Tuesday, August 21, 2012

What is the Law of Large Numbers Actually?

The following is a rant.  If you are easily annoyed by meaningless semantic arguments feel free not to pay attention.

Since Apple became the largest company of all time, "law of large numbers" seems to have become a CNBC buzzword.  It's clear from the context of the conversations that the term is being used to argue that it's difficult to continue to grow at a high pace from a large base, but that's not really what the "law of large numbers" is about.  The law of large numbers is a statistical term that says that the more samples you take of a population, the closer the mean will accurately represent the mean of the population.

From Wikipedia:
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.
This seems to be a slightly different concept than the idea that "Apple's market cap can only get so big before it falls."

Maybe it would be better to specify that Apple could succumb to the "law of large market values." After all, the limit of Apple's market cap doesn't have anything to do with the limits of numerology.  There's nothing that says that the number 1 billion cant increase to the number 1 trillion or more.  The constraints on Apple's market cap are driven by the size and penetration of its end markets.  If there were a company that had a monopoly on Oxygen, it's reasonable to assume that it could have a much higher market capitalization than Apple.

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