Mariano Rivera is on the shelf, and absence makes the heart grow fonder. All one has to do is look around the majors to see just how good the Yankees have had it.Consider St.Louis, where the Cardinals will probably outlast the fading Reds to win their division but have to be concerned about their ability to survive the opening round of the playoffs given the erratic performance of their closer.

Jason Isringhausen has been Tony LaRussa’s trusty bullpen ace since 2002, but he’s never exactly been Mr. Automatic. In fact, this season the only thing automatic about him is that he induces nail-biting terror. He’s blown nearly a quarter of his save opportunities, an unacceptable rate for a closer on a contending team.

Yesterday, Isringhausen gave a game away to the Nationals in dramatic and demoralizing fashion. After St. Louis’s Preston Wilson hit a two-run homer in the top of the ninth off of Chad Cordero, Washington’s closer, to erase the Nats’ 5–4 lead, Isringhausen entered in the bottom of the ninth to seal the come-from-behind win. He walked Felipe Lopez, hit Nick Johnson with a pitch, and walked Ryan Church, loading the bases. He threw two pitches to the next batter, Jose Vidro.The first was a ball and the second resulted in a tworun game-winning single.

Isringhausen’s struggles are not surprising. There is always a great deal of turnover in the closer’s position, and even the very good ones don’t last long. Whether due to injuries, ineffectiveness, retirement, free agency, or trades, just one team in baseball has had the same closer since 1997 — the Yankees. Only two other clubs have had as few as two, the Angels, who transitioned from Troy Percival to Francisco Rodriguez last year, and San Diego, where Trevor Hoffman has been the closer since 1994 and would have had an unbroken run through the present day if an injury hadn’t limited him to just nine games in 2003. Rod Beck did the late-inning honors that year.

Most teams have been through six or seven closers in the time that Rivera has ruled the ninth in New York.The Chicago Cubs have had eight in 10 years.The Red Sox have had the good luck to pluck a player like David Ortiz off the scrap heap and have him turn into an instant MVP candidate — most often when a club picks up another team’s inexplicable disappointment they find that even when dressed in new pajamas he’s still inexplicably disappointing (for reference, see virtually every player Dan Duquette signed on the cheap during his years as GM there) — but they haven’t been able to secure themselves a solid closer for more than a year at a time. Heathcliffe Slocumb, Tom Gordon, Tim Wakefield, Derek Lowe, Ugueth Urbina (one of two migratory rent-a-closers in recent years, along with Jose Mesa), Byung-Hyun Kim, Brandon Lyon, Keith Foulke, Mike Timlin, and Jonathan Papelbon have all had the title of closer since 1996.

This year, 18 teams have a different closer than they had last year and several are on their second or even third closer from the beginning of the year, including Arizona, which started with Jose Valverde, experimented with Jorge Julio, and is now going back to Valverde.

Ironically, the range of save percentages for closers is not that large. Even a reliever of Rivera’s caliber blows a few here and there, as the best closers in the league convert 85% of their saves. The distance from there to Isringhausenville is not far. Yet, that distance also covers things like postseason berths, first-round playoff losses, and World Series titles.

Still, it’s not really the saves that matter. A pitcher can pile up a lot of saves without pitching particularly well because the save rule is written so that a pitcher can come into a game with a three run lead, allow two runs to score, and still walk away with a positive mark next to his name. This favors the closer, because even the worst reliever in a bullpen can usually retire three batters before three runs score.

Some teams realize this, and so the high turnover in their closing department has been purposeful.The A’s have had six closers during the Rivera years, trading pitchers like Billy Koch and allowing Isringhausen and Foulke to leave as free agents because they understood that saves command a high price and that money was better spent elsewhere, and as long as they chose wisely, they should be able to find replacements of about the same quality, and for the most part, they have.In 2004,they temporarily ended the cycle of closers and replacements by making Huston Street their first-round pick.Street will cover the ninth inning for the A’s until such time as arbitration or free agency makes him too expensive.

Still, despite the fact that Oakland philosophy is the right one for a cashpoor franchise, there’s something to be said for knowing who the closer will be each year. The minting of new closers absorbs a certain amount of psychological bandwidth each season. This is something the Yankees have been able to avoid for nearly 10 years.

It’s a good thing too — Joe Torre has many strengths as a manager, but improvisation is not one of them. Each season he feels his way through establishing a new middle-relief and set-up pecking order.That takes time, and the Yankees lose a few games as Torre tries to figure out who the consistent relievers are. Once he’s found his hierarchy he sticks with it. When something goes wrong, say, when a Kyle Farnsworth isn’t available to fill his usual role, Torre feels his way through the middle innings like an extremely near-sighted man who has just dropped his glasses.

Someday such moments will likely be the norm. Rivera’s current injury is supposed to be minimal, but at 36, a more serious one is inevitable. On that day, the Isringhausens will strike the Yankees. It will be a shock.

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