The Braves competed in the National Basketball Association (NBA) as a member of the Atlantic Division of the Eastern Conference.

The Braves were one of three NBA expansion teams that began to play in the 1970–71 season (the others being the Portland Trail Blazers and Cleveland Cavaliers).

By opening night, Paul Snyder, a then 33-year-old entrepreneur who had recently cashed in on the sale of his Freezer Queen business, had bought the franchise for $4 million.

Because the Braves only had third choice of dates (behind the Sabres and Canisius College Golden Griffins) at the auditorium, from 1971 to 1975 the Braves were forced to play a total of 16 home games at Maple Leaf Gardens in Toronto; in addition to alleviating the auditorium's scheduling issues, the Braves also played internationally in the hopes of expanding their fan base beyond Western New York and into the Greater Toronto Area[5] (a similar strategy was employed by the National Football League (NFL)'s Buffalo Bills from 2008 to 2013).

[6] The NBA had two previous teams in Upstate New York, the Rochester Royals and the Syracuse Nationals (who are now known as the Sacramento Kings and Philadelphia 76ers, respectively).

The team's first head coach was Hall of Famer Dolph Schayes and the franchise's first star players were Bob Kauffman and Don May, who were acquired in the 1970 NBA Expansion Draft.

The Braves by this point were a modest success, both on the court and off; the team was drawing close to the league average in fans, had solid broadcasting ratings and was turning a consistent profit.

In a 2016 interview with The Buffalo News as part of a retrospective on the Braves, Snyder laid particular blame on Canisius president Father James Demske for making it difficult to get good home dates at the Aud.

Building a new arena wasn't financially realistic at the time, leaving Snyder with no option but to sell the team.

Years later, Snyder attributed these feuds to his own inexperience with sports ownership and now speaks in more conciliatory tones regarding his hockey competition.

Snyder had a handshake deal to sell the team for $6.1 million to hotel owner Irving Cowan, who would move the Braves to the Hollywood Sportatorium outside of Miami.

Ramsay, unwilling to have his career hurt by the change in ownership, left for the Portland Trail Blazers, who would win the NBA championship in the upcoming 1976–77 season.

[8] A provision in the team sale agreement stipulated that if Brown sold the contract of any Braves player, then the money would go to Snyder and the purchase price would be reduced.

Since Steve Ballmer bought the team, the history of the Braves have been acknowledged through occasional throwback uniforms during Clipper games and Buffalo throwback merchandise being made available through team venues, though any explicit Native American references outside the city name, the Braves name itself, and "feather B" logo have been de-emphasized, with the original "feather sunburst" logo remaining unused.

[12] The Clippers refused to relinquish the Braves trademark in 2005 when an expansion American Basketball Association franchise wanted to use it, so that team instead became the Buffalo Rapids.

Miller also called play-by-play on the team's telecasts over WBEN-TV (channel 4, now WIVB-TV), the local CBS television affiliate.