Begzos began his career as a ticket manager for the Oklahoma City 89ers.[1] He then served as the general manager of the San Antonio Brewers. In 1973 he was named the Texas League's executive of the year. When the Dallas Chaparrals of the American Basketball Association moved to San Antonio, Begzos became the team's sales manager. The team struggled to draw fans early on due to the area's unfamiliarity with basketball and a strike that delayed the start of the team's first season. In order to draw fans, Begzos offered Larry Braun and David Boyle, two local sports fans he knew from his time with the Brewers, discounted seats if they could help bring in fans. The pair formed the Baseline Bums and placed in ad in the local newspaper for "loud beer drinkers" to join their group. The Bums were, according to Pat Putnam of Sports Illustrated "basketball's loudest and frequently most profane cheerleaders". The Spurs ended up averaging 6,594 spectators a game during their first season.[2]
General manager Jack Ankerson left the team after the inaugural season to take the same job with the Virginia Squires and Bergzos was chosen to succeed him.[3] He held this position for five seasons, during which time the Spurs made the playoffs every year and were one of the four of the remaining six accepted into the National Basketball Association as part of the ABA–NBA merger. By his final season as GM, the team's average attendance per game had risen to just under 12,000.[4]
In 1979, Begzos left the Spurs to become executive vice president and general manager of the Kansas City Kings.[4] During his first season as GM, Begzos acquired Mike Green, Len Elmore, and Ernie Grunfeld, but the Kings were unable to repeat as Midwest Division champions and lost in the first round of the playoffs to the Phoenix Suns. The following year, Begzos signed free agent Leon Douglas, traded for seven-time All Star JoJo White, and negotiated a long-term contract with Coach Cotton Fitzsimmons. The Kings got off to a 5–6 start and on October 29, 1980, the team fired Begzos.[5] On November 7, 1980, Begzos' attorney confirmed a Kansas City Star report that his client had been fired over postage stamp reuse. According to the lawyer, Begzos had purchased $240 worth of stamps from a neighbor for $120. Begzos then sold the stamps to the team for what he had paid for them. Once postal inspectors informed the team of the situation, Kings' president H. Paul Rosenberg demanded Begzos resign. When he refused, Begzos was fired.[6]