As Mike states regarding D = 13/11 13/10 for an early game 32, "Dmitriy and Stick are both right, but Dmitriy gives the reasoning used under the old rules."
In the Nactation tutorial, around diagram #22, 65R-52S-xx is discussed, first with a roll of 43, then with a roll of 32 (see diagrams #22x and #22y). I have reproduced the latter situation in the left-hand diagram below.
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Nactation was originally (and is still primarily) intended as a way to describe early game moves. My original definition of D was to play from the midpoint to the outer board with two checkers (e.g., opening 43D as shown in diagram #2 of the tutorial), and if that was not possible then to come down with one checker (e.g., with 41D from 13pt to 8pt as shown in #22x). I defined it that way so that 32D did not ambiguously mean to bring one checker down with 13/8, and (for another example) 64R-42D did not mean to bring one down with 13/11*/7.
In time, people wanted to use Nactation several moves into the game, and it needed to evolve. It was easy enough to expand the definition of D to include moves originating from anywhere in the far outer board (not just the midpoint), but move portions within the outer board became more commonplace and needed to be properly handled (resorting to assumption was becoming burdensome). As other letters already included a down component, it made sense to expand the generic meaning of "down" to include moves within the outer board such as 11/7 or 10/8 -- in that way, not only would D be more comprehensive, but also B, H, M, N, O, etc.
At the same time, more ties needed to be broken in other areas of the board. The most important area, from the 24pt to the 18pt, had already been handled, by making V a back-up to U, and from that birthed the concept of a "family." Any character (letter, symbol or numeral) could be a family (with U/V being double-sized). Lower-case letters were added, then italics (and for those interested in having all possible plays covered in exceedingly unlikely positions: underlining, emboldening and color).
Initially, the only tie-breaker I created was "closer to the 6pt." In terms of matching up capital letters to strong backgammon plays, this concept worked beautifully for nearly everything everywhere except for blots and spares in the outer board (7pt through 12pt). For them, the exact reverse worked much better.
Instituting the blot/spare closer-to-6pt-is-worse wrinkle complicated the 6pt convention, granted. However, there were benefits in addition to the aforementioned, and the diagrams above help demonstrate one such example: I could remove the clause under D that "D means two-down when possible rather than one-down." The wrinkle handles that, as playing a checker to the 8pt (e.g., 32d = 13/8) is lower-ranked than playing a checker to the 10pt (e.g., 32D = 13/11 13/10).
Nack