded. Is this a new phone?

        It’s also kind of funny, because I was thinking about what you wrote above reminded me of different rates of learning in different age brackets. My nephew learned how do use his daddy’s iPad in an hour, according to my sister. Age at the time: 2 years. That setting that gave you problems was apparently designed with my nephew in mind (or his parents).

        Setting aside the question of how one is using one’s iPad (obviously, your working needs will be different from a 3-year old), it’s not news that learning comes easier to the young than it does to the old, broadly speaking.

        The fact is that as we get older, we have more to UNLEARN in order to learn. I suppose this resistance to learning is built into Horace’s curve.

        And not strictly relevant to the topic, has anyone else accidentally tried tapping on the screen of a laptop or desktop, momentarily forgetting it doesn’t have a touch screen? Or is that just me?

  • cristene

    Horace – a fabulous analysis. Two things strike me – and it is at the heart of the difference between Samsung and Apple and what will come. Apple innovated around a single platform and device – which actually improves the ability of the market to learn. Conversations around one set of areas/issues/concerns/features that are relevant to all owners. Once a base level of learning in these same areas has been achieved, then there is an opportunity for the fast followers (of which Samsung is the most formidable) for them to enter a “proven” market. The conversation then turns to choice. And I think that is where Samsung has pivoted the game. Multiple choices and rapid increases in functionality allow them to remain continuously relevant. And their willingness to be a *good* partner (as defined by the carriers and retailers) allowed their rapid ascension. The challenge is, as always, the size of the pie. The US is a nicely defined pie. When we layer on a globally defined pie the water gets increasingly murky – because the investments of the two dominant players become accessible to new entrants and a redefined S-curve – consider Xiaomi. This starts a new S-curve. The question I have: where do you think the start of the new curve is?

  • normm

    Apple’s straight-line behavior on your P/(1-P) graph is an important observation. Straight lines have a lot of predictive power! It’s also worth pointing out that Apple’s behavior has been a straight line for about six years, and that it extrapolates to beating Android in the US next year, and having an iPod-like dominance in about four years from now.

    Also, wouldn’t a simpler way of looking at this be that this is like the logistic growth of a dominant bacterium in a petri dish — Apple is eating up the market! Since iOS is better (and available free with contract for those who need that), it is only limited by people finding out that it is better, and by total population.

    • LTMP

      Past performance is not a guarantee of future performance.

      A lot of factors go into to determining what is “better”. Since late adopters differ from early adopters in many ways, it is possible that Android phones lower costs might be more important in that determination as we progress along the adoption curve.

      Also, the market is not a closed petri dish. New “bacteria” can be introduced at any time.

      Apple’s learning goal is (probably) to understand the changing definition of “better” as the market evolves and progresses.

      • normm

        Past performance is no guarantee, but six years of a straight line is suggestive, regardless of how you try to explain it!

      • LTMP

        It is suggestive, yes, and I certainly hope that you’re right.

    • marcoselmalo

      “that it extrapolates to beating Android in the US next year, and having an iPod-like dominance in about four years from now.”

      Counter argument: Supply constraints.

      • normm

        Apple has had supply constraints on all releases, and yet it has followed the S curve (straight line on the diagram) for six years. Why is now different?

      • marcoselmalo

        iPod like dominance? You think that the iPhone will have 80% of the total market for phones in the U.S.?

        I’m bullish on Apple, but I think your prediction is on the far edge of optimistic. Let’s check back in 4 years, and if you’re right, I’ll buy you a cup of coffee.

      • LTMP

        If he’s right, I’ll buy him a Starbucks store. I’ll be able to afford it just from my dividends.

      • marcoselmalo

        What normm is saying isn’t impossible. Apple could decide to make a plastic economy phone at a $300 price point, like many were predicting/hoping before their predictions/hopes were dashed by the 5C. Or a lot of other things *could* happen that would make the supply constraints disappear as if by magic. A lot can happen in four years; perhaps there will be some breakthroughs in manufacturing.

        I’m just not seeing how a line on a chart supports his argument. If we graph oil consumption, we might conclude that oil consumption will increase forever, completely ignoring the supply side of the equation.

      • normm

        Remember that this is a plot of p/(1-p), so 100% penetration is infinity on the plot. It seems to me the thing most likely to derail this trend is the move to lower priced unsubsidized cellphone contracts, so Apple no longer has a “free” option.

