Former White Sox 3B-man Bill Melton:
It was his MO (skipping batting practice). If the game started at 7:30, he got there a quarter to 7, 7 o’clock. He never took batting practice. When he did get there an hour early, he always liked to take ground balls at second base, shortstop, any place but first base. He actually had terrific hands. This guy was a terrific first baseman.
and manager Chuck Tanner:
Nobody had to take batting practice if they could hit like him. (Bleep), he used to sit in the dugout with a bat and not take it. Before 9 o’clock at night, he hit more home runs than anyone in baseball. I talked to him all the time. He said, ‘Y’know, this batting practice, you got guys throwing 40 mph, it throws my timing off.’ I said I don’t care if you do. I witnessed him hitting left-handed in BP.
and another quote from Chuck Tanner:
I don’t know why (Allen is not in the Hall). He’s the best player I ever managed, that carried the team by himself.