The Worst Films Named "Best Picture" (and other academy injustices)

• The disclaimer is that we are only going to consider the films honored since 1940, simply because we don't know that much about the earlier ones.
•  The note is that the scores in parentheses represent IMDb weighted ratings. When we refer to "best" or "worst", or the differential between them, we are citing the mathematical evaluation by IMDb members, not our own evaluation.

People often discuss their pet injustice among nominated films, like Citizen Kane's loss to How Green Was My Valley. People assume that  undeserving Oscar winners have unjustly edged out worthy nominees. That has not usually been the case. The most typical circumstance that produced a mediocre winner was a combination of (1) a poor field of nominees, and (2) a year when the very best pictures were not nominated for one reason or another. Out of Africa may be the worst film ever to win the Best Picture nod, but there was no clear injustice involved. The field of nominees was weak. The best film of the year was probably Terry Gilliam's Brazil, which was not only ignored by the academy, but was shelved by its own studio until Gilliam flushed it out of hiding with a personal campaign.

The same case could be cited for such uninspired winners as Driving Miss Daisy, The English Patient, Gigi, and Around the World in Eighty Days. Each was a reasonable choice among a field of nominees that was weaker than usual.

Of course, there were also some choices among nominees that don't seem wise today. There are even a few that don't seem comprehensible. It seems incredible that so many people once voted for Chariots of Fire over Raiders of the Lost Ark, for example, but the academy has always been subject to societal pressures which cause it to vacillate in its evaluation of pure entertainment movies. The academy received so much flack for choosing lightweight pictures like Gigi, Oliver, My Fair Lady, and The Greatest Show on Earth, that it became very sensitive about choosing pure entertainment movies over films with serious aspirations. So it happened that, on a mathematical basis, the single worst choice between nominees occurred in 1981, when a great entertainment film, Raiders of the Lost Ark, lost out to the noble but mediocre Chariots of Fire. 

Amazingly, that wasn't the most glaring difference between a winner and another film from the same year. The ultimate hose job occurred in 1952, when the Academy made every possible mistake. It gave the award to a mediocre film. There was a much better nominated film. The best film wasn't nominated at all! The winner that year, incredible though it seems, was The Greatest Show on Earth, an insipid circus movie which featured cameos from everyone in Hollywood. High Noon was the nominated loser. The unnominated classic was Singin' in the Rain. 

The other most glaring cases of the Academy's failure to recognize genius were

(1) the Oscar won by Around the World in 80 Days, a trite film, in a year when John Ford's masterpiece, The Searchers, went unnominated.

(2) the Oscar won by Gigi in a year when Hitchcock's Vertigo was not nominated.

Although the judgment of history has been different, Ford's westerns and Hitchcock's psychological thrillers were consistently underappreciated or unappreciated by Hollywood. Rear Window is in a virtual mathematical tie with three other films for the distinction of being the best eligible film to remain unnominated.

What were the most obvious cases of one nominee beating out another far superior nominee?

What were the most obvious cases of one nominee beating out another far superior eligible movie, whether it was nominated or not?

What were the worst pictures to win a best picture Oscar?