David Laurila makes his case for more closers in the Hall of Fame:

Personally, I don’t think there are enough closers in the Hall of Fame. It’s not as though the role isn’t important, and it certainly isn’t recent. The first 15-save season came exactly 100 years ago, with Firpo Marberry doing the honors with the Washington Senators (the right-hander added two more saves in that year’s World Series). Marberry subsequently logged the first 20-save season in 1926, and by career’s end he’d led the American League in saves and appearances six times each. Marberry isn’t in the Hall of Fame, but when you factor in his historical significance — ditto his higher JAWS score than all of Rollie Fingers, Lee Smith, and Bruce Sutter — he arguably should be.

FanGraphs.com

Of course, managers used Marberry differently than modern closers. Twenty six of his ninety nine saves came when he entered the game with at least one out already recorded in the inning. Marberry operated as a fireman, a term in use for pitchers who entered the game in a dire situation. You never hear that term used anymore, as closer took over. In comparison, only seventeen of Billy Wagner’s 422 saves came with outs already recorded in an inning. Closers no longer put out fires, they prevent fires from happening.

My feeling is that for a closer to make the Hall of Fame, they need to be the best of their generation. I don’t think Wagner makes the cut in that regard.