The team that would become the Gwinnett Braves began its existence over 100 years ago in 1901 as the Atlanta Crackers. The team remained independent for 49 years until it made an affiliation with the Boston (and then Milwaukee) Braves in 1950 as part of the now defunct Southern Association. The squad would bounce around affiliations and leagues, eventually ending back up with the Braves in 1965 (right before its move to Atlanta the following year) in the top AAA International League, moving to Richmond, Virginia, as the Richmond Braves.
The franchise would stay for 43 seasons, until local political squabbles prevented an upgrade of its aging stadium in 2009, resulting in the AA Flying Squirrels moving into Richmond and the Braves coming south to new digs at Gwinnett Stadium. As is standard these days, the naming rights were quickly sold to a local air conditioning company, and the G-Braves have played at Coolray Field ever since.
Coolray Field is a great value, especially for AAA, in a pretty park with solid facilities, but it's a little too small in scale, with too few fans in the seats, things to do around the park, or extras to make the facility stand out compared to its International League brethren.
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