Moving averages and the iPad

On Monday, all the real Apple bloggers read the press release, listened in on the conference call, and rushed to update their graphs of Apple sales figures. Most of the graphs looked like this one by Jason Snell

Six Colors iPad sales graph

or this one by Federico Viticci

MacStories iPad sales graph

in that they plotted the raw numbers provided by Apple. The advantage of these plots is that there’s no screwing around—the numbers are what they are, and there’s no interpretation between the figures and you. However…

Apple’s sales figures are strongly seasonal, and because the graphs jump wildly from quarter to quarter, it’s often hard to see trends. When I wrote about the iPad last fall, I included this screenshot from the October 2013 Special Event:

Cook and iPad sales

By plotting cumulative sales instead of quarterly sales (and by doing some unspecified smoothing as well), Apple eliminated the jitter. It also, presumably, hoped to hide the downward trend in iPad quarterly sales—cumulative sales always go up. But for those of us who remember our calculus, the downward curvature at the right end of Tim’s graph told the tale.

There are myriad other ways to smooth a graph without switching to cumulative figures. One of the simplest is the moving average. In this technique, instead of plotting the raw data, you plot the average of a few data points in the neighborhood of each time value.

For many data sets, the best size of this neighborhood is not obvious. With Apple’s sales figures, though, I think it’s clear that the best choice is to average over four quarters: the quarter that you’re plotting and the three previous. This smooths over the seasonal jumpiness while not including so much past data as to ignore real trends. As an example, the 2015 Q2 value of a four-quarter moving average of iPad sales is 14.9, which is the average of 13.3, 12.3, 21.4, and 12.6.

Here’s my plot of Mac, iPhone, and iPad sales using a four-quarter moving average for each. I should also mention that the dates along the horizontal axis represent regular calendar dates, not Apple’s annoying fiscal year. In this graph, a year goes from January through December, not October through September.

Moving average sales graph

I think this way of presenting the data makes the iPad’s situation much clearer. Sales are not “flattening”, nor are they “flat.” They were flat in 2013, but now they’re going down, and they have been for a year. What’s most interesting to me is how the upward trend, still very strong in 2012, just stopped dead in 2013. This is something you can’t see—or at least I can’t see it—in the graphs of raw data.

A few other points:

I didn’t write this post to dump on the iPad. Although I know it’s not right for me, my wife has had one for 3–4 years and I doubt she’ll ever want to go back to a more conventional computer. Yes, the iPad’s one-app-at-a-time limitations sometimes grate on her, but its straightforward UI more than makes up for that.

The real questions are when will iPad sales level off again—this time coming down from above instead of up from below—and what are Apple’s plans to reverse the trend. There’s no reason to get hysterical and start thinking the iPad will turn into the iPod, but iPad sales have been in this state for two years, and there are no outward signs of any change from Cupertino. I do wonder if the iPad has been starved of attention because of the iPhone (which must be tended to because it’s 70% of revenue) and the march to bring out the Apple Watch.

Update 4/30/15 8:02 AM
Kieran Healy, holder of the Krzyzewski Chair of Sociological R at a small college near the University of North Carolina, has taken a more professional approach to the smoothing of the sales figures, breaking them down into three components: underlying trend, seasonal, and remainder. To my eye, his iPhone results look a little oversmoothed, but there’s always room to quibble about smoothing algorithms and parameters.

Most interesting, I think, is how clearly Prof. Healy’s results show something we all kind of expect: whereas the seasonal components of both the iPhone and iPad have a one-quarter peak during the holiday quarter, the Mac has a two-quarter peak, encompassing both the back-to-school and holiday quarters.

If you want to do your own smoothing or other manipulation of the sales data, I’ve put it in a zip archive for downloading. The archive holds three files, one for each product, and the lines of each file look like this,

2010-Q3 3.27
2010-Q4 4.19
2011-Q1 7.33
2011-Q2 4.69

where the Apple fiscal quarter and the sales number are separated by a tab.

Ben Packard, in an email, suggests my reason for dismissing the durability explanation for the iPad sales decline is weak. The Mac, he says, has been around long enough for there to be substantial numbers of owners at every stage of ownership, but far more iPad users are still on their first iPad. Whatever the long term replacement cycle of iPads turns out to be, we’re still in the first one, too early for variations in when people bought their most recent iPad to have evened out.

It’s a legitimate criticism. I was too glib in making a direct comparison between the Mac and the iPad and didn’t flesh out the argument as much as I should have. I think the iPad durability argument fails because its lower price and more rapid hardware improvements here in the early stages of the product’s life should make its ownership cycle shorter than the Mac’s. From a functionality standpoint, those who bought iPads during the ramp-up in 2011 and 2012 should be getting new ones. If they aren’t, and Tim Cook says new iPad sales are going substantially to first-time users, that means they’re finding no compelling reason to upgrade despite the huge improvements in the product itself.

You might say that’s because those old iPads are working just fine—which is exactly the durability argument—but I think there’s a subtle difference. I think the definition of “just fine” for the iPad has been downgraded because people either aren’t using them as much or aren’t using them for demanding tasks. Apple’s improvements in the iPad hardware, which have been substantial, haven’t made current owners want to go out and buy a new one because the hardware improvements don’t matter if all they’re using it for is to surf the web and check Facebook. Those are phone tasks. Apple hasn’t made iPad’s software environment different enough from the iPhone’s to drive new sales.