It is unfair to say that Abbott & Costello forged a career in radio, film and television simply by recycling old burlesque routines. The team had a unique way of working with established material that is worth examination.
The comic pair acquired their most famous routine, "Who's on First?", from an early burlesque routine called "The Baker Scene." Here is an excerpt from the routine:
Comic: I'd like to get a job in that bakery. Who's the boss?
Straight Man: Yes.
Comic: That's what I'm asking. Who's the boss?
C: Who's the guy you're working for?
C: I'm asking you for the last time, what's the name of your boss?
SM: No, Watt's the name of the street.
No recorded version of the routine is known to exist, but a variation of the routine in which the bakery has been replaced with a candy factory can be found on a 1946 recording of the "It Pays to Be Ignorant" radio show.
Abbott said that, before he teamed with Costello, his repertoire included a version of "The Baker Scene" called "Who's the Boss?". Clearly, Abbott and Costello exploited the basic premise of "The Baker Scene" to create something that was far more elaborate and funnier than the original routine. It worked to their advantage to jettison an ample part of the routine that dealt with the bakery term "loafing," the double meaning of which served to further complicate the wordplay, and keep the chatter focused on Costello's confusion and frustration over the odd names presented to him by Abbott. The pair later adapted the excised "loafing" dialogue into a separate routine.
It is perhaps more important than anything else that, by adopting the baseball theme, the team succeeded into making the routine highly appealing to the American public. A fellow named Who waiting to tag out a runner on first base is more intriguing than a fellow named Who kneading dough in the back of a bakery.
The writing credit for "Who's on First?" is generally given to Abbott & Costello's longtime head writer John Grant, but authorship of the routine has fallen into controversy in recent decades. The controversy is discussed at length on John Thorn's "Our Game" blog.
Grant proved again and again that he could work wonders in adapting old routines for Bud and Lou. His work speaks for itself and it seems a waste of time to consider the insubstantial claims of pretenders. Of course, one cannot deny the invaluable contributions that Abbott & Costello themselves made to the routines. The duo managed, in their own inimitable way, to take the hoariest of routines and make them fresh and lively for all time.