OFF THE FIELD
| 1992 | MLB-NL | NL MVP (Voting Rank: #22) | |
| 1993 | MLB-NL | Baseball America National League All-Star RP | |
| | MLB-NL | NL MVP (Voting Rank: #24) | |
| 1994 | MLB-NL | Baseball America National League All-Star RP | |
| 1996 | MLB-AL | AL MVP (Voting Rank: #19) | |
| | MLB-AL | AL Rolaids Relief Pitcher of the Year | |
| | MLB-AL | Played in MLB All-Star Game (AL) | |
| | MLB | World Series Most Valuable Player | |
| 1998 | MLB-AL | AL MVP (Voting Rank: #16) | |
| | MLB | Baseball America Second-Team Major League All-Star RP | |
| | MLB-NL | Played in MLB All-Star Game (NL) | |
| 1999 | MLB-AL | AL Cy Young Award (Voting Rank: #6) | |
| | MLB-AL | Played in MLB All-Star Game (AL) | |
| 2006 | MLB | Hall of Fame Ballot Voting (4 votes - 0.8%) | |