It was a very tough call between Paige and Williams. I ultimately went with Paige.
"Do you think Paige faced tougher competition in North Dakota than Jackman did in Boston?"
Actually, I did some research regarding the Bismarck, ND team that Paige played for and they were truly world-beaters taking on the best semi-pro (and even local Minor League) teams out there. James A. Riley goes on about the team at some length, and his book was a biographical research piece. Bill Jackman (who Riley contends may have been the fastest submarine-delivery pitcher of all time) is unfortunately dragged down by the teams he played for and thus hard to judge (often, teams only kept won/loss records for pitchers and tossed anything concerning ERA unless the pitcher pitched an incredible game or threw a shutout). The only time he really seems to play with very good barnstorming teams was the late 1920's, and he really shines (he goes 52-2 against all levels of competition). That is definitely a point in his favor. But his peak was also quite a bit shorter than Paige's (I'll admit that's not saying much, since Paige had an unbelievably long peak) as his fastball slowed down in the mid-1930's.
"They put me in the Hall of Fame? They must really be scraping the bottom of the barrel!"
-Eppa Rixey, upon learning of his induction to the Baseball Hall of Fame.
Motafy (MO-ta-fy) vt. -fied, -fying 1. For a pitcher to melt down in a big game situation; to become like Guillermo Mota. 2. The transformation of a good pitcher into one of Guillermo Mota's caliber.