      • pk_de_cville

        See Japan, where the 5s, yes the 5s, starts at ‘free’ for all telecoms and, not surprisingly, takes 76% Oct marketshare. Subsidies may go away some day, but not in this decade.

      • pk_de_cville

        I’m certain Apple will dominate premium and mid market levels.

        But there is a requirement:

        Apple must be successful in defending its user experience related IP. Apple cannot dominate in a market where it designs and teaches and others quickly copy Apple’s user experience.

        The hounds of unrestricted fast followers will make dinner of the fox. Androids have had their snack.

        Now, its time for Apple to have them pay the bill and to teach the hounds not to do it again. Good Luck Apple.

        (Samsung, How long will you run your hounds? And will the market turn against your instincts?)

  • Bill Esbenshade

    Great post! Speaking anecdotally, I was a Wintel PC user for about 20 years when I bought my first iPhone, the most amazing device I’d ever owned up to that point. I then stumbled into an Apple store intending to browse and ended up buying a MacBook Pro, and shortly after that an iPad.

    That process involved learning about just how much better, easier to use Apple products were, even if I had to install Parallels to run a couple Wintel programs. I learned about the superiority of Apple products through the experience of using Apple products.

    I suspect there are a lot of long time Wintel customers who went through the same learning/discovery experience, ultimately deciding that Parallels was a small price to pay for a computer that booted so much faster, worked with fewer problems/hiccups, and was so much easier to use than a Wintel machine. These benefits were accentuated by seamless integration with the iPad and iPhone.

  • Hosni

    Pretty much every social phenomenon is practiced by between 0% and 100% of the population. Because trends typically cannot exceed 100% or fall below 0%, the log function often does a fairly good job of describing actual experience simply as a matter of mathematics. The “S-curve” is nearly a straight line in middle ranges, then flattens in the “tails” as the phenomenon approaches 0% or 100%.

    (Certain forces such as laws or economic constraints can set the minimum higher than 0% and the maximum lower than 100%, but the tails of the “S” curve flatten out as the phenomenon approaches the min/max levels.)

    For example, the share of American households owning pets over time can likely be described fairly well with a log function. The log function has nothing specifically to do with “learning processes,” and it neither a new discovery nor exciting that total smartphone use in the US would follow this pattern.

    When the market is divided among two or more competitors, nothing in the S-curve analysis suggests that Apple’s sales or market share (or that of any other seller) will take on the appearance of a log function. If its market share has peaked, that is because of competitive forces. Apple could subsequently boost its market share by lowering price or improving the quality of iPhone.

    • normm

      Apple has bee following the S curve for six years: it’s a straight line on the p/(1-p) diagram. This is experimental fact, not theory. The obvious extrapolation of a straight line is that this will continue.

      • Hosni

        From your comments, you apparently believe that if Apple increased the price of iPhone and iPad by 50%, Apple would continue following that straight line. And that if Apple went back to non-retina displays and 32-bit chips, it would stay on that straight line.  Or if it were discovered that iPhones cause cancer, then Apple would stay on that straight line.

        If you believe the S-curve is “fact,” then you are mistaken. The log-function (sometimes) describes a trend that exists for fundamental reasons. It does not provide guidance for the future.

      • normm

        I believe nothing of the kind. Obviously the smartphone industry as a whole could suddenly decide to increase prices by 50% and then that S-curve would also change. But I don’t think they’ll do that, and I don’t think Apple will either.

        And I don’t understand your earlier comment about Apple’s market share having peaked! The graph shows that it’s penetration ratio in the US is growing exponentially, with a constant coefficient, and has been since the iPhone was first launched. Are we looking at the same graph?

      • Hosni

        The point of my post is that you (and others) wrongly imagine that the S-curve has some theoretical explanatory power for Apple’s experience in the US market. The S-curve is a log function which describes social phenomena constrained between 0% and 100%. That’s why the S-curve was first enunciated by a sociologist. However, that analysis provides ZERO support for the notion that the experience of individual members of the relevant ‘society’ — i.e., the collection of smartphone sellers — will follow an S-curve.

        My hypotheticals (increase the price, reduce the performance) were offered to show that any number of things could derail iPhones from the recent trend line … which, I should add, bears less resemblance to the letter “S” than it does to an inverted “V.”

