Most Consecutive Shutouts Won in a Season
AL 5
Baltimore (09-02-1974 to 09-06-1974)
Baltimore (09-26-1995 to 10-01-1995)
NL 6
Pittsburgh (06-02-1903 to 06-06-1903)
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In MLB, it is 84 consecutive save opportunities converted by Eric Gagne of the Los Angeles Dodgers between August 28, 2002 and July 3, 2004.
8 , Boston Red Sox in 2004 , four game sweep of cardinals and 4 game come back against the Yankees