I concur in general but the performance is strongly connected to the energy and momentum of a weapon or missile. I'm a bit tired to write it again and again and give the maths, in the unlikely event somebody is interested he could find the threads on RAT or on this forum with search.
If slings were without effect it would not have been used. Clearly. Mardonios was perhaps killed by a slingshot. Xenophon describes its use against the Persian archers, the Romans used it to good effect against the Parthians. And so on. Slings were surely effective against people without armour (death or blindness from headshots, broken bones, flesh wounds or at least concussions) and effective against people with armour in the sense that with soft armour without adequate backing materials perhaps bones could be broken and hits on the helmet could result in unconsciousness. Or just headache. Same would have happened from an arrow stopped by the armour, so I don't like the ap stat for slings.
Please take into account that you need about 600 to 700 Joule to injure a person wearing a modern helmet (without penetration) and that projectiles from slings normally had energies between 50 and 100 Joules. Of course a modern helmet has better shock absorbing qualities but ancient helmets also had substantial padding to cope with the much lower energy.
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