Just looked up Gagne, who was extremely bad for the Sox in 2007. He pitched 18 innings and gave up 14 runs with a 6.75 ERA. But.....look at his stats for 3 years:
2002 4-1 1.97 ERA 52 Saves 82.1 innings 114 K's .862 WHIP
2003 2-3 1.20 ERA 55 Saves 82.1 innings 137 K's .692 WHIP
2004 7-3 2.19 ERA 45 Saves 82.1 innings 114 K's .911 WHIP
WOW! Dominant for 3 years. Probably as good as any closer ever for 3 years.