Benford’s Law

Benford’s Law predicts the frequency of the leading digit in numbers met in a wide range of naturally occurring phenomena. In data following Benford’s Law, numbers start with a small leading digit more often those with a large leading digit. Here we demonstrate that Benford’s Law also describes a wide range of computational phenomena. In particular, we show that a number of different statistics associated with computation like space and runtime often follow Benford’s Law. We also show that search cost on input data that follows Benford’s Law is often very different to that on more uniform data. These results could be used to improve algorithm performance (for example, for load balancing or disk de-fragmentation), as well as to help model algorithm performance. Benford’s Law can also be used to generate data for benchmarking algorithms that may be more realistic than purely random data.