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David McDAlong with approximately 1/365th of humankind I share April 20th with HOFer Dave Bancroft, Don Mattingly, Adolph Hitler and Bob.
The first ML game ever played at Fenway was on April 20, 1912.
(from http://www.angelfire.com/ny5/thehighlander/Highlander14page6.htm):
The Red Sox actually played their first game at Fenway 11 days before, defeating Harvard University in an exhibition game played in a snowstorm. Then the Red Sox and Highlanders had to sit out two rainouts before facing off on Saturday April 20. The future grandfather of President John F. Kennedy, Boston Mayor John "Honey Fitz" Fitzgerald, threw out the first ball in the park that was built at a cost of $350,000 that would come to be known as "Boston's Sistine Chapel."
They played on into extra innings. Boston prevailed finally winning, 7-6, on a Tris Speaker RBI in the bottom of the 11th inning. Red Sox spitballer Bucky O'Brien and Sea Lion Hall defeated New York's Jumbo Jim Vaughn.
Also of note on this date in baseball history (1945): Braves manager Casey Stengel is struck by a taxi, fractures a leg, and will miss much of the season. The cabdriver is nominated Sportsman of the Year in Boston by a local newspaper, weary of Stengel's humor in the face of the Braves' pitiful record.
You can go to this page and type in a date to find what happened on a specific date in baseball history: http://www.baseballlibrary.com/baseballlibrary/chronology/