The very first player I would give my vote to is left-handed closing pitcher Billy Wagner. Wagner pitched from the years 1995 through 2010 and solidified himself as one of the best relievers of all-time. Not only do I think he is the greatest lefty reliever ever, but I think he is the best non-Mariano Rivera closer to take the mound.
Wagner owns a career 187 ERA+/2.31 ERA, along with a 2.73 FIP and 0.998 WHIP in 903 career innings. Among all-time relievers with at least 500 innings pitched, there is only one arm with a better ERA+, and that’s Mariano at 205. Only one left-handed relief pitcher has more saves than Wagner’s 422, that being John Franco at a slim margin of 424. Wagner has the 3rd best WHIP behind just Kenley Jansen and Craig Kimbrel. Only 24 relievers have ever struck out over 1000 batters. Wagner ranks sixth all-time.
It’s a real shame Wagner called it quits when he did. In his last season in MLB with the Atlanta Braves, the lefty had a career best 1.43 ERA. That was his age-38 season. Guys like Rivera and Trevor Hoffman pitched into their early-40s. It might be better to go out on a high note than like Hoffman who struggled in his final MLB season, but we’re talking about maybe getting to 450+ saves if he stuck around another year or two.
Still, I don’t think that should hurt his candidacy. 903 innings from Wagner is 10x more valuable than 1000+ innings from most relievers. He’s still arguably the second greatest reliever of all-time. WAR is not a good way to compare relievers, but for what it's worth, Wagner has nearly the same bWAR as Trevor Hoffman despite nearly 200 fewer innings pitched.