To find out, I took the stats for the three best, most commonly-used bullpen arms on each team. The basic cutoff for "commonly used" was 43 innings, because that gave me four or more players for 28 of the 30 major-league teams. The exceptions were the Blue Jays, who had three, and the Phillies, who only had two. Since I needed three, for Philadelphia, I added in the next-highest number of innings (Michael Schwimmer's 34.1 innings). At the other end, the Rockies - thanks, I think, largely to their four-man rotation experiment - had eight relievers who reached the mark. I used the standard B-R.com measure of 80% appearances or more in relief, to exclude starters.
That gave me a total of 159 pitchers, but I excluded the eighteen who played for multiple teams over the course of a season. I then picked the three for each team who had posted the lowest ERA over the course of the year, and combined their statistics to provide an overall number for each franchise's "A bullpen". Here are the stats for that part of the bullpen, for all 30 teams, sorted by ERA+. The full spreadsheet, including the players included for each team, and their individual numbers, can be seen here.
The Diamondbacks trio, of J.J. Putz, David Hernandez and Brad Ziegler, came in equal ninth in the overall rankings, with an overall ERA+ of 162. That's certainly not bad, yet actually feels lower than it seemed - particularly in the latter half of the season, they were remarkably reliable at preserving leads in the late innings. But their achievements pale in comparison to the Rays. Tampa's trio, Fernando Rodney (0.60 ERA), Jake McGee (1.95) and Wade Davis (2.43) combined to go 10-4 with a 1.62 ERA in over two hundred innings of work. Rodney, with five ER in 74.2 IP, has the lowest-ever season ERA with 50+ innings of work, beating Dennis Eckersley's 0.61 mark from 1990.
A little lower, something stands out about the third-placed Boston Red Sox - a near-total lack of saves. That's a result of the team not using their best pitchers in save situations, and they paid the price. With Jonathan Papelbon gone, and Andrew Bailey on the DL, Boston turned to Alfredo Aceves, who sucked. He put up a 5.36 ERA and blew eight saves: Aceves became the first pitcher since Yhency Brazoban for the 2005 Dodgers, to put up double-figures in both saves and losses, going 2-10. There's little doubt the Red Sox would have been better off turning to Junichi Tazawa (1.43 ERA) or Scott Atchison (1.58 ERA) to protect late-inning leads. But they persevered with Aceves until late August, when Bailey returned - to post an ERA north of seven down the stretch.
You might think a similar situation was the case for the Orioles, who you see were also credited with only three saves from their A-pen. However, that's more due to their remarkable depth. Jim Johnson's 2.49 ERA made him only their fourth-best reliever, going by that stat. They became the first team since 1969 - coincidentally, also the Orioles - to have four bullpen arms with 50+ IP and ERAs below 2.50. Throw in Luis Ayala's 2.65, and they were the first team in history to have five relievers that good. In total, they threw 332.2 innings with a 2.46 ERA: a large part of why Baltimore went 29-9 in one-run games and made the post-season for the first time in 15 years.
On the other hand, a decent bullpen is no guarantee of a good record in close contests. We needn't look far for a counter-example. Good relievers, used in high-leverage situations - yet the D-backs went 15-27 in one-run games, tied with the Cubs for the worst in the majors. For us, the problem was less stopping the opposition from scoring, and much more putting anything up ourselves: We hit below the Uecker Line in late and close situations, Arizona's .199 batting average being fourteen points below the next-worst National League team, and a whopping forty below the NL mean.
Interestingly, the Rays were even worse, hitting .197: such ineffective clutch hitting largely undid their great bullpen, a mediocre 21-27 one-run record contributing to their demise as much as the Orioles' great results, Tampa finishing three back in the wild-card. So, if there's any conclusions to be drawn, it's that great bullpen arms alone are not necessarily enough. Yes, they can certainly help, as the Orioles show, and four of the top five bullpens were on teams which reached 90 or more wins. But they need to be used when the team really needs a zero to be put up, and you still need to score in order to win, so must also be combined with at least a certain degree of offense.