ExecuSpeak Dictionary: Law of Large Numbers

PHILADELPHIA (TheStreet) -- Listening to expert commentators talk about the expectation of slower growth in China, there is a reference to the "law of large numbers" as part of the explanation. So how does that work?

While the law of large numbers is a statistical principle, it can be understood without leaning on the arithmetic.

Growth is measured in percentage points. For example, the Chinese economy has been growing at a rate of 8% to 10% per year. And a commentator said it might soon start to slow to only 7.5%. Even though the rate of growth is slowing, percentage-wise, the volume of growth might remain the same -- thus the dismissive remark about the law of large numbers, because this analyst did not want to even imply that growth was stopping. 

Alternatively, the Republic of Georgia is touting that in recent years it has quadrupled GDP and achieved 8% growth during the second quarter of 2012. Wow! Except that peering into the numbers reveals a much smaller economy -- so growth slowing to 7.5% in China is a world issue while growth of 8% in Georgia is an advertisement.

When very large numbers are involved in calculations it can have an impact on ratios, comparisons, percentages or any relationship between two numbers, especially when there is an attempt to compare common relationships between two differently sized economies.

For the purposes of the example, let's switch to weight loss, since we can all relate to that. A 10-pound weight loss for a person who weights 100 pounds is 10%. The same 10-pound weight loss for a person who weighs 200 pounds is 5%. The percentage of weight lost is lower though the volume of loss is still 10 pounds. Alternatively, a 10% rate of loss for the 200-pound person is 20 pounds; the rate remains the same but the volume of weight lost (20 pounds as compared with 10 pounds) is twice as high. The same principles apply to economies, to corporate growth and to running times. The sheer size of the numbers has a significant impact on rates of growth or slowdowns.

Another way to consider the law of large numbers is to think about the "Law of Averages." On average, there is a 50-50 chance that a coin toss will result in "heads." Does that mean every 10 coin tosses will result in five heads and five tails? Not necessarily, though it is more likely with 100, 1,000 or 100,000 coin tosses. The larger the number of events, the more likely that law of averages will be able to predict the final outcome.

The law of large numbers is not an explanation, though. It is a fact that needs to be noted.