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The Rose Bowl became an exclusively Big Ten-Pac-10 affair in 1947 and remained that way until the BCS came into being, but before that the PCC, the Pac-10's forerunner, took on all comers from out east. Alabama was actually a frequent participant, appearing in six Rose Bowls.
These are what pass for highlights from the 1938 edition against Cal; someone actually says "and how":
Apparently, in 1938 off tackle runs qualified as devious trickery.
Amazingly, this stands as Cal's most recent victory in the Rose Bowl. Alabama would make a final appearance in 1946, defeating USC 34-14.