On first pass, Benford’s Law looks a lot like Zipf’s Law.

What differentiates Benford’s Law from Zipf’s Law?

> It has been argued that Benford's law is a special bounded case of Zipf's law,[22] with the connection between these two laws being explained by their both originating from scale invariant functional relations from statistical physics and critical phenomena.[24] The ratios of probabilities in Benford's law are not constant. The leading digits of data satisfying Zipf's law with s = 1 satisfy Benford's law.

I’ll take some time to try and better understand your post.