How is damage for bow melee attacks calculated?

I was interested in how damage for bow swings when you're too close to enemies was calculated, but couldn't find any kind of formula for it where I would normally go to see damage formulas for various weapons.

I tried testing out what stats effect its damage and got an unusual result I wasn't expecting. On a pure DEX character at level 13 using the free starter bow against blue snails, it did between 1 and 8 damage per hit. On the build where DEX was at the minimum to become a bowman and the rest of the points went into STR tested the same way, the damage range was 5 to 8.

From previous looks at minimum and maximum damage for other weapon types, I would have expected one to have a high maximum damage and a low minimum damage, while the other has a minimum and maximum damage that are very close to each other, with a much lower average. That's how things work with pure STR versus pure DEX builds using any Warrior weapon. In actuality, the maximum damage was unchanged between the two builds despite the minimum damage changing as I expected. It still leaves me perplexed as to how the numbers are actually determined.

 

That's a different page than what I've been able to find on my own and had helpful information for another similar question I had a while back, but the formula for Power Knock Back doesn't match what I've experienced.

Using the formula and the characters' stats, I got a damage range of 3.87 to 35.64 for the all DEX character and 8.45 to 19.8 for the high STR character. Now given that Power Knock Back is a skill that doubles the damage of the bow swings, we could assume that formula is made using max PKB numbers, and since these characters don't have that skill we need to divide everything by 2. So it becomes 1.935 to 17.82 and 4.225 to 9.9.

Now if I understand damage calculation right, there will be no reduction in applied damage from the damage roll because the blue snails have 0 defense, and whatever number is rolled will simply be truncated and have everything after the decimal removed. Assuming that is correct, the only number that matched any of the numbers I observed is the 1.935, the minimum damage of the all DEX build assuming we have to divide by 2 because the formula given assumes max PKB.

I suppose it could be possible that I simply didn't roll low enough to get a damage of 4 from the high STR character to match that 4.225 calculated minimum damage. I find this really unlikely because I got more than just a couple 1 damage rolls as the all DEX character despite the relatively tiny margin to get that number in comparison to the missing 4 damage rolls, but I could give it some more testing a bit later.