1969, the first year of divisional play in both the American and National League. The first League Championship Series were best 3 of 5 games. Both the ALCS and NLCS went from a best 3 of 5 to a best 4 of 7 in 1985.
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The ALDS is the American League Division Series. The ALDS and its National League equivalent, the NLDS, are the first rounds of Major League Baseball's postseason. There are 2 ALDS series. The winners meet in the ALCS (the American League Championship Series). Meanwhile the same happens in the NL. The ALCS and ALDS winners meet in the World Series.
The first major league in baseball was the National Association whose first year was 1871.
You did not mention at what level of baseball you are asking. But in every level there is a playoff system. Most levels from Little League to the Major League it is called the World Series. In the Major Leagues the World Series is determined by a best-of-seven game series between one American League team and one National League team. Whoever wins 4 games first wins the World Series.
Major League Baseball incorporated its first World Series in 1874. Contrary to popular belief, the 1903 Boston Americans-Pittsburgh Pirates postseason meeting was not the first World Series.
For the American League the pennant winners were the Chicago Whitesox. (This was the first year the AL was elevated to Major League level. For the National League the pennant winners were the Pittsburg Pirates. No World Series was held this year.
The players' strike that killed the World Series was during the 1994 season.
1903 the Boston Redsox beat the Pittsburgh Pirates 5 games to 3
Their first year as a baseball team was in 1936 as a PCL minor league team. Their first year as a major league team was 1969
The first Major League Baseball team that won the first World Series of the 90s was the National League Champion; the Cincinnati Reds in 1990 and they defeated the Oakland Athletics by winning 4 games and therefore sweeping the series.
The Cincinnati Reds, is recognized as the first "professional" baseball team.
first to play