In 1951, Los Angeles had no Major League Baseball teams.
In 1961, they had two.
The Los Angeles Angels came into existence in 1961 as an expansion team, and while they were (and are) still secondary to the Dodgers, the constant name changes didn't help. They went from the Los Angeles Angels (1961-65) to the California Angels (1965-96), Anaheim Angels (1997-2004), Los Angeles Angels of Anaheim (2005-15), and back to the Los Angeles Angels.
The team did not go to their first postseason until 1979, and in 2002, they won their first Pennant, which is, to date, the only one they have captured. They made the most of their lone World Series appearance, winning it all.
This list is up to the end of the 2021 season.
Note: Baseball lists are based on an amalgamation of tenure, traditional statistics, advanced statistics, playoff statistics, and postseason accolades.