[Endoperez]

Slings are better than early, poor-quality bows used in Biblical times and during the early Roman empire. I'm not sure when bows evolved to the point where arrows had longer range than sling bullets, but Mongol recurve bows and English longbows both had better range. Those would be Longbows and Composite Bows in dominions terms.

Aezeal's guess about sling bullets not being armor-piercing also comes pretty close. The blunt trauma sling can deal is amazing, and armor doesn't help that much unless it is padded well. I think medieval armor had more protective layers of cloth and/or leather than e.g. Greek hoplites used.

I used to practice slinging and read about them quite a bit. Funny story: when I was doing my military service, we had to do a 60 km march across the woods doing all kinds of stupid stuff along the way. The first task we had to do was two-fold: to replace a person's backbag with one we made from natural materials and stuff we had with us; and to make a sling. I had my sling with me, of course, and got to shine for a moment. Unfortunately, I lost the sling later during the march, I guess it fell into a swamp when we were taking a "shortcut".