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

AirPods Pro Firmware Feature

Apple Releases New Firmware for AirPods Pro 2, AirPods Pro 3, and AirPods 4

Thursday November 13, 2025 11:35 am PST by
Apple today released new firmware designed for the AirPods Pro 3, the AirPods 4, and the prior-generation AirPods Pro 2. The AirPods Pro 3 firmware is 8B25, while the AirPods Pro 2 and AirPods 4 firmware is 8B21, all up from the prior 8A358 firmware released in October. There's no word on what's include in the updated firmware, but the AirPods Pro 2, AirPods 4 with ANC, and AirPods Pro 3...
CarPlay Pinned Messages

iOS 26.2 Adds New CarPlay Setting

Thursday November 13, 2025 6:48 am PST by
iOS 26 extended pinned conversations in the Messages app to CarPlay, for quick access to your most frequent chats. However, some drivers may prefer the classic view with a list of individual conversations only, and Apple now lets users choose. Apple released the second beta of iOS 26.2 this week, and it introduces a new CarPlay setting for turning off pinned conversations in the Messages...
iPhone Pocket Short

iPhone Pocket Now Available to Order, But Already Selling Out

Friday November 14, 2025 6:20 am PST by
Apple recently teamed up with Japanese fashion brand ISSEY MIYAKE to create the iPhone Pocket, a limited-edition knitted accessory designed to carry an iPhone. iPhone Pocket is available to order on Apple's online store starting today, in the United States, France, China, Italy, Japan, Singapore, South Korea, and the United Kingdom. However, it is already completely sold out in the United...
tvOS 26 Profiles

tvOS 26.2 Adds a Useful New Feature to Your Apple TV

Friday November 14, 2025 10:02 am PST by
Starting with the upcoming tvOS 26.2 update, currently in beta, additional profiles created on the Apple TV no longer require their own Apple Account. In the Settings app on the Apple TV, under Profiles and Accounts, anyone can create a new profile by simply entering a name and indicating whether the profile is for a kid. The profile will be associated with the primary user's Apple Account,...
Tim Cook WWDC 2018

Report: Tim Cook to Step Down as Apple CEO 'as Soon as Next Year'

Saturday November 15, 2025 2:40 pm PST by
Apple is preparing for Tim Cook to step down as CEO of the company "as soon as next year," according to the Financial Times. The company's board of directors and senior executives "recently intensified preparations for Cook to hand over the reins," the report said. While the report said that Apple is unlikely to name a new CEO before its next earnings report in late January, it went on to ...
apple silicon mac lineup 2024 feature purple m5

Apple's 2026 Mac Plans

Friday November 14, 2025 3:23 pm PST by
Most of Apple's Macs are slated to get M5 chips across 2026, and there's a possibility we'll even see the first M6 chips toward the end of the year. Updates are planned for everything from the MacBook Air to the Mac Studio. MacBook Air (Early 2026) The MacBook Air will be one of the first Macs to get a 2026 refresh, with an update planned for the first few months of the year. The MacBook...
walmart new ornametns

Walmart Black Friday Deals Begin Today With Low Prices on Headphones, TVs, and More

Friday November 14, 2025 7:55 am PST by
Walmart's Black Friday sale has officially kicked off today, with an online shopping event that's also seeing some matching deals in retail locations. There are quite a few major discounts in this sale, including savings on headphones, TVs, and more. Note: MacRumors is an affiliate partner with Walmart. When you click a link and make a purchase, we may receive a small payment, which helps us...
iOS 26

iOS 26.2 Available Next Month With These 8 New Features

Tuesday November 11, 2025 9:48 am PST by
Apple released the first iOS 26.2 beta last week. The upcoming update includes a handful of new features and changes on the iPhone, including a new Liquid Glass slider for the Lock Screen's clock, offline lyrics in Apple Music, and more. In a recent press release, Apple confirmed that iOS 26.2 will be released to all users in December, but it did not provide a specific release date....
best early black friday deals

Best Black Friday Apple Deals Live Now - Save on AirPods, iPads, and Apple Watches

Saturday November 15, 2025 1:45 pm PST by
We're officially in the month of Black Friday, which will take place on Friday, November 28 in 2025. As always, this will be the best time of the year to shop for great deals, including popular Apple products like AirPods, iPad, Apple Watch, and more. In this article, the majority of the discounts will be found on Amazon. Note: MacRumors is an affiliate partner with some of these vendors. When ...
homepod mini thumb feature

New HomePod Mini, Apple TV, and AirTag Were Expected This Year — Where Are They?

Wednesday November 12, 2025 11:42 am PST by
While it was rumored that Apple planned to release new versions of the HomePod mini, Apple TV, and AirTag this year, it is no longer clear if that will still happen. Back in January, Bloomberg's Mark Gurman said Apple planned to release new HomePod mini and Apple TV models "toward the end of the year," while he at one point expected a new AirTag to launch "around the middle of 2025." Yet,...

Top Rated Comments

jackc Avatar
179 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
179 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
179 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
179 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
179 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
179 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)