effective slug range

That's probably a hard one to answer definitively.
The shape and weight of many of the slugs cause them to drop velocity more rapidly than a conventional faster, lighter, and more streamlined bullet. A roundnosed Foster slug should resist wind drag more than a flatnosed slug like the Brennekes & the Remington Buckhammer.
"Effective" range is also hard to define.
If you could get the trajectory right & make a hit on a deer, rabbit or human at 200-300 yards, you could do some serious damage, but I wouldn't count on putting a bear down that far without a lucky shot. The slug weight encourages momentum to continue penetration, but again momentum and penetration both degrade with velocity loss. A 3-inch Magnum slug would obviously extend the useful range in terms of energy, but in a smoothbore barrel you run into accuracy problems beyond 100 yards (and there are individual barrels variations that can hold on a human-sized target farther out, but 150 yards might be the max there). A scope can help in extending range by increasing your ability to see the target better, but the intrinsic accuracy of the unrifled barrel and the aerodynamically inefficient slug shape still work against you.
Denis
 
DPris pretty well summed it up. I have fired 1000's of Foster type slugs and Sabots. Just in the vein of personal research. The Foster type in a smooth bore seem to be more limited from and accuracy standpoint than so much from the energy standpoint. With most of my tests with several guns, I feel that 100 to 125 yards is just about all you can reasonably expect. That is also with a "accurate" gun. For my smoothbore tests I used and older Ithaca Deerslayer and a Rem 870, in just about every case the Ithaca shot more accurately, but, they had a "special" bore where the Rem was just a smooth bore. After about 100 yards you are pretty much "lobbing" a slug with generally poor accuracy and drop. The sabots on the other hand seem to basically limit out around 200 yards. I generally prefer to get closer to the game than try shots that far away.
 
The definition of Maximum Effective Range can vary a bit, but if you define it as the maximum range at which you can expect to reliably strike a bear, deer, or human sized target with sufficient energy to produce a terminal effect, accuracy is more the limiting factor than energy.
You've got essentially the same situation as the British had with their Brown Bess smoothbore flintlock muskets in the 1700s. They were usually about .70 caliber, too (obviously shooting a lighter ball than today's shotgun slugs), and at typical military engagement distances (which were not really very long) they relied more on massed volleys to cause damage than individual marksmanship.
Denis
 
The most accurate are the sabot slugs in a rifled barrel . The best probably the Wincheter partition which puts a slug into 1-2" groups at 100 yds with velocity of 1900 fps !!
 
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