Nice post Jon.
Similar analysis for the leading digit of the magnitude (no unit conversion) of physical constants available in WL. In 1938 Benford did this analysis on 104 physical constants. WL has data on 282 constants. Leading digit 6 seems like a significant anomaly. I wonder why?
mantissa =
EntityClass["PhysicalConstant", All]["Value"] // QuantityMagnitude //
N // MantissaExponent // Map[First];
counts = mantissa * 10 // RealDigits // Map[First /* First] // Counts // KeyDrop[0];
frequencies = counts / Total[counts];
Show[ListLinePlot[Legended[predictions, "Benford`s\nPrediction"],
PlotStyle -> LightBlue, MeshStyle -> Blue, Mesh -> All,
AxesLabel -> {"Lead digit", "Frequency"},
PlotLabel -> "Benford's Law Prediction of Physical Constants",
Ticks -> {Range[9], Table[{i, PercentForm[i]}, {i, 0.05, 0.4, 0.05}]}],
ListLinePlot[Legended[KeySort[frequencies], "Actual"],
PlotStyle -> Lighter[Green, 0.7], MeshStyle -> Darker[Green],
Mesh -> All], ImageSize -> 500, PlotRange -> All]
