For what it's worth, keep in mind that the 1/8"-ish number became a pseudo-standard in FRC back when drivetrains were 38 long by 28 wide. Excluding this year, in 2013 and 2014 shorter chassis shapes were the norm, and honestly I think people stuck to 1/8" drop on those chassis sizes just out of habit. I don't think it's necessarily perfectly optimal, but the marginal benefit one would get from figuring out the "ideal" amount of drop for a drivetrain of a particular size / wheel type / tread type / etc is probably not worth the effort of finding it out. 1/8" works.
The more your wheel tread material compresses, the more drop you'll want. 1/8" is good for roughtop tread. Works for Colsons too, but you could also run a smidge less (3/32?) for them. Pneumatic wheels may want 1/4" drop. Your mileage may vary.
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Note also that "stiffness" in this sense is primarily in the plate/bar/channel in which each track of wheels runs; the required drop is not nearly as dependent on flexibility in other axes.
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Not exactly; how stiff your drive sides are relative to each *other* matters too. If opposite corners flex and both make contact, you'll have far more turning scrub.