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Almost half of US mobile subscribers have smartphones, iOS closes the gap on Android

0. phoneArena 29 Mar 2012, 09:48 posted on

Almost half of US mobile subscribers have smartphones at the end of February 2012 as smartphone adoption continues its steady growth…

This is a discussion for a news. To read the whole news, click here

posted on 29 Mar 2012, 17:48

43. networkdood (Posts: 6330; Member since: 31 Mar 2010)

Obviously, your Markov-chain model has a fatal flaw in its calculations.

posted on 30 Mar 2012, 13:45

67. hepresearch (unregistered)

Markov-chains are not fatally flawed... they've been used for ages in all sorts of situations. Economics, physics, engineering, electronic logic, you name it... Markov-chains help us to understand the movement of changing ratios of populated systems over time, whether that population consists of people, objects, money, signals, spin-states... whatever. They are based on the concept of linear-superposition of vectors in a space of any number of dimensions you need to describe the system you are working with. I have done nothing but adapted this for use in the mobile market context, and then filled it with relevant data supplied by as many of the statistical survey and analysis houses as I could find in the time I have had thus far to get something reasonable. Unless you are here to tell me that "y'j = yj Xij" is not equal to "yj (x1 + x2 + ... + xj + ... + xi)", then you really have no argument against the mathematical logic I have used, as it is age-old, tested, proven and sound.

posted on 29 Mar 2012, 21:00 1

55. remixfa (Posts: 14255; Member since: 19 Dec 2008)

and exactly how did you come to that conclusion seeing that android has been gaining more per quarter for almost 2 years now than apple? It has double the market penetration world wide, and even when the pendulum swings to apple's rise in sales for a new device launch, it doesnt swing enough that apple actually outsells android for a single month.

Your calculations have seeerious flaws.

posted on 30 Mar 2012, 00:36

58. hepresearch (unregistered)

The math is not flawed. It is basic linear algebra, which is not disputable at this point. What CAN BE disputed is the data used to supply the matrices. I am all for seeing better data sources if you have any that you prefer. The data I look for are statistics that show "brand loyalty", or loyalty to an OS, by percentages of users of a particular OS "x" who are switching to another OS "y" (or in the case where "x = y", they are actually staying with the same OS for their next phone), and the current market share for each OS "x" and "y". I have generally been including data for six primary OS's (Symbian, BlackBerry, iOS, Android, webOS, and Windows Phone), and a general entry for all feature phones, which gives a 7 x 7 unitary matrix representing the US market. I do my best to average all of the sources I can find in order to get a general value for each data point, but there are so many which are debatable these days... I can find a dozen different data sources that provide the same type of data, but with quite different values for the data points, all of which are contested by various groups in various ways. I've asked people before to provide data that they find to be favorable, but no one ever bothers to take me up on that offer.

Trust me, the math is sound. I've been doing this for 15 years in different applications from class work to teaching to particle physics research, and just last year applied this to the mobile industry... but it is the input data that determines where the model goes once the time-steps in the Markov-chain begin. If you don't like where my analysis ended up, then get me the data you think is more representative of the current market situation, and I'll run it.

posted on 30 Mar 2012, 14:13

68. remixfa (Posts: 14255; Member since: 19 Dec 2008)

ok, so your looking at brand loyalty and percentages.

you forgot a major slice of the pie.


The bulk of Apple's sales by far comes from upgraders, not from new lines. Thats why they have nice sales peaks after a new phone, but dont take a huge chunk of the actual market.

Also, if you look at this graph or any other, android is outselling iOS. iOS is in its yearly PEAK because of the i4s and ipad3 launch. It will dwindle down like it always does. Androids graph however is a pretty solid line up, that only increases each month.. it doesnt have heavy spikes and peaks like apple does by the nature of the different sales models in place.
Look at this graph again, even at iOS's sales peak, its still behind android sales. You cant take the top spot without top sales.

