I think of the magic number as arbitrary because I was there...
In the early 1980s, I wrote a computer program to do the value calc for a
large range of magic numbers (0.50, 0.51, and so on). Then I printed out
the results and picked the value that I liked best. This seemed very
arbitrary to me; yes, given the idea of average crowded-board mobility,
some magic constant is needed; and yes, the idea of crowded-board mobility
has a strong feel of Truth to it, which somewhat justifies picking it in
such a crude and self-predictive way.
But because I was there I never have felt strong faith in the magic
number!