To Beat the Law of Large Numbers, Apple Must Expand Its Product Line - MacRumorsOpen MenuShow RoundupsShow Forums menuVisit ForumsOpen Sidebar
Skip to Content

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

iOS 28 AI

Apple Taking New Approach to Developing iOS 28 and macOS 28

Sunday November 8, 2026 7:42 am PST by
Apple has made a change to its development process for iOS 28, macOS 28, and corresponding software updates, according to Bloomberg's Mark Gurman. In his Power On newsletter today, he said Apple separates development of each year's new operating systems into three major stages. Typically, he said each stage consists of four weeks of coding followed by a four-week "convergence" period where...
apple pro tell logo

Apple Launching Two More New Products This Friday

Monday November 9, 2026 4:22 am PST by
The Apple launches keep coming! The company is set to release two new products on Friday, November 13: the all-new Apple HomeView and the fourth-generation Apple TV 4K, both of which have been available to pre-order since mid-October. Apple HomeView: Apple's new smart home display, powered by Apple Intelligence with Siri AI, for entertainment and managing the home. Available in tabletop and...
duo aquarium

More Fun iPhone Duo Apps: 30 New Picks to Try

Friday November 6, 2026 3:27 pm PST by
When the iPhone Duo launched, we shared a list of some of the fun apps developers created for the new form factor. Two weeks out, developers are continuing to come up with fresh ideas, so we thought we'd share some of our favorites. Games Marbles Unhinged ($2.99) - Marbles Unhinged is a marble maze designed for the Duo. When you fold it, the floor turns into a ramp. If you stand the top...

Top Rated Comments

jackc Avatar
192 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
192 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
192 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)
192 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
192 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)
192 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)
Latest Stories
Here's What Apple Fixed in iOS 27.2.1 and macOS 27.2.1
Here's What Apple Fixed in iOS 27.2.1 and macOS 27.2.1
1 hour ago
Webex Gets iPhone Duo Support
Webex Gets iPhone Duo Support
2 hours ago
Meta's Muse AI Agent Comes to Apple Watch
Meta's Muse AI Agent Comes to Apple Watch
3 hours ago
Anker Launches Eufy Security Cam With Auto-Tracking Light
Anker Launches Eufy Security Cam With Auto-Tracking Light
3 hours ago
macOS 27.2.1 Fixes eMudhra Certificate Flaw in Command-Line Tools
macOS 27.2.1 Fixes eMudhra Certificate Flaw in Command-Line Tools
4 hours ago
Anthropic Launches Claude Fable 5.2 and Mythos 5.2
Anthropic Launches Claude Fable 5.2 and Mythos 5.2
5 hours ago
Apple Releases macOS Golden Gate 27.2.1
Apple Releases macOS Golden Gate 27.2.1
6 hours ago
Apple Releases iOS 27.2.1 With Bug Fixes
Apple Releases iOS 27.2.1 With Bug Fixes
6 hours ago
Apple Releases watchOS 27.2.1 and visionOS 27.2.1 With Security Fixes
Apple Releases watchOS 27.2.1 and visionOS 27.2.1 With Security Fixes
6 hours ago
Apple Watch Ultra 4 Gets $99 Amazon Discounts, Starting at $699.99
Apple Watch Ultra 4 Gets $99 Amazon Discounts, Starting at $699.99
6 hours ago
Apple Pay Ad Features Martial Arts Convenience Store Food Fight
Apple Pay Ad Features Martial Arts Convenience Store Food Fight
7 hours ago
Apple Continues to Say Some AI Features Will Have Fees for Extra Usage
Apple Continues to Say Some AI Features Will Have Fees for Extra Usage
7 hours ago
Apple Announces Türkiye Expansion Plans as Tim Cook Visits
Apple Announces Türkiye Expansion Plans as Tim Cook Visits
8 hours ago
Singapore Saved Apple $2.7 Billion in Taxes This Year
Singapore Saved Apple $2.7 Billion in Taxes This Year
8 hours ago
Apple Music's 2026 Artist of the Year is Olivia Dean
Apple Music's 2026 Artist of the Year is Olivia Dean
8 hours ago
This Could Be Your Last Chance to Pre-Order the HomeView at a Discount
This Could Be Your Last Chance to Pre-Order the HomeView at a Discount
9 hours ago
Some HomePod Mini 2 Buyers Returning Units Over Mac Speaker Issues
Some HomePod Mini 2 Buyers Returning Units Over Mac Speaker Issues
9 hours ago
MacBook Pro With PROLED XDR Display: Details You Might Have Missed
MacBook Pro With PROLED XDR Display: Details You Might Have Missed
9 hours ago
Satechi Offers MacRumors Readers 30% Off Select Accessories in Early Black Friday Sale
Satechi Offers MacRumors Readers 30% Off Select Accessories in Early Black Friday Sale
9 hours ago
Leaker Envisions a Shorter iPhone With a New iOS Layout
Leaker Envisions a Shorter iPhone With a New iOS Layout
10 hours ago
Apple to Give You More Control Over When Your Mac Passwords Lock
Apple to Give You More Control Over When Your Mac Passwords Lock
11 hours ago
Siri Is Getting a Better Memory
Siri Is Getting a Better Memory
11 hours ago
iPhone 18e Could Feature Bigger Display and Battery
iPhone 18e Could Feature Bigger Display and Battery
12 hours ago
Apple's Siri Boss May Leave - Here's Who Could Take Over
Apple's Siri Boss May Leave - Here's Who Could Take Over
12 hours ago
Apple Launching Two More New Products This Friday
Apple Launching Two More New Products This Friday
12 hours ago
Apple Store Subscription Sign-Up Controversy Exposed
Apple Store Subscription Sign-Up Controversy Exposed
21 hours ago
Siri AI Rumored to Become 'More Like an Agent' as Early as Next Year
Siri AI Rumored to Become 'More Like an Agent' as Early as Next Year
1 day ago
Apple Taking New Approach to Developing iOS 28 and macOS 28
Apple Taking New Approach to Developing iOS 28 and macOS 28
1 day ago
Early Apple Black Friday Deals on Apple Watch, MacBook Air, and More
Early Apple Black Friday Deals on Apple Watch, MacBook Air, and More
2 days ago
'Backglow' Lets You Customize New MacBook Pro's Glowing Apple Logo
'Backglow' Lets You Customize New MacBook Pro's Glowing Apple Logo
2 days ago