A lot has been made lately about Apple breaking or ignoring the law of large numbers.

The performance stoked analysis, such as “Apple shows a flagrant disregard for the law of large numbers” and “Here’s how Apple gets away with breaking the ‘laws’ of business.” (Jean-Louis Gassée, an industry analyst and former Apple executive, correctly acknowledged the dual-law phenomenon in a blog post on Sunday, “How Many Laws Did Apple Break?”)

And let’s not forget M.G. Siegler’s excellent Medium post, “Apple, The Oil Company?”.

To a mathematician, the law of large numbers has to do with probability theory. From the Wikipedia page:

In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.

In other words, if you flip a coin 5 times, you might get 5 heads in a row. That is not a good model of the probability of flipping a coin. Do it 100 times, you’ll likely get closer to a 50-50 mix. 1000 flips will yield an even better model. In this case, 1000 is probably a large enough number for this model. That’s the law of large numbers.

So when all these articles started appearing touting Apple and the law of large numbers, there was some understandable confusion. Turns out, there’s a financial model also known as the law of large numbers. From the Investopedia page:

A principle of probability and statistics which states that as a sample size grows, its mean will get closer and closer to the average of the whole population. The law of large numbers in the financial context has a different connotation, which is that a large entity which is growing rapidly cannot maintain that growth pace forever. The biggest of the blue chips, with market values in the hundreds of billions, are frequently cited as examples of this phenomenon.

In this context, Apple appears to be growing beyond the limits of such a large company. They are “breaking the law”.

If this interests you, read the rest of the Investopedia page. Thanks to M.G. Siegler for pointing me in this direction and to Stu Mark for stirring this particular pot.