One slinger can take on 2-3 bowmen with an excellent chance of victory. Even fully-upgraded they have trouble vs. horse archers, though. We recommend placing a few regular chariots in among your archer chariots to KO slingers. Almost any melee unit can readily destroy slingers, in stark contrast to the trouble that missile units have. They do not lead to an effective rush of their own, because they are way too slow at killing villagers or non-tower buildings.
Slingers are very cheap, and are the only normal unit that costs stone to buy.
Hence, players who normally never build walls or towers themselves finally have a use for that starting 150 stone. The slinger will probably never be the backbone of anyone's strategy, but he is handy, cheap, and useful through the end of Bronze. Actually, if you buy all the upgrades that apply to him, he is fairly potent vs. his chosen foes even into Iron, but most folks have stopped building him by then in favor of more destructive offensive units. Alchemy also increases the slinger's attack strength. When a slinger is fully upgraded, he has an attack of 5, a range of 6, and 5 piercing armor.