This is very difficult to answer as it depends on many things, like:
- slinging projectile
- slings (length, material)
- skill of the slingers
- maybe arrow
- bow (quality, power)
Most of this is not known. There are some ancient reports that the range of slingers was superior to that of the archers. So probably at least in some situations the range of the slinger was superior.
My slinging range is (at the moment) 50 meters. Yureks is about 350 meters. Your's is probably somewhere in the middle. And the modern world record with a stone is 440 meters. We do not know what the range of the Archaeans, Balears, Cretes, etc. was. If they had intensive training their whole live they might have had ranges of the current world record or more. Others might have had little training so they can use the sling as backup weapon. These might have had a range of 100 meters.
And regarding "effective range"... that depends on what you want achieve. At least some current tests of bow arrows against chain mail and plate armor show that the arrows barely can penetrate a bit. (We do not know the power of the ancient bows, so such tests are a bit tricky.) This is at shooting ranges of less then 10 meters. Can these then penetrate good armor at 50 or 100 meters? Probably not. But they still can be usefull, e.g. to lower the enemy morale or to get lucky shots on unprotected areas. If a troop of slingers managed to get a load of lead glandes onto an enemy unit 400 meters away I believe it gave them a military advantage. A lead glans which falls down from 50 or 100 meters certainly does hurt.
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