Washington has long tradition
The Senators were pretty awful in the 1950s, too. And then, with the original franchise moving to Minnesota in 1961, a new franchise with the same name stunk up Washington City until the club moved to Texas' Metroplex in 1972.
What people forget, though, is that for quite a number of years, the Washington Senators were actually a pretty good team. From 1910 through 1943, they didn't finish last even once. Over that same span, they finished better than .500 in 16 seasons, won three American League pennants, and won the World Series in 1924.
All of which is my long-winded way of saying that despite what you might have heard, these aren't exactly the St. Louis Browns we're talking about. The history of the big leagues in Washington includes some wonderful players. And yes, the city was represented by various major league teams in the 19th century, too, particularly the National League's Senators from 1891 through 1899. However, none of those 19th century players was quite able to make my all-time Washington team.
Catcher: Muddy Ruel (1923-1930)
Best known for scoring the winning run in Game 7 of the 1924 World Series, Ruel was a solid hitter who topped .300 in three of his first five seasons with the Senators.