Of course they do. Benford's Law is just an artifact of how counting works. Let's say we are measuring widget production. Right now we're making 1 widget per

Of course they do. Benford's Law is just an artifact of how counting works. Let's say we are measuring widget production. Right now we're making 1 widget per period. Each period we increase production by 10%. After a random number of periods, what do we expect the MSD (most significant or left-most digit) to be? After a random (large) number of periods, if we add up how frequently different numbers show up as the MSD, what will the distribution be? Well, let's think about it. It takes 8 periods before our production number gets over two (and thus stops having an MSD of 1), and another 4 periods before our production number gets over three (and thus stops having an MSD of 2). If we keep going, the results look like this: 1 -> 8 periods 2 -> 4 periods 3 -> 3 periods 4 -> 2 periods 5 -> 2 periods 6 -> 2 periods 7 -> 1 periods 8 -> 1 periods 9 -> 2 periods 1 -> 7 periods 2 -> 4 periods 3 -> 3 periods 4 -> 3 periods And so on. If we were to stop there, we have counted 41 periods. The most common MSD is 1 (taking place 36% of the time), followed by 2 (19%), 3 (14%), 4, and so on. Benford's Law! Of course, you might say, that just shows up because I chose to stop there. But actually, it works to a greater or lesser extent, pretty much regardless of when we stop (or where we start). It works regardless of the units being used. It also works if we're adding a flat amount instead of a percentage increase, or if we're adding a random amount, or if the number is not monotonically increasing. It also works in other bases. (In fact, thinking about the example of binary may be illuminating. The MSD is always 1 for any number > than 0.) It also works if we're generating random samples between 1 and some BIG_NUM. If you generate 1000 numbers between 1 and, say, 2^24, you might find that that the MSD of 48% of those samples is 1, while no other digit is found as the MSD in more than 7% of samples. Pick a different BIG_NUM, and you'll see a different distibution. 2^20 gives you a much flatter distribution; in the test I just ran I saw 16% with a MSD of 1, versus 9-12% for all other digits. But the point is, lots of potential BIG_NUMs produce samples which skew heavily towards having an MSD of 1, and thus a random BIG_NUM has a highly skewed expected distribution. And so on. :) It's actually kind of fun to play with. But at the end of the day, this is just a product of using a positional number system.