First, let's take Hoyt Wilhelm and Dennis Eckersley out of the equation, because they both spent significant time as starters. And John Smoltz, while pretty good as a reliever, was a starter for the vast majority of his career.
That means that there are only 6 relievers in the Hall of Fame. In order of election, they are: Rollie Fingers, Bruce Sutter, Rich "Goose" Gossage, Trevor Hoffman, Mariano Rivera and Lee Smith.
Let's look at a few other relievers of note: Dan Quisenberry, star reliever of the 1980s; Jeff Reardon, another 1980s reliever, and the all-time leader between Fingers and Smith; John Franco, the all-time save leader among lefthanded pitchers; Billy Wagner, right behind Franco in that regard, and who, a few days ago, fell 5 votes short of election; and Francisco "K-Rod" Rodriguez, who has the most saves of any pitcher not in the Hall, eligible or otherwise, and holds the single-season record.
And if you think I missed any relievers worth considering, let me know. Just don't suggest any that are not yet eligible.
Saves: Rivera 652, Hoffman 601, Smith 478, Rodriguez 437, Franco 424, Wagner 422, Reardon 367, Fingers 341, Gossage 310, Sutter 300, Quisenberry 244.
Earned Run Average (ERA): Rivera 2.21, Wagner 2.31, Quisenberry 2.76, Sutter 2.83, Rodriguez 2.86, Hoffman 2.87, Franco 2.89, Fingers 2.90, Gossage 3.01, Smith 3.03, Reardon 3.16.
Earned Run Average (ERA): Rivera 2.21, Wagner 2.31, Quisenberry 2.76, Sutter 2.83, Rodriguez 2.86, Hoffman 2.87, Franco 2.89, Fingers 2.90, Gossage 3.01, Smith 3.03, Reardon 3.16.
ERA compared to the league average (ERA+), with 100 being exactly average: Rivera 205 (making him the all-time leader, among all pitchers), Wagner 187, Rodriguez 148, Quisenberry 146, Hoffman 141, Franco 138, Sutter 136, Smith 132, Gossage 126, Reardon 122, Fingers 120.
Walks and Hits (BB + H), Divided by Innings Pitched (WHIP): Wagner 0.998, Rivera 1.000, Hoffman 1.058, Sutter 1.140, Rodriguez 1.155, Fingers 1.156, Quisenberry 1.175, Reardon 1.199, Gossage 1.232, Smith 1.256, Franco 1.333.
Walks and Hits (BB + H), Divided by Innings Pitched (WHIP): Wagner 0.998, Rivera 1.000, Hoffman 1.058, Sutter 1.140, Rodriguez 1.155, Fingers 1.156, Quisenberry 1.175, Reardon 1.199, Gossage 1.232, Smith 1.256, Franco 1.333.
Why do I not count Wins + Saves? Because it's not that hard to blow a lead, then still be your team's pitcher of record when they retake the lead. For a reliever, Wins is a misleading statistic.
Why do I not count Strikeouts (K's), or K/Innings Pitched, or K/BB? Because, while strikeouts help, outs in general matter more than how you get them.
The main case for Wagner is his career save total: He's 2nd all-time among lefthanded pitchers, right behind Franco. But most people supporting the election of Wagner do not support that of Franco. Also, until he was surpassed by Hoffman, and both were surpassed by Rivera, the all-time leader in saves was Smith. And yet, it took the Veterans Committee (or whatever that's called now) to get him in. The writers did not consider his all-time leadership in a major pitching category to be enough to elect him. Given where he ranked in the other categories, they had a point.
Based on Saves, ERA, ERA+ and WHIP, a case can be made for both Wagner and Rodriguez.
Based on Saves, ERA and ERA+, a case can be made for Franco. However, his WHIP is noticeably higher than the next-lowest reliever mentioned.
Based on ERA, ERA+ and WHIP, a case can be made for Quisenberry. But the cumulative one, saves, is one on which he trails by a lot.
Based on Saves and WHIP, a case can be made for Reardon. But ERA and ERA+ don't help him.
Then again, based on the preceding judgments I've made, Fingers, Sutter and Gossage might not have enough saves. And Gossage and Fingers might not have a high enough ERA+. Gossage and Smith each have a WHIP that seems a bit high. Each of those assessments could be explained by things being different in their era, which would then help their contemporaries, Quisenberry and Reardon.