Apple will NEVER over take android again. Its impossible. The very nature of its open source vs iOS super walled garden makes it impossible. Single device sales, sure, but never OS vs OS.
Your math is flawed because you are not adding up the entire picture.

posted on 31 Mar 2012, 22:59

72. hepresearch (unregistered)

New-comers to smartphones ARE included because there is a covariant component y'j = yj (x7) and its contravariant element y'7 = y7 (xj) which represent people who have had a feature phone, or no phone, who are now entering the smartphone market for the first time... so yes, I did include these people... but remember, I have only been able to measure this in the US thus far, so this entire exercise is US only, and I really don't know too many people in the US who don't yet have a phone of some sort. Likewise, this only projects 76% iOS ownership among all phone users in the US by 2018, so elsewhere in the world we could see other regional trends and variations which I cannot possibly hope to compute at this time; I simply have not had enough time of my own yet to collect enough data...

I already thought of this... and like I have said before the math, as in the logic technique itself, is NOT FLAWED, although I do not dispute that the data MAY BE... hence my request for more accurate data if you can get me a reliable source that you believe in, other than the ones I go to at places like Nielsen, Gartner, NPD, CNET, Canalys, etc...

posted on 01 Apr 2012, 04:17

74. remixfa (Posts: 14255; Member since: 19 Dec 2008)

i still cant fathom how your numbers come up the way they do. Even in "just the US", android outsells apple EVERY quarter without hesitation, even when apple releases a new product. When they havent had a new product in quite a while, android outsells apple by huge margins.

Apples sales graph is a mountain of ups and downs. Android's sales graph is a pretty linear 40-50 degree angle up and climbing. The business models are completely different, and over all sales far and away go to Android. There is no way that your model is anywhere close to accurate. If anything, its reversed. 76% will be on android. 50% already are.

And the american market is only 50% saturated with smartphones.

posted on 02 Apr 2012, 08:55

77. hepresearch (unregistered)

After isolating various parts of the analysis, here is why:

A Markov-chain is defined as the repeated use of a stochastic (meaning all linear elements in a given row or column ALWAYS sum to 100%) mixing matrix in iterations... for example, the resulting market share vector {y'1, y'2, ..., y'j} of the first transition is produced by multiplying the initial market share vector {y1, y2, ..., yj} by a single iteration of the stochastic matrix Xij, where Xij is the same number of columns across as it is rows deep. Every matrix element xij where x is not equal to j produces a movement, in percentage of initial subscribers, from one OS to another, and every element xij where i equals j represents the percentage of users who are loyal to their current OS. When one iteration of the stochastic matrix has been applied, we call the resulting market share vector a "primed system". Now, if we consider over what period of time one iteration is supposed to take to actually cycle, then if we double that time we can actually multiply the primed result by the same matrix again... thus we get a double-primed system as a result, and so on... now if one was to solve for the Equation of State, which is simply an infinite Markov-chain, one would find that after a long time the stochastic matrix will simply not alter the initial state into an appreciably different +1 primed system. At this point, y'j = Xij yj = yj, but Xij is still not a scalar value and has not changed since the first iteration.

Now, with this little preview in mind, I would cite the data which has the largest influence on the previously mentioned Android-iOS controversy... remember that about 89% of iOS users will stay with iOS, while only about 53% of Android users will stay with Android for their next upgrade. This means that if we take x11 = 0.89 and x22 = 0.53, then we have the diagonal matrix elements that represent this behavior (there is some variation between figures touted by analysis houses on these, but these are the rough avearges). As it turns out, even though we can say that x33 is very small, and is the number of people currently with feature phones who are staying with feature phones, they are picking Android phones (x32) over iPhones (x31)... however, the number of Android folks moving to iPhones (x21) is much larger than the number of iOS folks moving to Android (x12). The problem then arises... does the larger (x32) over (x31) overwhelm the dominance of (x21) over (x12)? The answer is that when the base of feature phone users y3 eventually runs out, (x21) being dominant over (x12) becomes the only major factor, and iOS booms past Android in a big hurry simply because iOS hold its existing customers that much better than Android does. Unless Android does something HUGE to turn this around soon, it is the inevitable end result after quintuple-priming... considering each matrix iteration to represent the average US upgrade cycle of 16 or 17 months... which is about 2018.

posted on 02 Apr 2012, 09:09

78. hepresearch (unregistered)

In other words, because x21 is higher than x12, and because x11 is the highest element of the entire matrix altogether... Apple is essentially at the "top of the food chain", if you will. Thus, this result is automatic over longer-terms as long as iOS continues to garner such extreme loyalism, and as long as Android fails to garner an equal loyalism. Also, it is worthy of noting that, as the number of feature phone users declines, more remaining feature phone users will be of the type who seek convenience and ease of use, and as feature phones dissappear further, they are likely to go to the iPhone or iPad over other Android devices simply because of media coverage, popularity, good reviews, and Apple's legendary UI simplicity.

