Judging from the shortbow damage, you have not considered the random number. That's bringing a fault into the calculation (through it obviously makes the calculation a lot easier. - I'd say calculateable. I have no idea, how one can calculate the distributions of open ended d6s.)
I'f used Excel to calculate it and the result was as follows:
Damage
per hit:
Prot 10 -- 12 -- 16
Shortbow -- 1.37 -- 0.593 -- 0.043
Longbow -- 3.35 -- 1.93 -- 0.353
Crossbow -- 5.1 -- 4.19 -- 2.59
Arbelest -- 9 -- 8 -- 6.04
Multiply this with the number of shots per interval of your choise.
...
Okay, I do and see, that the DRNs don't make to much diffrence. The open-endedness comes on top of this but should not chance that much more.
Well, at least, it shows, that at Protection 12, the Longbow is still quite en par with the crossbow but nobody can argue away the heavy loose in damage once Prot>Damage
Of course, this was in reswponse to CUnknown. Tuidjy has given more important points.
I would not value hits as high because routing enemies will often come back again but one should definitly not ignore this point, too.
Oh and of course one thing you can put into a formular even less well:
If you shoot fast enough, you will more likely catch the opponent in the ideal distance.