DBMM Scales are all wrong

When thinking about the battle of Granicus, my inclination as a mathematical physicist was to first simulate different configurations. Wargames were developed for this purpose (in addition to training, etc.). After a brief search, it appeared the best rule set for ancient and medieval battles is "De Bellis Magistrorum Militum" (referred to by its acronym, DBMM, by the wargaming community).

DBMM uses miniatures and its unit of length is a "pace". The height of an adult human is given as 1.83 meters or 6 feet, and a pace is 0.75 meters or 2.5 feet (so a Roman mile would be 2000 paces, allegedly). Let us stipulate this all as true. Then the height of an adult human would be between 2.4 paces and 2.44 paces (take the height of a human in meters, then divide by the length of a human in meters; or take the ratio of the figures in feet).

We are also told if we use 15mm miniatures (i.e., the adult human is represented by a figure of height 15mm), then 1 pace is between 6.1475mm and 6.25mm. A syntagmata would then be roughly 16 yards by 16 yards, or 21.33 paces by 21.33 paces. This would be a base between 131.15mm and 133mm wide and long.

But the rules clearly specify the syntagmata would be 15mm, which makes no sense: it's 9-times too small. The alternative would be to scale things so the "element" [base consisting of 4 figures in 15mm] really represents only 4 soldiers, which would require 8-by-8 elements to represent a syntagmata (which is too huge).

I could do these calculations for any suggested scale, and we get similar errors in scale: with 2mm miniatures, we would need 17.5mm-by-17.5mm for a syntagmata but the rules state it needs to be 10mm; for 20mm or larger scale, we get another 9-times too small layout.

The distances provided by the rules are equally erroneous: 80 paces in 15mm scale would be between 491.8mm and 500mm (the rules state it would be 40mm, a 12-fold error), and 80 paces in 2mm scale would be between 65.5mm and 66.67mm (the rules state it would be 30mm, a 2-fold error).

To put this in context, the battle of Granicus requires at least 1346 yards for the Macedonian deployment, or the height of 673 adults stacked atop each other. This would be 10095mm at the 15mm scale (or about 10.1 meters, i.e., 33.12 feet) and 1.346 meters at the 2mm scale (i.e., 4.4 feet).

I'm still experimenting with DBMM rules to simulate a few of the ancient battles of Alexander the Great, but the distances given by the rules are entirely wrong. Worse, the rules use internally inconsistent distances, so it's impossible to use multiples of paces (or ratios of measurements) in a coherent manner unless you recalculate everything from scratch.