        Finally, let me address one specific sentence in your comment: “And I don’t understand your earlier comment about Apple’s market share having peaked!” That statement was preceded by the word “If.” That term relates to hypothetical statements … as in “You can see from this hypothetical situation that the S-curve has no relevance for predicting the future.”

        Nothing about the iPhone’s performance is either described by or constrained by the S-curve. This entire discussion is specious.

      • normm

        Apple’s straight red line on the p/(1-p) chart is exactly what an S curve for p looks like in such a log plot. That’s actual data, and I don’t see how it could be much more convincing.

      • Hosni

        norm – “Apple’s straight red line on the p/(1-p) chart is exactly what an S curve for p looks like in such a log plot.”

        Sorry, but no. In a chart with logged values on the vertical axis and time on the horizontal axis (figure 2), a STRAIGHT LINE indicates that the graphed variable is growing at a CONSTANT annual rate, such as 20%/year.

        The (almost) straight red line in fig. 2 does NOT describe a variable with slow-growth “tails” relating to an S-curve. Neither fig. 1 nor fig. 2 describe iPhone sales before Jan. 2010 nor after Sept. 2013.

        You can read about logarithmic transformations elsewhere. The function graphed in fig. 2 is expressed: log Y = a + bX. The slope of the curve (b) is the growth rate of Y (iPhone sales) with respect to the X (time) variable. When the curve is a straight line, then b is constant.

      • Check your variables again. The Y variable in fig. 2 is not iPhone sales, nor its penetration (P). It’s P/(1-P) as normm noted, and relatively simple algebra shows that when log[P/(1-P)] is linear, then P is logistic.

        log[P/(1-P)] = a + bx (a, b are constant)
        P/(1-P) = e^(a+bx)
        (1-P)/P = e^-(a+bx)
        1/P – 1 = e^-(a+bx)
        1/P = 1 + e^-(a+bx)
        P = 1/[1 + e^-(a+bx)] which is the logistic function.

      • normm

        Sir, if p/(1-p) grows as a straight line on a log graph, then p itself grows as an S-curve on a normal plot. I’m a PhD physicist, so please don’t try to teach me elementary math.

      • Norm is right. This is a graph of the log of a ratio (F/(1-F)), not of the underlying variable F. Please look more carefully at the methodology. See the attached excerpt from Grübler

      • Rogers’ work seems to be grounded in the notion that learning processes are the underlying causes of the rates of technology diffusion. He asserts that each adoption of an innovation in a social system is equivalent to a learning trial by an individual (Rogers, 1983). The symmetric diffusion pattern results from the way messages about an innovation are emitted and processed by social learning. In his defense, equating the learning curve with the logistic curve is a matter of both recognizing the similarity in shape and of creating an equivalency due to causal similarity. In other words, not only are numerous experiments with learning showing behavior similar to diffusion of technology but there is a fundamental equivalency between what societies do in response to information and what individuals (who make up society) do.
        (The logistic function is not a log function, as far as I’m aware (, so I’m not sure how you are equating S-curve with log function).
        The question I’m asking is: if a particular competitor within a system which, in total, has a logistic behavior has, in its own right, logistic behavior then is it also governed by the same learning processes? This is all the more curious as other competitors do not behave the same way. I would point the finger to the one competitor which exhibits logistic behavior as perhaps having a different communication with the consumer.

    • Walt French

      Let’s just suppose that Apple *DID* offer a new model that consumers felt was a simple addition to the overall marketplace; i.e., that only cannibalized other manufacturers’ phones (or non-consumption). And that this resulted in a simple doubling of Apple’s sales.

      So there’d be a step function to the sales chart; Apple’s cumulative penetration would kink upwards. All the nice linearity of Apple would go haywire.

      There’d be the temptation to split off this Apple iPhone ][; perhaps that’d allow the original and modified product to each have a straight-line saturation curve. And people would be troubled that “Android” has always been a heterogenous, shifting mix, yet is not split into its dozens of pieces.

      I offer up this as a thought experiment. Perhaps it’ll help us set expectations for what the charts “should” look like.

      • Hosni

        Walt – The charts “should” have no particular shape, other than constraining TOTAL smartphone use between 0% and 100% of the adult population.

        The red-orange line in figure 2 can be explained without reference to an S-curve:
        1- The TOTAL demand for smartphones is up for grabs by all competitors. Apple, by controlling the features and prices of its products, can capture whatever share of the market that it wants.

        2- However, the share of the market that Apple “wants’ to capture is that share which maximizes profits.

