Drew Storen, Ryan Madson and Joakim Soria ... they are three reasons why I don't chase saves.
Look, injuries can befall any player. I get it. It's just bad luck. And I'm not saying I wouldn't love to have any of those guys on my Fantasy team.
However, you run the risk by chasing saves on Draft Day. All three of these players on average we drafted from the 9th-13th round in CBSSports.com Head-to-Head and Rotisserie formats (mixed leagues). You could get closers like Rafael Betancourt, Brandon League, Carlos Marmol, Huston Street and Chris Perez a few rounds later, and all you run is the risk of losing a late-round pick if something goes awry.
Just look at the list of closers that you probably picked up off waivers last season -- League, Betancourt, Joel Hanrahan, Madson, Sergio Santos, Fernando Salas, Kyle Farnsworth, Mark Melancon and Javy Guerra.
I would much rather use my early-to-mid-round picks on hitters and starting pitchers. There is still great value if you are looking for saves in the late rounds and eventually on waivers.