Official Major League Trademark is set in Futura Bold
MAJOR LEAGUE BASEBALL appears to be set in Beton Condensed Bold with the original curved-leg R (digital versions only seem to include the straight leg, which was an alternate in the original).
Amending my previous ID of Futura—should have been Spartan.
"THE SPORTING NEWS" at top could be Vogue Extra Bold with alts. I'm not sure there was a Spartan or Futura with a flat sided G.