        3- The share of the market that maximizes Apple profits is a function of iPhone features (R&D), component/production costs, iPhone price, carrier subsidies and the features/prices of competitor products. If Apple lowers price, its R&D produces breakthroughs (e.g., fingerprint scanners), component costs decline or carrier subsidies become more generous, then Apple’s profit-maximizing market share increases (and vice versa). If competitors introduce better products or lower their prices, Apple’s profit-maximizing market share decreases (and vice versa).

        4- From the foregoing, we conclude that the number of iPhones produced and sold in the US market reflects Apple’s response to conditions that are partly under its control and beyond its control. These factors fluctuate over time rather than moving along a fixed trend line.

        5- Ergo, the red-orange “line” in fig. 2 is a series of points relating to the intersection of iPhone supply and demand each quarter. iPhone supply and demand exist in an entirely different chart which is (regrettably) neither drawn nor alluded to in the article, which relies instead on a rule of thumb borrowed from sociology.

        My interpretation of the two charts:
        Figure 1 shows iPhone sales (adoptions) slowing simply because it is becoming increasingly difficult to provide a reason for the minority without a smartphone to buy one. Some people have very little desire/need for a pocket computer. Fig. 2 shows that total US smartphone sales parallel iPhone sales (adoptions) because Apple is the industry leader, and its introduction of new products/features expand the overall market. The other lines in fig. 2 reflect competition between the remaining smartphone makers, which they do by varying price and by introducing key features that largely mimic those of iPhone.

        In fig. 2 Android’s (gold) curve was parallel to the total market and iPhone in April 2012 and has since flattened relative to both. The implication is that over the past 16 months Android phone makers have been unable to match the market appeal of iPhones due to price reductions on older models and various innovations (aluminum case, frequent iOS updates, iCloud support and compatibility with iPad, A7 processor, etc.). Sellers that rely on low prices and copying features from the industry leader no longer experience rapid growth when prices (for most Android phones) are barely above cost and the industry leader implements difficult-to-copy features.

  • poke

    I think the graph indicates the degree to which competition is an “opt-in” phenomena and is less basic than the relationship with the customer. If you define your products in terms of “speeds and feeds”, you’re opting into competition with other companies that do so, because the relationship you’ve established with customers is inherently cost-benefit.

    You might even say that there aren’t really multiple individuated actors involved in the non-Apple smartphone market: there’s a group of companies that share customers between one another according to conditions set up by their shared culture (“we offer a, b and c at price x” implies “if somebody else can do better, go to them”). That culture permeates everything these companies do: How they conceive of products, how they develop products, how they price and market products, and the basis on which they sell products to their customers. It’s also how they choose or develop their customers: they get customers who share their values and their utilitarian outlook. (Of course, this outlook is shared by analysts and most theorists, so it’s wrongly perceived as the only possible way of doing things.)

    Apple, on the other hand, has a different relationship with its customers and essentially operates independently of the rest of the market. Thus, you have two curves representing the customer-company relationship: one for Apple and one for a group of companies that define themselves in terms of one another according to a shared business culture. Apple remains outside of the competition going on between the others because it chooses or develops customers who have different values and a less utilitarian outlook. The learning process going on in each case is separate: one set is learning the cost-benefit outlook of the smartphone technology market (as non-Apple smartphone companies conceive of it), the other is learning the “liberal arts” (virtue/craftsmanship-oriented) outlook of the iPhone.

    • normm

      Apple seems to be following a logistic curve (straight line in the p/(1-p) diagram). This means it’s taking over the entire market. In this case everyone else combined is necessarily following a curve that’s headed towards zero penetration.

  • berult

    Thoroughfare of yore…of lore…of sore…of…trains of thoughts;

    iPhone’s job-to-be-done slates Jobs be redone by wrought…

  • Very interesting analysis. I’m also curious about whether the learning process works the other way. For example, the RIM curve is now also linear but in the other direction. Does this imply that RIM users are “learning” (or have learnt) not to buy?

  • obarthelemy

    How does this analysis work in other markets ?

  • victor

    Great post horace,
    Regarding the phenomena of the agregated trajectory of the industry vs the individual trajectory of each company i believe there are two seminal s curve articles from Clay where he pointed the same phenomena.

    • Can you point me to those articles?

