What does a pigment's richness refer to?
A paint that is "Rich in pigment" has a higher concentration of pigment (and less white filler). A paint that is rich in crimson or ultramarine pigment has high saturation. A paint that is rich in umber or black pigment has low saturation.

So the term "rich" can't be consistently translated into the "hue, saturation, value" system of designating colors. Some rich colors have high saturation, and some rich colors have low saturation.