When the Yankees sent left-handed reliever Wayne Franklin down to the minors after Wednesday night’s game, Joe Torre defended him. He was somehow able to overlook Franklin’s performance during his five-game stay, which included being pounded for nine hits and five earned runs in 3 2/3 innings.

Though four of the five games in which Franklin appeared were wins, he blew leads in three of them. Torre’s decision to praise Franklin is excusable – it’s a manager’s prerogative to have favorites. What’s not excusable is the kind of lazy, doctrinaire thinking that leads to the use of a pitcher like Franklin in the first place. A 32-year-old journeyman who has long since proved he is not much of a major league pitcher, Franklin has survived simply by virtue of being left-handed.

The idea that left-handed batters are at a disadvantage by batting against left-handed pitchers and gain an edge when batting against right-handers, while right-handers gain a large advantage when batting against left-handers, goes back to the beginning of the 20th century.

But the idea that a poor to mediocre lefty is somehow more valuable than a mediocre to average righty has its basis in the statistical revolution that has gripped baseball since Bill James began converting fans in the 1980s. Now there seem to be no holdouts. These days, most major league rosters are burdened with a glut of mediocre southpaws masquerading as relief specialists.

These pitchers, who survive at the expense of useful reserve players and right-handed middle relievers, are used as what baseball writer John Sickels called LOOGYs – Lefty One Out Guys. The idea is that these lefties are to be used only in the case of a left-handed batter coming to the plate in a key situation. If you’re Orioles manager Lee Mazzilli and Robinson Cano comes to the plate with two runners on in the seventh inning, you call to the bullpen for lefty Steve Kline. Then, regardless of what happens with Cano, you pull Kline for a right-handed pitcher before Gary Sheffield takes two steps out of the on-deck circle.

The only problem with this practice is that it doesn’t work. In addition to the collateral damage from having up to 13 pitchers squatting on the roster, a manager who employs all but the best LOOGYs – which in truth means a quality pitcher, one who can pitch to any batter but is miscast in the one-out role – is fooling himself by thinking he can control the batter-pitcher matchup on defense. Because a pitcher must face at least one batter before being removed from the game, the LOOGY’s manager is defenseless against a righthanded pinch-hitter.

Let’s say the Yankees are playing the Red Sox and Trot Nixon comes to the plate in a key situation. Lefties tie Nixon in knots, so Joe Torre calls for Buddy Groom. Nixon’s lefty troubles are obviously no secret to his manager, his general manager, and every fan at Fenway. Nothing prevents Francona from pulling a right-handed hitter off the bench.

The Yankees are cornered because Groom can’t be removed. This year, opposing right-handed batters are hitting .321/.403/.566 against Groom, which is to say that the average righty facing Groom is a better hitter than Nixon is when batting against righties (.301/.377/.522). Because the manager on offense has the ability to change hitters, LOOGYs almost always face a high number of right-handers, thus defeating the defensive manager’s intent.

None of this is to say that a good lefty reliever wouldn’t help the Yankees, say, hobble David Ortiz in a key situation (though he is doing quite well against them this year, batting .328/.388/.547, Ortiz has been diminished by lefties in the past). The key word is “good.” Forget the platoon for a moment. In an important eighth-inning at bat, who has a better chance of retiring Hank Blalock: Tom Gordon, who is a righty but has held lefties to a .169 average this year, or Franklin, who can’t get anyone out no matter which side of the plate they’re standing on?

For another example, Cleveland lefty Arthur Rhodes is routinely brought in by the Indians to retire one left-handed batter despite giving up a .333 batting average to lefthanded hitters.

On July 9 in the Bronx, he came in to face Hideki Matsui with a four-run lead and two runners on. Matsui blasted his second pitch into the right-field bleachers.

If a team doesn’t have a good left-handed reliever, there is no shame in doing without one. The 2002 Anaheim Angels won a World Series without having a single lefty in the pen.

They never suffered for this decision because they rightly concluded that it is more intelligent to have the six best pitchers in the organization in the major league bullpen than the four best righties followed by two pitchers who might be the 20th- and 21st-best pitchers available but happen to be left-handed. Going that way leads to unnecessary losses, as it has for the Yankees.

With Franklin gone, Torre has said that Groom will be his gutty broom and handle lefty relief situations out of the pen. The Yankees will lose games this way, and will lose them for a theory, while perfectly good right-handed pitchers sit unused in the bullpen, or even the minors.

The Yankees need to trade for a decent lefty like Colorado’s Brian Fuentes or call up a righty like Colter Bean and have some mental flexibility about how to use the bullpen. Either way, the mental flexibility part is non-negotiable.

Mr. Goldman is the author of “Forging Genius,” a biography of Casey Stengel, released this year.