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With respect to Shogi and such cases, I think of promotion
pieces as counting 1/2, so Shogi charts at 11/81. Not regarding this 13%
as an outlier, what factor(s) makes 0.13+ work in Shogi? Answer: the
weaker, Pawnlike character of most pieces, also quantifiable. (Piece-type
Density, only one convenient measureable factor, falls off in
effectiveness much below 64 squares, certainly by Tori Shogi's 49.) With
standards like 'simplicity' and 'elegance,' can they ever be
quantified? I think so. Another criterion is Average Moves per
recorded game. I submit there is an optimum that players prefer, about 30
or 35, lower than most chesslike games deliver.  With the prospect of
variants of variants, and thousands of game-rules sets, numerical
relationships help evaluate, and some even fail by the numbers.