Android is having their meteoric rise now because of the freedom-loving among us, but iOS will begin to climb faster, and eventually overtake Android in the US... I'm thinking around 2015 or 2016 (which is about when Android is projected worldwide to overtake Windows in general as well)... so we should see a peak to Android shortly as feature phones become less prevalent, and as first time smartphone buyers also become less prevalent. iOS on the other hand should continue a slow and steady increase year-on-year, but with an ever increasing pace in the next three to five years. A number of people (usually the techy nerd crowd, like me) will certainly pay out good money for a powerful, highly functional phone, but the real high-payout long-term money is gratuitously shelled out by the overwhelming masses of people who care for nothing but convenience.

Android isn't going away by any means, but they will not be the top-"dawg" in US market share for long; this is simply because there are many many more "convenience users" than there are "power users".

posted on 02 Apr 2012, 09:26

79. remixfa (Posts: 14255; Member since: 19 Dec 2008)

OK, but here is where your running into trouble. Every time one of those polls comes out that says "do you plan to stay with your current OS", it always shows iOS with a huge margin of loyalty (which is very true) and shows android with the 50-60% margin. When it comes to actual sales time, most of those android people stay with android. The perceived loyalty and actual loyalty are very different. Many people that go from android to iOS ultimately come back to android since they are used to options. That is why no matter what those prelim charts say, android has double the marketshare of iOS and is growing a wider lead every month.

if android has 1000 phones sold, and apple has 500 phones sold (double the market share) and we go by their percieved loyalty..

89% of iOS x 500 =445
53% of android x 1000 = 530

where do the rest of the customers go? not all iOS people go to android and vice versa. Android users that are dissatisfied with the OS are in my experience very open to WP7. I watch it every day. But then again, Android users who are dissatisfied with their current device just pick another android device on their next upgrade more often than not. The % of them that go to iOS is much smaller than the little stat you picked shows.

No matter what, your calculations are wrong. In order for them to be right, 100% of everyone that is dissatisfied with their android device would HAVE to go to an iOS device. The actual sales numbers prove that to be false month after month. If your stat numbers had an ounce of truth, the actual sales numbers would be sliding that way. Instead they are very quickly sliding in the opposite direction.

Apple fans expected the playing field to even out when the iphone went to most every carrier. It didnt. Android is still gaining steam above and beyond apple's best sales. Its OS vs OS, not phone vs phone which is more or less what the stat you are pulling from implies. It is impossible to beat android because of its open source ubiquity vs apples very close and controlled ecosystem.

posted on 02 Apr 2012, 10:34

80. hepresearch (unregistered)

Where is your statistical evidence to back up your assertion that Android owners SAY they are going to try a different OS, and then stick with Android when push comes to shove? Do you realize that you are suggesting that, when surveyed, Android owners have a greater tendency to lie en-mass in one particular bias than iOS owners do? If your argument is with the source of the statistics, then it is not my fault. I am working with everything that is already measured and available.

If you have ever studied anything about crowd psychology, then you will remember that as a population, people tend to tell the truth... this does not preclude their ability to lie to each other, but the fact is that the average of all lies will be close to the sum of all truth, since we have equal ability to exaggerate in both directions from the central truth. Not only that, but the crowd-mind analysis relies on this fact by being able to predict all sorts of societal events without having to take into account anything but what people say. They are assumed to be true, and the model still works incredibly well. It has been used to predict the outcome of all sorts of things, from the initial popularity of the original iPod to the Iranian nuclear program controversy, and in general it has never been wrong.

Furthermore, you are criticizing the fact that I simplified the model to just Android, iOS, and feature phones in order to explain it in my prior comment... you say that this is flawed... however, you have forgotten that I already tried to explain to you that I HAVE included other OS's. My stochastic matrix analysis is 7-dimensional, including every major OS now openly available in the US. I have already taken Windows Phone, webOS, Symbian, and BlackBerry into account in my primary analysis, but I found it necessary to simplify it for the purposes of highlighting the immediate argument in question, and now you have criticized me for simplifying it to try to help you understand.

