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 Blue Feature Tighter Crop

iPhone 17 Pro Launching in Three Months With These 12 New Features

Saturday June 14, 2025 5:45 pm PDT by
The iPhone 17 Pro and iPhone 17 Pro Max are three months away, and there are plenty of rumors about the devices. Below, we recap key changes rumored for the iPhone 17 Pro models as of June 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 X through iPhone 14 Pro have a...
apple watch ultra 2 new black

Apple Watch Ultra 3 Finally Coming After Two-Year Hiatus

Monday June 16, 2025 8:45 am PDT by
Apple will finally deliver the Apple Watch Ultra 3 sometime this year, according to analyst Jeff Pu of GF Securities Hong Kong (via @jukanlosreve). The analyst expects both the Apple Watch Series 11 and Apple Watch Ultra 3 to arrive this year (likely alongside the new iPhone 17 lineup, if previous launches are anything to go by), according to his latest product roadmap shared with...
Logitech Logo Feature

Logitech Announces Two New Accessories for WWDC

Friday June 13, 2025 7:22 am PDT by
Alongside WWDC this week, Logitech announced notable new accessories for the iPad and Apple Vision Pro. The Logitech Muse is a spatially-tracked stylus developed for use with the Apple Vision Pro. Introduced during the WWDC 2025 keynote address, Muse is intended to support the next generation of spatial computing workflows enabled by visionOS 26. The device incorporates six degrees of...
iPadOS 26 App Windowing

Apple Explains Why iPads Don't Just Run macOS

Friday June 13, 2025 7:46 am PDT by
iPadOS 26 allows iPads to function much more like Macs, with a new app windowing system, a swipe-down menu bar at the top of the screen, and more. However, Apple has stopped short of allowing iPads to run macOS, and it has now explained why. In an interview this week with Swiss tech journalist Rafael Zeier, Apple's software engineering chief Craig Federighi said that iPadOS 26's new Mac-like ...
iphone 16 pro models 1

17 Reasons to Wait for the iPhone 17

Thursday June 12, 2025 8:58 am PDT by
Apple's iPhone development roadmap runs several years into the future and the company is continually working with suppliers on several successive iPhone models simultaneously, which is why we often get rumored features months ahead of launch. The iPhone 17 series is no different, and we already have a good idea of what to expect from Apple's 2025 smartphone lineup. If you skipped the iPhone...
terminal macos tahoe

Apple's Terminal App Gets Colorful Redesign in macOS Tahoe

Monday June 16, 2025 4:12 am PDT by
Apple's Terminal app is getting a visual refresh in macOS Tahoe, and it's the first notable design update since the command-line tool debuted. The updated Terminal will support 24-bit color and Powerline fonts, according to Apple's State of the Platforms presentation at WWDC25. The app will also adopt the new Liquid Glass aesthetic with redesigned themes that align with macOS 26's broader...
iOS 26 Feature

Apple Seeds Revised iOS 26 Developer Beta to Fix Battery Issue

Friday June 13, 2025 10:15 am PDT by
Apple today provided developers with a revised version of the first iOS 26 beta for testing purposes. The update is only available for the iPhone 15 and iPhone 16 models, so if you're running iOS 26 on an iPhone 14 or earlier, you won't see the revised beta. Registered developers can download the new beta software through the Settings app on each device. The revised beta addresses an...
apple watch ultra snow

6 Features Coming to the Apple Watch Ultra 3

Tuesday February 25, 2025 9:00 am PST by
The Apple Watch Ultra 3 is expected to launch later this year, arriving two years after the previous model with a series of improvements. While no noticeable design changes are expected for the third generation since the company tends to stick with the same Apple Watch design through three generations before changing it, there are a series of internal upgrades on the way. By the time the ...

Top Rated Comments

jackc Avatar
174 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
174 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
174 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
174 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
174 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
174 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)