To Beat the Law of Large Numbers, Apple Must Expand Its Product Line

The New York Times today addressed Apple's record growth in both revenue and stock price in the context of the "law of large numbers".

Apple is so big, it’s running up against the law of large numbers.

Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob Bernoulli, the law states that a variable will revert to a mean over a large sample of results. In the case of the largest companies, it suggests that high earnings growth and a rapid rise in share price will slow as those companies grow ever larger.

If Apple’s share price grew even 20 percent a year for the next decade, which is far below its current blistering pace, its $500 billion market capitalization would be more than $3 trillion by 2022. That is bigger than the 2011 gross domestic product of France or Brazil.

Put another way, to increase its revenue by 20 percent, Apple has to generate additional sales of more than $9 billion in its next fourth quarter. A company with only $1 billion in sales has to come up with just another $200 million.

Apple has posted annual revenue growth of 16%, 56%, and 69% over the past three years respectively, with sales rising from $39 to $61 to $103 billion. Staggering growth for a company this large, but Apple seems to be continuing the trend for fiscal 2012. Apple reported more than $46 billion in revenue for the first quarter, and provided guidance of $32.5 billion in revenue for the second quarter.

This $78 billion in revenue for the first half of fiscal 2012 (which will likely be higher, as Apple traditionally underestimates on guidance) represents yet another massive increase in revenue from the year-previous quarters. The Q1 2012 number is a rise of more than 73% over the prior year, and the Q2 guidance would represent a 32% increase growth.

appleq112topchart
The enormous growth Apple has shown in recent years is largely on the backs of two products: the iPhone and the iPad.

The iPhone, as a product category, has grown from a mere $630 million in sales in 2007, to more than $47 billion in fiscal 2011. The iPad, for its part, tallied more than $20 billion of Apple's revenue last year. Between the two of them, Apple's main iOS devices account for more than 65% of Apple's total sales. Remove those two and Apple is a much different company.

It's all a bit of a theoretical exercise, of course. The iPhone and iPad halo effects are real, and have had a beneficial impact on other parts of Apple's businesses -- but the point remains: Apple's astounding growth is the direct result of the company's move into new product categories.

applerevegrowth
As the above chart shows, Apple's overall year-over-year revenue growth is impressive, but if the iPhone or iPad is backed out, the revenue growth is much less awe-inspiring. Without the iOS devices, Apple only showed 12% and 8% revenue, versus 56% and 69% otherwise.

To continue doubling its total revenue every two years, there are two main possibilities:

Apple would need to show extraordinary -- perhaps impossible -- growth in its iPad and iPhone divisions. Massive sales growth from the iPhone (which has grown more than 90% each of the past three years) and iPad can drive Apple's revenue growth for quite a while, but not forever.

If the iPhone were to continue its 90% annual growth for two more years (which would count 5 consecutive years of near 90% annual sales increases), in 2013 Apple would have nearly $170 billion in revenue coming just from the iPhone. The iPad, which grew an astounding 330% from 2010 to 2011, would report $78 billion in sales that same year -- $248 billion between the two.

Impressive (hypothetical) growth, and given Apple's astounding first quarter numbers, perhaps doable. But follow those numbers out to 2015 and the numbers begin to grow to improbable sizes.

The more likely prospect is for Apple to launch into yet another product category, in addition to the growth of its existing businesses. The possibilities are endless, but there is one new product that seems to be getting more attention than the others.

One thing is for sure: whatever is coming out of Apple's Cupertino R&D labs next is key to the company's continued explosive growth.

Popular Stories

iPhone 17 Pro 34ths Perspective

iPhone 17 Pro Launching Later This Year With These 10 New Features

Sunday March 23, 2025 10:00 am PDT by
While the iPhone 17 Pro and iPhone 17 Pro Max are not expected to launch until September, there are already plenty of rumors about the devices. Below, we recap key changes rumored for the iPhone 17 Pro models as of March 2025: Aluminum frame: iPhone 17 Pro models are rumored to have an aluminum frame, whereas the iPhone 15 Pro and iPhone 16 Pro models have a titanium frame, and the iPhone ...
iOS 18

iOS 18.4 Expected Next Week - Here Are the Release Notes

Friday March 28, 2025 2:01 pm PDT by
With the second release candidate of iOS 18.4 that Apple seeded out today, the company finally provided us with release notes that give a full rundown on what to expect. There's an Apple Vision Pro app, new Apple Intelligence features for notifications and additional language support, plus an Apple News Food feature for Apple News+ subscribers, and several updates that should improve the...
macbook pro blue green

When Will Apple Release the M5 MacBook Pro?

