Buuxi weedha soo socota: Brinkman's 35 sano oo uu garsoore ka ahaa ciyaaraha AL ayaa ka sarreeyay rikoodhkii uu dhigay Larry Barnett (1968<unk>1999). Brinkman ayaa kaalinta shanaad kaga jira tirada ciyaaraha ee uu ka soo shaqeeyey horyaalka Major League. Saddex ka mid ah afartii ciyaartoy ee ka horeeyay ayaa ku jira Hoolka Fame. Brinkman wuxuu garsoore ka ahaa seddex World Series: 1978, 1986, 1995). Wuxuu garsoore ka ahaa shan American League Championship Series (
1976, 1980, 1987, 1992, 1997), iyo seddex ciyaarood oo All-Star ah (1977, 1991, 1996), kubbadaha iyo weerarrada 1991. Brinkman wuxuu ka soo shaqeeyay taxanaha qaybta 1981, 1995, 1998, 1999, 2004 iyo 2005. Wuxuu sidoo kale garsoore ka ahaa A. J. Burnett oo aan wax guul ah gaarin San Diego Padres bishii Meey 12, 2001. Brinkman wuxuu ahaa madaxa shaqaalaha ALCS sanadihii 1987 iyo 1997, iyo sidoo kale 2005 NLDS. Hawlgabnimadiisa waxaa lagu dhawaaqay August 22, 2006. Garsoorihii hore Bob Davidson ayaa ku soo laabtay si uu ugu badalo Brinkman liiska horyaalada waaweyn. Waxa uu ahaa ciyaaryahankii ugu dambeeyay ee ciyaarta Comiskey Park sanadkii 1990.