      • victor

        The articles are:
        Christensen, Clayton M. “Exploring the Limits of the Technology S-curve, Part 1: Component Technologies.” Production and Operations Management 1 (fall 1992): 334–357.

        Christensen, C. M. “Exploring the Limits of the Technology S-curve, Part 2: Architectural Technologies.” Production and Operations Management 1 (fall 1992): 358–66.

        Both articles were reprinted in the book strategic manegement

  • Jessica Darko

    Your numbers for android are made up. Take them out and you get a very different graph and you would be asking very different questions completely.

    You’re really making me want to start a blog where I start calculating actual market share for various mobile OSes and calculate real android numbers. I’d really rather not do this, because you’re a better analyst than I am, and i have a day job already.

    But using info that is out there, and not relying on wishful thinking from analysts or made up numbers from google, you can calculate real android numbers by correlating an objectively collected statistic with iOS’s share of that same statistic for where you have real shipping numbers.

    Or at least use the same measuring stick . If you’re going to rely on google “activations, then rely on iOS activations as well. iOS activations are around 4 billion to date with an additional 500-700 million coming next year. This is easy to calculate– every release of the OS times the number of devices that are less than 2 years old. (I think the android counts are even more inflated than this, but we don’t have to be as dishonest as google to come up with a good comparison.)

    Realistically, iOS has %75 of the market, when using the same measuring stick.

    • obarthelemy

      “if android has %10 of the mobile browsing share while iOS has %90 during a given period, and during that period there were 90M iOS devices sold, it stands to reason that there were 10M Android devices sold”. Not.

  • josedante

    What if Apple’s pattern doesn’t reflect a “learnable advantage” but it’s trajectory towards 100% penetration in a subset of the market – let’s call it the high end. Trajectory which, reasonably enough, happens to follow the logistic curve. We could calculate peak marketshare for Apple in smartphones.

  • RichardinMelbourne

    One of Rogers’s assumptions is the technology is static and unchanging over time, for example 2G phones (Rogers 2003). Yet Rogers died in 2004 before 3G and iPhones. Dynamic technologies such as iPhone may require new theory I argue @valuemgmt. See more critique on Rogers in Hall’s Chapter of Oxford Handbook of Innovation 2005.

    • If you look at other technology adoption curves, the underlying technology did evolve. Take trains for example, the adoption curve was a century but what we saw in 1820 differed greatly from 1920. Same with autos and aircraft and consumer electronics. Having said that, the degree of change might be affecting the observation that individual firms don’t follow logistic curves (unless they are monopolies.)

  • Another hypothesis is that the learning advantage is the easiness factor, how easy is to use the met needs of a platform and find and use previously unknown needs.
    In this hypothesis the natural advantage of a platform can be somewhat measured, it is the effort that is required to use its features.
    It is like the state of minimum energy of a system, users (in great numbers) will always go for the easiness and if the difference between platforms is sensible they will learn what platform requires less effort to meet their needs.

    In this case iOS has sensible differences of easiness that have been cautiously cultivated by Apple.
    One store, one payment method, controlled App -> security, no fake, one simple interface shared by all devices, consistency etc…

  • Ian Ollmann

    This one is at least two standard deviations in quality relative to your already high mean. We’ll done, Horace!

  • Chaka10

    This is a great piece for seeking to bring some theory to bear on the smartphone analysis. Thanks. However,… like others who have commented, I’m also not sure about the “learning behaviors of individuals” explanation. The normal distribution (bell curve shape) of smartphone adoption in a population suggests that process may be driven by the actions of MANY INDEPENDENT RAMDOM FACTORS, each of which only has a partial contribution to the process as a whole. (The Central Limit Theorem posits that the normal distribution is the limiting result of such processes, and applies even when the component factors have different probability distributions.). I can think of several component factors underlying adoption, including for starters, a person’s wealth, education, age, profession, state of mobile broadband coverage in the relevant area for such person, etc.

    In any case, as I’ve said before, “looking at the macro curve of smartphone adoption wouldn’t have been very helpful for understanding the trajectory of Symbian or Blackberry devices a few years ago” (see my Curves within Curves comment to the Asymco piece, “When will the European Five reach smartphone saturation”).

    As I also said in the same comment, “[t]aking another step back, the smartphone curve itself can be thought of as an internal curve within the broader S curve for all mobile phones. From that perspective, mobile phone adoption is well towards saturation, and the smart-feature components are just changes in [platform] mix.”