When looking at an expression like min(10%, 20%), it seems reasonable at first glance to assume that it always resolves to 10%.
In most properties in CSS, %s always resolve against non-negative values, so this does indeed happen whether you're looking at the raw %s or their resolved values.
However, @dbaron points out that in bg-position, if the bg-image is larger than the bg positioning area, a % resolves to a negative value. Thus it matters which stage you're looking at for the min() and max() functions.
What should we do? Note the more complex example of min(10% + 10px, 20% + 5px); you can't make a judgement based purely by looking at the unresolved %s, but after resolution, due to the BG cases, either one could end up the smaller.