I think you could've gone with guys like Delmonico and Palka to prove your point and have an actual White Sox connection, but OK. BTW, Happy pre-birthday wishes to Bob "Spook" Speake who will be turning 91 in August.
Hawk played with a guy in Pawtucket who hit better than Ruth, but alas had a bad case of the Gout that cut short his career....plus he couldn't hit a change up.
I respect the hell out of Rodney for how long he pitched effectively in MLB. I looked him up and he signed to pitch in the Mexican League this year...at age 44.