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ManBearScientist, I think there is a slight issue with your math. You calculated shortbows as if they have the Agile trait, but they do not. So most of the attack rolls for shortbows would be the same as longbows unless the volley trait came into play.
Regardless, thanks for this in depth analysis. It really helped me figure out what to do with my archer ranger.
A ranger with a longbow, Flurry, and Hunted Shot can start combat by using Hunt Prey, then using Hunted Shot, then a normal strike at +7/+4/+1 for 1d8+1 damage.
A ranger with a shortbow and the same tactics can attack at +7/+5/+3 for 1d6+1 damage.