Strategy for closers really depends on your overall pitching strategy and the type of league you're in. In a typical 5X5 roto league, having a good stable of closers will get you ERA, WHIP and Saves. Typically good closers will have a lower WHIP and ERA than starters. They will also have less Ks. If they get as many Saves as (proportinatley speaking) Starters get wins, then you will be winning 3 of 5 pitching categories. That means you'll win pitching.
That's over a full season. If you're playing head-to-head, then you have a different game because you will have to deal with the week-by-week fluxuations of a closer. For example - if a closer gives up a 3-run homer then he's screwed your team ERA. That's when it's necessary to have a few solid starters (people that get occasoinal wins, but have very low ERAs and WHIPs like Woody Williams, Rick Reed, Greg Maddux traditionally have). Those people will serve to minimise any individual variance in your relievers.
Now, by "good stable" of relievers... I'm talking about having at least 2 closers for top-10 teams (Yankees, Braves, Mariners, A's, Astros, etc) and 2 closers for teams with decent pitching (Cubs, Expos, Twins). You can't have duds like Braden Looper or inconsistent pitchers like Kelvim Escobar on your staff, otherwise you'll be in trouble.
I have won a league (although an open Yahoo league) with 4 closers and 3 top starters. And in my comptitve pool (with ALL active owners) one of the perennial top teams goes with a 4-closer approach, spending 3/4 of his pitching budget on closers. He's finished no lower than 4th in a 12 team league in 5 years.
...of course, I go with 1 or 2 closers, and generally finish in the top 3, but he's my biggest challenge every year.