Devoted readers will remember that we’ve discussed both Zipf’s Law and Benford’s Law recently. As we mentioned, these aren’t proven as theorems, or even laws in the sense of the laws of physics, but more observations that often numerical data follows predicatable patterns. A third such is the Pareto Distribution. This is the source of the 80-20 rule in economics (the rule of thumb that 80 percent of the results come from 20 percent of the causes. For example, that 80% of your sales will come from 20% of your clients).
But we will leave it to Terence Tao to explain all three. You can read his recent blog post on the mathematics of these three rules of thumb here.