Slings outranged archers and it wasn't even close. theres plenty of source material for it.
if you don't wanna spend the time heres a short read/watch:

read [www.warhistoryonline.com]

video

so video game creators/modders who (like)creating historical games/mods stop making bows have more reach then slings as there range was at least double during the classical period with slings reaching 400m (even out ranging many catapult systems) and bows didn't even reach yet 200