Clearly, Hall voters took the pitchers' effects on their teams into account. So let's look:
Rollie Fingers, In: Reached the postseason with the Oakland Athletics in 1971, '72, '73, '74 and '75; and the Milwaukee Brewers in 1981 and '82. Won Pennants in 1972, '73, '74 and '82. Won the World Series in 1972, '73 and '74. Was key to all of that.
Bruce Sutter, In: Made the postseason only once, but he was critical to it, helping the St. Louis Cardinals win the 1982 World Series -- over Fingers and the Brewers.
Goose Gossage, In: Made the postseason with the New York Yankees in 1978, '80 and '81; the San Diego Padres in 1984. Won Pennants in 1978, '81 and '84. Won the World Series in 1978. Was key to all of that.
Dan Quisenberry, Out: Made the postseason with the Kansas City Royals in 1980, '81, '84 and '85. Won the Pennant in 1980, beating Gossage and the Yankees; and '85. Won the World Series in 1985, beating the Cardinals after they foolishly traded Sutter. Was key to all of that.
Jeff Reardon, Out: Made the postseason with the Montreal Expos in 1981, the Minnesota Twins in 1987, the Boston Red Sox in 1990, and the Atlanta Braves in 1992. Won the Pennant in 1987 and '92. Won the World Series in 1987. Was key to all of that, although results varied: He had a 0.00 ERA in 4 games for the '87 Twins, but a 13.50 ERA in 2 games that may have helped cost the Braves the '92 Series.
Lee Smith, In but had to wait for the Vets Committee: Made the postseason with the Chicago Cubs in 1984, and the Red Sox in 1988. Didn't win the Pennant either time. Clearly, this didn't help his bid for election.
Trevor Hoffman, In: Made the postseason with the Padres in 1996, '98, 2005 and '06. Won the Pennant in 1998. Was key to all of that.
Mariano Rivera, In: Made the postseason with the Yankees in 1995, '96, '97, '98, '99, 2000, '01, '02, '03, '04, '05, '06, '07, '09, '10 and '11. Won the Pennant in 1996, '98, '99, 2000, '01, '03 and '09. Won the World Series in 1996, '98, '99, 2000 and '09. May well have been the biggest key to all of that, including 1998 over Hoffman and the Padres.
Billy Wagner, Out: Made the postseason with the Houston Astros in 1997, '98, '99 and 2001; the New York Mets in 2006; the Red Sox in 2009; and the Braves in 2010. This is where the case for Wagner takes a huge hit: He may have been the worst pitcher in postseason history, going 1-1 with a 10.03 ERA and a 1.971 WHIP. In addition, he was with the Philadelphia Phillies in 2005, when they missed the National League Wild Card berth by one game. If ever a pitcher could not be counted on when you needed him most, it was Billy Wagner.
John Franco, Out: Made the postseason with the Mets in 1999 and 2000, winning the Pennant in 2000, although he was no longer the closer by that point. Nevertheless, he did save Game 3, their only win in the 2000 Series. He helped the Cincinnati Reds reach 2nd place 4 straight seasons, 1985-88, and it certainly wasn't his fault that they didn't reach the Playoffs; but they traded him to the Mets before he could be a part of their 1990 title team. That doesn't help much.
Francisco Rodriguez, Out: Made the postseason with the team now known as the Los Angeles Angels in 2002, '04, '05, '07, '08; and the Brewers in 2011. The fact that he helped those teams, among the least successful in the post-expansion era, reach the postseason is remarkable. The fact that he was key to the Angels' only Pennant and only World Series win in 2002, his rookie season, speaks volumes. In between the Angels and the Brewers, he pitched poorly for the Mets, which may, thus far, have made a difference in keeping him out, but I'm not sure it should.
CONCLUSION: Among these names, Wagner and K-Rod are the closest to being Hallworthy. Quis, Reardon and Franco are certainly worthy of consideration. I can't definitively say that any of them should get in. But I don't think much of a fuss should be made if and when any of them get in.
There will be, though. There are plenty of people who will say the Hall has been "watered down" with the election of guys who should have remained in "The Hall of Very Good."
But some of those people were fine with the election of steroids cheats like David Ortiz, so to Hell with them.