Brinkman‘s 35 years of umpiring AL games surpassed the record set by Larry Barnett (1968–1999). Brinkman is fifth all time in number of games worked in the Major Leagues. Three of the four ahead of him are in the Hall of Fame. Brinkman umpired in three World Series: 1978, 1986, 1995). He officiated in five American League Championship Series (1976, 1980, 1987, 1992, 1997), and in three All-Star games (1977, 1991, 1996), calling balls and strikes in 1991. Brinkman worked the Division Series in 1981, 1995, 1998, 1999, 2004 and 2005. He also officiated in A. J. Burnett's no-hitter against the San Diego Padres on May 12, 2001. Brinkman served as the crew chief for the ALCS in 1987 and 1997, and also for the 2005 NLDS. His retirement was announced on August 22, 2006. Former umpire Bob Davidson returned to replace Brinkman on the major league roster. He worked home plate for the final game at Comiskey Park in 1990.