Wednesday March 26, 2025 4:53 pm PDT by
Apple regularly refreshes the MacBook Pro models, and a new version that uses M5 series chips is in the works. Apple just finished refreshing most of the Mac lineup with M4 chips, and now it's time for the M5. Rumors suggest that we could see the first M5 MacBook Pro models this fall. Design There have been no rumors of a design update for the M5 MacBook Pro models that are coming this...
Facebook Feature

Facebook's New iPhone App Feature Turns the Clock Back to 2007

Thursday March 27, 2025 1:59 pm PDT by
In the mid-to-late 2000s, Facebook was all about staying connected with friends and family. However, as the social media platform added new features and grew over time, that core experience began to get drowned out. That changes starting now, according to Meta, which today introduced a new feature that will "bring back the joy" of classic Facebook. Specifically, Meta has redesigned the...
Magic Mouse Green

What to Expect From the Magic Mouse 3

Saturday March 29, 2025 10:15 am PDT by
Apple is reportedly working on a new Magic Mouse. Below, we recap what to expect. The two key rumors for the Magic Mouse 3 so far include a relocated charging port, along with a more ergonomic design. It was briefly rumored that the Magic Mouse 3 would also feature voice control, but that was misinterpreted information. Relocated Charging Port While the Magic Mouse switched from...
Foldable iPhone 2023 Feature Homescreen

Six Things to Know About Apple's Upcoming Foldable iPhone

Friday March 28, 2025 3:54 pm PDT by
We've been hearing rumors about a foldable iPhone for almost a decade now, but it looks like we might finally see the device come to fruition in 2026. We're going to be waiting many more months for the foldable iPhone, but so far we're hearing good things. Apple wants to make it creaseless. It's taken Apple multiple years to design a foldable iPhone that it's satisfied with because Apple ...
iOS 18 4 Ambient Music Control Center

How to Use iOS 18.4's New Ambient Music Feature in Control Center

Thursday March 27, 2025 7:45 am PDT by
The upcoming iOS 18.4 update for the iPhone adds an Ambient Music feature to Control Center. Below, we take a closer look at how it works. iOS 18.4 is currently in beta, so the Ambient Music feature is not widely available yet. The update will likely be released to the general public next week. To use the feature on iOS 18.4, open Control Center and tap on the plus sign in the top-left...
Foldable iPhone 2023 Feature 1

'iPhone Fold' to Feature Metallic Glass Hinge That Resists Deformation

Thursday March 27, 2025 4:21 am PDT by
Last week, we covered a report claiming that Apple's book-style foldable iPhone (or "iPhone Fold," as we are provisionally calling it here) will use liquid metal hinges to improve durability and help minimize screen creasing. Today, a Chinese leaker provided more details on the properties of this hinge material that help to clarify why Apple chose it for its first foldable device. According...
top stories 2025 03 29

Top Stories: WWDC 2025 Announced, iPhone 17 Pro and iOS 19 Rumors, and More

Saturday March 29, 2025 6:00 am PDT by
Apple's big developer event is a little over two months away, and rumors about what we can expect to see in Apple's next major operating system updates are becoming increasingly frequent. A public release of iOS 18.4 is also imminent with a number of updates and improvements, although we won't be getting the major Apple Intelligence Siri upgrades that had reportedly been planned for this...

Top Rated Comments

jackc Avatar
171 months ago
I don't think you need the golden theorem to explain the point, the writer got a little overzealous
Score: 19 Votes (Like | Disagree)
nagromme Avatar
171 months ago
Hopefully they’ll focus first on having a passion for making great things--things that meet a need really well--rather than following the dictates of a mathematical model! The latter may be necessary to sustain maximum growth, but it’s not sufficient—and could even harm the philosophy that has caused all of Apple’s growth to date!

“The charts say we need to be in some new areas... what product lines can we add?” sounds like an approach worthy of many of Apple’s failed competitors...

Of course, as a user and not a stock owner, I don’t care whether Apple’s bottom line grows on the same curve forever. I just want them to keep making good stuff that’s so simple it seems obvious, yet can’t be duplicated!
Score: 18 Votes (Like | Disagree)
snowmoon Avatar
171 months ago
APPL doomers have been around for years, maybe some year they will be right, but it's not going to be in 2012.
Score: 15 Votes (Like | Disagree)
DeltaRage Avatar
171 months ago
"Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob Bernoulli, the law states that a variable will revert to a mean over a large sample of results. In the case of the largest companies, it suggests that high earnings growth and a rapid rise in share price will slow as those companies grow ever larger."

Ugh. So wrong. So so wrong. It suggests nothing of the sort. In fact, it suggests nothing at all about Apple. He even has a paragraph about Bernoulli. Painful.
Score: 13 Votes (Like | Disagree)
iSee Avatar
171 months ago
Apple is so big, it's running up against the law of large numbers.

Also known as the golden theorem, with a proof attributed to the 17th-century Swiss mathematician Jacob Bernoulli, the law states that a variable will revert to a mean over a large sample of results. In the case of the largest companies, it suggests that high earnings growth and a rapid rise in share price will slow as those companies grow ever larger.

That's not what the law of large numbers suggests. Kind of sad that the New York Times is so badly misusing that term.

Apple's numbers are amazing.
Score: 13 Votes (Like | Disagree)
Capt Crunch Avatar
171 months ago
I don't think you need the golden theorem to explain the point, the writer got a little overzealous

Seriously. The law of large numbers is not a law about anything that involves large numbers.

This just in: "Apple needs to spend its cash reserves if it's to beat the Heisenberg Uncertainty Principal."
Score: 12 Votes (Like | Disagree)