Less than you might imagine, if recent history is any guide. It is true that teams seem to overpay for closers when only money is on the line, but they seem to hold on to prospects and players much more tightly. Here are four recent winter trades for closers.
Rafael Soriano - December 11, 2009: Traded by the Braves to the Rays for Jesse Chavez. I mean, who wouldn't want Jessee Chavez? In fairness, though, Soriano was not really the closer for Atlanta, quite. And he finished on a down series of appearances.
J.J. Putz - December 11, 2008: The Mariners gave up Putz, Sean Green, Jeremy Reed, and Luis Valbuena. They got back Mike Carp, Ezequiel Carrera, Endy Chavez, Maikel Cleto, Aaron Heilman, Jason Vargas, Franklin Gutierrez. Carp looked like he might be a player. A wRC+ of 138 in AA merits attention. Carrera cannot have been a major prospect, but he finally made it to the majors with Cleveland in 2011 as a back-up outfielder. He was never more than a slap hitter with speed and a decent glove in center. Vargas has been a starter for the Mariners since 2009. He throws harder now than when he first hit the majors, an astonishing 87.8 mph. He's not really been all that good, but he has racked up 5.9 fWAR at moderate cost. Cleto never really did much for the Mariners, but he made the majors as a marginal reliever with the Cardinals. Heilman's best days were already behind him. (I'm guessing you don't remember his time in the Pirates' organization. I sure didn't.) Chavez is a potentially useful back-up outfielder. He even had a nice year with the Rangers in 2011. Gutierrez has played a good deal for the Mariners and had a couple of decent years. He hit better than his start with the Indians might have suggested, but not quite well enough to have much impact. He has also been hurt a lot.
Jose Valverde - December 14, 2007: Traded by the Diamondbacks to the Astros for Chris Burke, Juan Gutierrez and Chad Qualls. Burke was a useful player before the trade, but immediately lost the ability to hit. Gutierrez put up fWAR of 1.4, -0.9, and 0.0 for the Diamondbacks. Qualls pitched well in relief for Arizona for two years, then became the player you've come to know and love.
Brandon League - December 23, 2009: Traded by the Blue Jays with Johermyn Chavez to the Seattle Mariners for Brandon Morrow. Morrow has put up 9.6 fWAR during his three years with the Jays. He's averaged 9.63 K/9 and 4.22 BB/9. Chavez is a one-dimensional slugger who struggles in the field. This is the one clear instance of getting significant value for a closer plus a minor leaguer with some potential.
Since the Bucs don't need a bunch of random bits and pieces, it may prove tricky to make a sensible deal.