I am trying to work with you here, to help you understand what I am trying to get across here, but I can't do this if you are not going to work with me. I understand where you are coming from, but I am trying to show you how things work in a linear system, which this is... even though you disagree.

posted on 03 Apr 2012, 11:11

81. remixfa (Posts: 14255; Member since: 19 Dec 2008)

I understand what you are telling me and why your pulling the data the way you are. You ask for evidence against your predictions. The evidence is in the actual sales. People may not be lying. They may just want aa different device.. but that doesnt mean they are leaving the ecosystem. Not liking your HTC doesn't mean you auto upgrade to apple. Many will go samsung or moto.
The proof is the constant difference between "intended upgrade" vs actual sales which reflect a much higher OS loyalty than suggested. Android is still moving ahead of iOS every quarter.. it has yet to cede any actual ground. If your numbers were right we wouldn't see that.

Garbage in garbage out.

The equasion might be good but the numbers are not.

posted on 03 Apr 2012, 14:29

82. hepresearch (unregistered)

Wrong again... my numbers suggest that we will still see Android surging ahead for another 12 months, then taper off a bit in the next 6, and then begin losing ground in the months that follow. The end result is still the same. As feature phone users move en-mass to smart devices, they are getting more Android phones than iPhones, but when the population of remaining feature phone owners declines below a certain point, the movement of Android users (and not just from an Android to a different Android... no, I mean the ones who really DO move to an iPhone from an Android!) to iPhones actually overwhelms the first-time smart device sales figures.

If I take your example, and expand a little upon it:

Apple "y1" = 500 users
Android "y2" = 1000 users
everything else "y3" = 2000 users

Set up the market share vector Yj = {y1, y2, y3}
Set up the mixing matrix Xij = [{x11, x12, x13}{x21, x22, x23}{x31, x32, x33}]
The resulting primed vector Y'j = Yj Xij

If we have x11 = 0.89 and x22 = 0.53 (these are the straight averages for these loyalty metrics), and x12 = 0.07 (this is the HIGHEST value I could find for this metric, so as to disadvantage iOS as much as possible), and x21 = 0.21 (this is the LOWEST value for this metric I could find... so I am essentially stacking-the-decks in Android's favor here), then, because of stochastic unitarity (the rule which conserves total market share in each row and column to 100%, and thus makes certain that no users are ever lost or unaccounted for) we must also have x13 = (1 - 0.89 - 0.07) = 0.04, x23 = (1 - 0.53 - 0.21) = 0.26. Furthermore, we then know that x33 = (1 - 0.04 - 0.26) = 0.7, and since Android is selling three-to-one over iPhones to first-time smartphone acquirers we have x31 + x32 + 0.7 = 1, where x31 = x32 / 3... thus we complete our matrix with 0.3 = 4 x31, so that x31 = 0.075 and x32 = 0.225. Continued in next comment...

posted on 03 Apr 2012, 14:45

83. remixfa (Posts: 14255; Member since: 19 Dec 2008)

lol, ok

how about this.

i agree that your numbers are off, you agree that they are not. so lets agree to disagree and in 12 months we will see whos right. :)

posted on 03 Apr 2012, 15:15

85. hepresearch (unregistered)

That's fine, I have no problem with that... in 12 months, though, I expect Android to be at their peak ahead of iOS, so we might not see any difference at that point... give it 24 to 36 months to be sure. Either way, I agree with you, that we should just be content in our disagreement until things happen the way they do.

Just the same, there is nothing yet to stop Android or WP from doing something sufficiently amazing to bump iOS back into negative territory... although I suspect that Apple is using an "Overton Window" approach to their litigation in order to incentivize Google to feel false security when they survive lawsuits, and then not innovate as quickly as they could have... but, it's just a theory for now.

posted on 04 Apr 2012, 01:35

86. remixfa (Posts: 14255; Member since: 19 Dec 2008)

so.. what your saying is..

if iOS wins, you were right..

if Android wins or WP7 over takes iOS, you were right.

so.. no matter what.. you were right?

dude, even that is an arguement i cant win. ha!

posted on 04 Apr 2012, 08:14

87. hepresearch (unregistered)

What I'm saying is that if iOS wins by 2016 or so, then I am unfortunately right on, and without actually trying really hard to be right or thorough. If I turn out to be right, it would be like shooting a 3-point free-throw across the entire length of the basketball court with my eyes closed after having only glanced at the basket for an insignificant instant.

