Having a strong bullpen is critical to winning in October. The old cliché of good pitching beating good hitting generally holds true in the postseason, and the resultant low-scoring tactical battles magnify the importance of the firemen who come in to excruciatingly tense late-inning situations. Indeed, Nate Silver and Dayn Perry of Baseball Prospectus found in Jonah Keri’s “Baseball Between the Numbers” (Basic) that successful postseason teams generally share three characteristics: good defense, a power pitching staff (measured by strikeout rate), and a quality closer (measured by wins added above replacement level, WXRL).

In terms of that final element, the advantage among the teams currently leading the American League would seem to be with the Angels, whose closer, Francisco Rodriguez, has already racked up 50 saves on the season and is virtually assured enough chances to break the single-season record of 57 set by Bobby Thigpen with the White Sox in 1990. Rodriguez’s performance has earned the Angels 4.7 wins above a replacement-level reliever, but that figure is not the best in the AL: Minnesota stopper Joe Nathan has actually had a better season than Rodriguez despite having amassed 15 fewer saves, as just seven runs have scored against Nathan in 56 innings (1.13 RA), contributing to Nathan’s 5.5 WXRL.

The two other division-leading teams do not have closers quite as effective as Rodriguez and Nathan, but the Rays and White Sox have their pens to thank for their fortunes this season nonetheless. Both clubs have seen their relief corps undergo remarkable comebacks from ugly performances in 2007, and that improved end-game work has contributed substantially to both teams’ reversals of fortune.

Tampa Bay’s improvement is perhaps the most dramatic in baseball history. Last season the then-Devil Rays’ bullpen was atrocious: By Adjusted Runs Prevented (ARP), a statistic measuring game context-free performance, Tampa Bay was the worst relief unit of the last 50 years, at -95.4 runs. This year, the revamped Rays unit has an ARP of 59, the second-best figure in the majors. In 2007 the Rays’ WXRL was -1.8, meaning that their relievers were nearly two wins worse than a marginal group of journeymen, but so far this year, they lead the majors with 13.1 WXRL, which projected out over the rest of the season would rank their bullpen amongst the 10 best in the past 50 years.

Tampa Bay’s massive turnaround can be traced to four transactions: the signing of veteran closer Troy Percival in the offseason, the low-key 2007 deadline deals to acquire Dan Wheeler from Houston (for Ty Wigginton) and Grant Balfour from Milwaukee (for Seth McClung), and the conversion of J.P. Howell from a starter to a reliever. All four of these pitchers rank in the AL’s top 18 in WXRL, while Howell, Wheeler, and Balfour are all in the league’s top 14 in ARP.

Chicago’s bullpen improvement act has not been quite as spectacular, but it is impressive nonetheless. A big part of the team’s problem in a disastrous 2007 season was its relief corps, which finished third from the bottom of the majors with -50 ARP. Among the seven relievers who threw the most innings out of the Chicago pen, six had an ERA of 4.79 or higher, the one exception being closer Bobby Jenks. Overall, White Sox relievers posted a 5.49 ERA and a 1.61 WHIP. Those numbers have fallen to 3.59 and 1.28 this year, and Chicago’s ARP is now up to 41, the sixth-best overall total.

The Sox have benefited from another excellent season by Jenks, who has a 1.68 RA despite his lowest strikeout rate since entering the league (just five Ks per nine). However, he’s not alone this years — the club’s two expensive off-season relief signings, Octavio Dotel and Scott Linebrink, have combined to allow just 34 earned runs in 95 2/3 innings with a 111/30 K/BB ratio. A less-heralded acquisition, D.J. Carrasco, ranks 11th amongst AL pitchers in ARP after not pitching in the majors since 2005, while lefty Matt Thornton has dropped his RA from 4.95 last year to 2.85 so far in 2008.

More than any other field unit, bullpens are subject to the variance inherent in small sample sizes due to the smaller workloads that relievers handle. Even given the normal ups and downs of bullpen life, though, the surges in Tampa Bay and Chicago this year are noteworthy. The Rays have increased their ARP total from 2007 by over 154 runs (and counting), which is already the largest single-season jump in the Prospectus database, with the 2003-04 Rangers (+114) a distant second. Chicago is currently at +91, which is the ninth-best year-to-year increase. The vicissitudes of reliever performance also makes the steady work of the Angels’ relief corps in this decade even more impressive in contrast, for the bullpens led by Rodriguez and Scot Shields have finished no worse than sixth amongst AL teams in WXRL every season since 2002, including in the top three five times.

The “Secret Sauce” formula developed by Silver and Perry specifies a good closer as being an indicator of success, however, rather than a good bullpen in general. What does that mean for this year’s AL contenders? The White Sox, Angels, Twins, Red Sox, and Yankees all have an outstanding stopper who is the clear-cut bullpen leader, but the situation in Tampa Bay is more complex. The Rays’ pen is the best and also the most well-balanced — one could argue for any of their top four relievers as the leading man. Percival will be the ninth-inning ace when healthy, Wheeler is filling in well while the veteran closer rehabs, but the most dominant of the group so far has been Balfour. He’s in the midst of a historic campaign: Among all pitchers with at least 40 innings in a season, the Australian right-hander has the lowest-ever hit rate (3.8 H/9), with just 18 safeties allowed in 43 frames.

Tampa Bay and Chicago are both on their way toward reversing 90-loss 2007 seasons, and in each case, the bullpen has been a fulcrum for their teams’ turnarounds. Now, with the two squads both likely heading to the postseason, their respective relievers will soon be in the spotlight. Whether Jenks and his setup crew can continue their resurgence, and whether the Rays’ four-headed monster can continue standing up to the fearsome lineups of the AL’s other contenders will be two compelling questions that will be answered in the next two months.

Mr. Peiffer is a writer for Baseball Prospectus. For more state-of-the-art commentary, visit baseballprospectus.com.