| Year |
Relief Pitcher Award |
| 1981 CL |
Myles Brooks (CC) |
| |
4-4, 29 SV, 2.13 ERA, 55.0 IP, 60 K, 20.4 VORP |
| 1982 CL |
Will McBride (NEW) |
| |
4-4, 27 SV, 2.58 ERA, 66.1 IP, 60 K, 21.1 VORP |
| 1983 CL |
Ray Gilliam (LIB) |
| |
5-4, 28 SV, 1.50 ERA, 60.0 IP, 65 K, 25.8 VORP |
| 1984 CL |
Bo Pratt (PC) |
| |
5-1, 30 SV, 1.91 ERA, 56.2 IP, 73 K, 21.9 VORP |
| 1985 CL |
Bo Pratt (PC) |
| |
4-8, 22 SV, 1.86 ERA, 63.0 IP, 66 K, 24.0 VORP |
| 1986 CL |
Myles Brooks (CC) |
| |
5-6, 31 SV, 1.76 ERA, 56.1 IP, 68 K, 22.2 VORP |
| 1987 CL |
Earl Gordon (LIB) |
| |
7-2, 23 SV, 2.10 ERA, 55.2 IP, 44 K, 21.7 VORP |
| 1988 CL |
Miguel Pellicer (NEW) |
| |
3-2, 36 SV, 1.81 ERA, 59.2 IP, 77 K, 23.8 VORP |
| 1989 CL |
Miguel Pellicer (NEW) |
| |
3-4, 31 SV, 1.31 ERA, 48.0 IP, 56 K, 21.1 VORP |
| 1990 CL |
Miguel Pellicer (NEW) |
| |
2-2, 37 SV, 1.14 ERA, 63.1 IP, 96 K, 27.7 VORP |
| 1991 CL |
Miguel Pellicer (NEW) |
| |
8-2, 25 SV, 1.25 ERA, 57.2 IP, 77 K, 23.8 VORP |
| 1992 CL |
Miguel Pellicer (NEW) |
| |
6-4, 41 SV, 1.39 ERA, 71.1 IP, 92 K, 29.5 VORP |
| 1993 CL |
Miguel Pellicer (NEW) |
| |
3-4, 28 SV, 1.07 ERA, 59.0 IP, 71 K, 25.8 VORP |
| 1994 CL |
Neil Stinson (PCP) |
| |
4-2, 33 SV, 2.07 ERA, 74.0 IP, 99 K, 21.0 VORP |
| 1995 CL |
Hal Phipps (LBG) |
| |
6-4, 34 SV, 1.97 ERA, 82.1 IP, 85 K, 24.7 VORP |
| 1996 CL |
Hal Phipps (LBG) |
| |
3-1, 42 SV, 1.01 ERA, 62.2 IP, 79 K, 25.6 VORP |
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