Essentially, I am saying that if I turn out to be wrong in about 3 years or so, it is not likely to be because the data at this time I used was very wrong, or because the mathematical logic is flawed... it will be because the stochastic matrix is subject to transformations which I cannot predict, and which I have not taken into account in this basic model for lack of information for lack of my own effort. What this means is that if nothing changes from the current state, then iOS will beat everyone else... but, if a significant enough change occurs, like a real market shaking device launch or an unexpected bankruptcy or the like, I will most likely end up being very very wrong... and there are SO many ways that could happen.

I hope I am wrong. I want to be wrong. And, if even the slightest changes occur, I will most certainly be wrong... but, so far, I have seen the market follow almost EXACTLY (within 0.2% error) the predicted path which this gave me 7 months ago thus far, and I can only hope that some Android OEM, probably Samsung, will soon release a device that very quickly takes the wind out of Apple's sails. Or Nokia could release a new Windows Phone 8 device later this year that crushes the iPhone like an empty aluminum can... either way, I plan on being wrong, but I am annoyed that the data shows that, so far, I am right in the worst way.

If Android or WP overtakes iOS, it should be because they improve their devices and services enough to actually change the mixing matrix (and thus, Android or WP must have equal or greater loyalty than iOS at that point), and that should be something that can mathematically be taken into account by covariant-contravariant matrix shifts (which I do NOT currently account for because I do not have enough information). When that happens, though, I will finally get some data on the rate of change of individual matrix elements, and may be able to model that covariant-contravariant behavior (actually, in the same way that Einstein modeled the General Relativity equations - the Ricci tensor, Ricci scalar, and the Minkowski metric are related in the covariant-contravariant context as well to produce gravitation by the curvature of space around massive objects).

posted on 04 Apr 2012, 08:23

88. hepresearch (unregistered)

In short, I predicted a roughly inverse-parabolic trajectory for Android that peaks in another year and a half, so that Android will continue to make huge gains, and Apple will begin to sneak up and creep up afterward with steady gains as Android flattens out. All of the OS's I projected trajectories for are following them nearly perfectly right now, and for it being 7 months later, that worries me quite a bit. Yes, Android is making big gains right now, but if it continues to follow this path and fails to depart from it at some point, then iOS will inevitably take over as Android continues on to the cruel downslope in the stretch that is yet 2 to 3 years out.

The application of chaos theory ought to unbalance this at some point, and I see Android being chaotic enough to do it... however, as recent design trends suggest that Google is taking more direct control over Android in order to "compete" with Apple's iOS "better", I fear they will control it too much, and remove the possibility of sufficiently market-shaking chaotic developments. A heavily controlled system like iOS is too steady on its own to upset the cart, so to speak. I am running out of patience while watching Android become more like iOS, and in doing so they will seal their fate and hopelessly lock themselves onto the path that I already fear they will follow.

So, if iOS wins, I'll be able to claim I was right, but I will be highly disappointed. If iOS stays behind Android in the longer term, I will be wrong, you will be right, and I will be pleasantly surprised... and if things improve as you and other Androiders are saying, then I am much much more likely to be wrong... and that gives me some hope.

posted on 03 Apr 2012, 15:07

84. hepresearch (unregistered)

So, now you see that we have:

{y'1, y'2, y'3} = {y1, y2, y3} [{x11, x12, x13}{x21, x22, x23}{x31, x32, x33}]

With our values substituted in for solution:

{y'1, y'2, y'3} = {500, 1000, 2000} [{0.89, 0.07, 0.04}{0.21, 0.53, 0.26}{0.075, 0.225, 0.7}]

So that we get the base linear primed groups:

y'1 = x11 y1 + x21 y2 + x31 y3
y'2 = x12 y1 + x22 y2 + x32 y2
y'3 = x13 y1 + x23 y2 + x33 y3

Remember, this primed system is considered to be about 16 or 17 months out from the initial system...


y'1 = 445 + 210 + 150 = 805
y'2 = 35 + 530 + 450 = 1015
y'3 = 20 + 260 + 1400 = 1680

Now, this sort of illustrates my point. Although we have made generalizations to the non-iOS/non-Android OS's, the behavior is of the same type, and behaves in a fairly similar (though highly exaggerated and accelerated due to lack of fine interaction) way...

