Given the number of bulletin-board posters and callers on talk-radio shows asking, “Are the Tampa Bay Rays for real?” it’s obvious that the public still isn’t used to the inverted standings in the American League East. As the Rays sit in first place with the best record in baseball, the Yankees sink heavily to the bottom, like something wrapped in a tarp that Tony Soprano rolled off the back of his yacht. Yet, if the Rays are the fishes while the Yankees only sleep with them, the two teams share a commonality that should puncture one of baseball’s long-held myths about team construction.

Assembling a bullpen remains the final frontier of constructing a baseball team. As a group, relievers don’t have much in the way of predictability. For every rock-steady Mariano Rivera, there are hundreds of pitchers who might be good next year or might not. By comparison, starting pitchers are as dependable as a treasury bond and position players are glacial in their rate of change. Relievers, principally because of the small sample sizes that constitute each season’s usage, bounce around like ping-pong balls in a wind tunnel. From one year to the next, there is 60% turnover among the top relievers in baseball.

That inconsistency is what makes building a relief corps a general manager’s no. 1 headache. Each winter, he can open up the team checkbook and spend liberally on last season’s best relievers, but he’s going to get burned more often than not. While some general managers may be more accomplished than others at identifying the pitchers who are more likely to carry over their success from year to year, for most it is a haphazard, experimental process that leaves them like Mark Twain’s Huck Finn and Jim, looking up at the stars and wondering “whether they was made or only just happened.” For most, bullpens just happen.

No team’s management knows this better than that of the Rays. Last season, their bullpen just happened to be among the worst in history. The unit, which was fronted by journeyman Al Reyes, had an all-time high relief ERA of 6.16. In real terms, they were even worse, letting inherited runners score with such abandon that a more accurate representation of their ineptitude would be closer to 7.00. No team in baseball had further to go than the Rays if they wanted to have a respectable bullpen this year, but given the randomness of relievers, the same randomness that had just produced a bloodbath each time manager Joe Maddon called to the pen, how to go about it?

As it turned out, only part of the answer was “get better pitchers.” The Rays attempted to do this by signing veteran closer Troy Percival, a pitcher who came with his own risks given that he was 38 and had already retired once, and also adding 35-year-old situational lefty Trever Miller. Failed starter J.P. Howell was relocated to the bullpen, and he has pitched well, but the rest of the primary cast includes carryovers such as Dan Wheeler and Gary Glover. The rest of the solution meant improving the defense, a process the Rays had begun in 2007, when they moved erratic infielder B.J. Upton to the outfield, and continued this offseason, when they acquired shortstop Jason Bartlett from the Twins. In addition to the direct benefits to the relievers in having a team with an improved ability to catch the ball, a better conversion rate on balls in play has meant that the starting pitchers have performed better and gotten to pitch more innings. This in turn has meant less exposure for the weaker elements of the pen. The Rays didn’t break the bank for big names, they just fiddled about the edges, and have been rewarded with a vastly better pen: This year’s relief ERA is 3.59.

The Yankees were in a similar, though not nearly as dire, position, with most of the members of the relief staff who had large roles in 2007 — Luis Vizcaino, Mike Myers, Scott Proctor, Ron Villone — gone by the end of the season or soon after. With the exception of Rivera, all that was left behind was unproven (even Joba Chamberlain, who seemed rotation-bound from the start of the 2008 season). The team retained veteran Kyle Farnsworth and signed LaTroy Hawkins, but there were good reasons to be skeptical about both.

The rest of the roles were wide open, and to a large extent they remain so. Yet, the bullpen has done an acceptable job overall, and will continue to do so even as Chamberlain moves to the rotation. With live arms on the farm, the Yankees will continue to experiment, and, if they’re wise, will continue the policy they followed last winter of not overspending or trading for veteran relievers. In the end, the question of whether a bullpen is made or if it happens is a chimera: Both approaches turn out to be one and the same.

Mr. Goldman writes the Pinstriped Bible for yesnetwork.com and is the author of “Forging Genius,” a biography of Casey Stengel.