Pap's K/BB ratio (8.5) was the tops among closers last year, but his WAR was only 2.1. Closers don't have the same value in Sabermetrics as they do in fantasy, because saves are not that important. A lot of saves
could probably be done by 2-3 other guys in the bullpen (though that's a stretch on the Red Sox). A saber GM, therefore, probably doesn't value a closer as highly as others would, and the Red Sox FO is probably saber oriented.
The other factor is Pap failed his last critical outing that cost them the playoffs, though he had an excellent year. But he sucked the previous 2 years, so the contract year is suspect in terms of getting a long-term contract. The same applies to Papi. Similar situation.
Maybe the thinking is let's get the draft choices and go with the cheap guy Bard who is next in line.
When you look at their payroll, you see it's tough to keep Pap or Papi if they are going to spend money on a RHd hitting outfielder, and maybe another starter. Or they might go with a Madsen or somebody else cheaper in the closer or setup role.
Giving big bucks long term to Pap is risky the way he has pitched the last few years. But Amaro is very aggressive, and the Phillies have to spend to keep their new ballpark full.