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Counting promotion ranks at 1/2 value for piece type density seems reasonable.<p> <i>Power Density</i> is a relevant concern as well. This could be quantified by the total value of the armies divided by the board size. For example (using beginner's values), FIDE chess has total army strength of 84 (allowing about 3 points for the 'playing value' of each King) on 64 squares. Power density=1.3125; lets replace the Queens with Amazons, the Rooks with Chancellors, the Bishops with Cardinals, and the Knights with Nightriders. I'd guestimate the total army value at 132 for a power density of 2.0625. I suspect that higher power density negatively impacts clarity, perhaps withou a proportionate increase in depth. Higher power densities certainly tend toward shorter games.<p> The question of game length suggests a third set of paired first-order criteria: strategy vs. tactics.