Rodriguez probably would have made somewhere between $12 and $15 million in arbitration, considering his 2011 salary and on-field performance. While Jonathan Papelbon landed a megadeal with Philadelphia earlier this offseason, there's little guarantee that K-Rod will be able to make that kind of money on his next deal. There's not even a guarantee a closer's role will be out there for much longer -- two spots were filled on Tuesday, with the Blue Jays trading for Sergio Santos and the Mets signing Jon Rauch to at least compete for the job. Huston Street is on the trade market, as is Andrew Bailey. Teams may decide it costs less to land one of those two via trade than it does to sign Rodriguez (or Francisco Cordero or Frank Francisco) to a free agent deal.
That's why the move was such a gamble on Rodriguez's part. There's no guarantee that he'll be able to land a closing gig on the open market, but it appears he absolutely did not want to be a set-up man for 1.5 seasons. Not only would there be questions about his so-called "ability to close," but that's nearly two season's worth of saves he'd be losing if he has his eyes set on the all-time saves record. He played nice in Milwaukee for a couple months, but nearly two years with the Brewers would likely mean missing out on 50 or 60 saves.
The Brewers are going to reap the benefits of Rodriguez declining, but they're also fortunate. Had K-Rod taken the Brewers up on their offer, it likely would have blown up any plan the Brewers had for the offseason. It's been covered before that raises to other players have the Brewers playing with a limited amount of cash this offseason. Having $12-$15 million tied up into a reliever that wasn't closing not only would have meant the Brewers would have to drop their pursuit of Aramis Ramirez and/or Jimmy Rollins, but they might have had to actually cut payroll at other positions. That's not even taking into account the fact that they would have had to put up with a plethora of "K-Rod is unhappy" stories throughout the season.
So in the end, both K-Rod and the Brewers get what they want. Rodriguez pitched for a winner for a couple months, gets to hit the free agent market, and will look for a chance to close (even if it means pitching for a bad team again). The Brewers made the playoffs with Rodriguez solidifying the back end of the bullpen, and will get compensation.