I kind of tested this very thing out last winter. The local Police setup to do Quals at our Club's range over a three day period. They had several classic poppers setup for various distances for shotgun slugs. The second morning, before they came back out to the range, I setup the classic popper closest to the 100 yd berm. The top of these classic poppers is about a 9" circle. I had my S&W 14 and a bag of WC's, that I loaded long before I started casting, they were Hornady swaged, unknown load. I started shooting at about 20 yards. The poppers were set heavy for 12 ga, so my 38's would just make a 'tink' and not knock it over. Anyway, I stepped back after each cylinder full...I started missing when I was at about 65 yards away. when I got back 100 yards, I'd still hit it once or twice out of 6.
So, my guess is (for pistol, iron sites, 4" Bull, 5 for 5) probably 25 yards.
I haven't shot iron site rifle enough in the last decade to know my ability, or lack there of.