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https://www.worldwidewords.org/qa/qa-ita1.htm
[Q] From Caroline Francis Carney: “Do you know the origin of the expression It’s not over until the fat lady sings? I believe that it’s a reference to opera. My friend Paul credits this saying to Yogi Berra in reference to a baseball game. Who is right?”
[A] It’s usually taken to be a reference to opera, so many performances of which seem to end with a set-piece aria by a well-built soprano, but its recent links are mainly with sport, so much so that some people think that is the origin. Commentators do often say the phrase to remind people that it’s the final result that matters, often in a spirit of reassurance to the supporters of the losing team. It has been suggested that it was the brainchild of the San Antonio TV sports editor Dan Cook. It’s probably not one of Yogi Berra’s phrases, though it has the same sense and much of the style of his “It ain’t over till it’s over”, which he is said to have coined in 1973.
These comparatively recent sports’ associations disguise the fact that it is actually a rather older expression, which occurs in several forms: “It ain’t over till the fat lady sings”, “The opera isn’t over until the fat lady sings”, or “Church ain’t out ’till the fat lady sings”. This last version appears in a 1976 booklet entitled Southern Words and Sayings. Ralph Keyes wrote a book with the title Nice Guys Finish Seventh in which he says that several informants recalled hearing the expression for decades before it suddenly became nationally known in 1978. The use of church here suggests that its origin wasn’t tied to opera, either, but to church-going.