Now double-prime it:

y''1 = 716 + 213 + 126 = 1055
y''2 = 57 + 538 + 378 = 973
y''3 = 32 + 264 + 1176 = 1472

So, you now see what I mean... yes, Android in this model is outselling iOS for new users three-to-one, but the higher loyalty of iOS users makes all the difference even in 16 or 17 months (although accelerated by a factor of 7/3 here) as the less-loyal Android users bleed over to iOS faster than they can be replaced when y3 declines below a critical point.

posted on 29 Mar 2012, 17:53

45. strikercho (banned) (Posts: 156; Member since: 20 Mar 2012)

Well, no surprise here. After the bitter experience with Handroid, people see where the truth is - and buy a real smartphone, an iPhone.

posted on 30 Mar 2012, 02:25

61. frydaexiii (Posts: 1444; Member since: 01 Dec 2011)

lol, anyone with any brains would know an iPhone is the dumbed down version of what a smartphone should be...Thanks to Android and what it can do, your so called "Smartphone" is now just a phone, hell it's a dumb phone.

Play games and videos, what else can it do?

Send a file via bluetooth to another phone? No.

How about editing a word file and transferring it to a PC that doesn't have iTunes? Also No.

Ok, maybe it isn't so good for work in the office, how about taking a song directly from your friend's PC? No?

posted on 01 Apr 2012, 18:20

75. jroc74 (Posts: 6006; Member since: 30 Dec 2010)

Hate to feed the...but I would think a smartphone more like a PC is a real smartphone. I would think a smartphone that you can do more with out the box is a real smartphone.

You can change the way a Windows or Mac PC look with themes out the box, change core software out the box. IMO the iPhone is too locked down out the box to be considered a real smartphone.

I dont consider an iPhone any less of a phone, I thinks its nice. Just responding to the troll...

posted on 29 Mar 2012, 17:54 1

46. rudlie (Posts: 205; Member since: 13 Mar 2012)

Android has meet mature point, now still at stagnant point before it will be declined.

posted on 01 Apr 2012, 18:22

76. jroc74 (Posts: 6006; Member since: 30 Dec 2010)

The iPhone had a stagnant point in 2010 and maybe some of 2011. It grew tho...I see Android growing some more too. I see Android and the iPhone being neck n neck for years to come unless something dramatic happens.

posted on 29 Mar 2012, 18:22 1

51. qxavierus (Posts: 48; Member since: 20 Mar 2012)

To the author of this article.
>And if we look at the last three months alone, Apple’s share has grown to 43%.

This is incorrect and misleading, because the Nielsen report (see the source link) says:
"Among recent acquirers who got their smartphone within the last three months, 48 percent of those surveyed in February said they chose an Android and 43 percent bought an iPhone."

Which has nothing to do with market share (the total volume of existing Android and iPhone devices).

posted on 30 Mar 2012, 00:43

59. hepresearch (unregistered)

... but it does have to do with current sales rates... iOS IS closing with Android in recent sales, for the time being.

posted on 30 Mar 2012, 14:15

69. remixfa (Posts: 14255; Member since: 19 Dec 2008)

closing in, during the apple sales peak, but not meeting or exceeding. android is still outgrowing apple. and that will be more pronounced when apples peak subsides and dips very low in the months prior to the next idevice launch... something that doesnt affect android, since it has constant launches through the year. your logic is flawed.

posted on 31 Mar 2012, 18:11

71. qxavierus (Posts: 48; Member since: 20 Mar 2012)

Think what you want, but iPhone has one very serious flaw - it's expensive! Therefore it is doomed to have less market share. History repeats itself (Apple/Microsoft)!

Apple may be winning the battle in the universities, but Android is winning the battle at the elementary schools. All schoolmates of my son have Android phones - just because they are cheaper. It is statistically impossible for iPhone to have bigger market share than Android.

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