Red Sox management is not necessarily smarter than Yankees management. Pitching coach Dave Wallace has a lot of experience, but it doesn’t rival that of Mel Stottlemyre. It’s hard to believe that Sox manager Terry Francona is more knowledgeable than Joe Torre. Theo Epstein is a callow youth compared to Brian Cashman. Yet those Red Sox know something that their Yankees counterparts do not: Alan Embree cannot help a major league pennant contender.

It is said that one definition of insanity is doing the same thing repeatedly and expecting a different result. Remember that – we’ll be coming back to it.

As a Yankee, Embree has pitched in 19 games. His record is 1-1, his ERA a moderately horrible 5.40 – Koufaxian compared to the 7.65 he put up with Boston. He’s blown just two saves on the season. And yet his impact has been more severe than his record would suggest. Against left-handers, the very batters that this lefty is supposed to retire, Embree has allowed 28 hits in 93 at bats, a .301 average. Eight of those hits have been doubles, four home runs, so portside hitters are slugging .516 against the 35-year-old. In yesterday’s loss to Toronto, Embree was asked to pitch to consecutive lefty batters in the service of protecting a one-run deficit. He walked one and allowed a hit to the other.

Embree’s general ineffectiveness is underscored when inherited and bequeathed base runners are considered. Embree has relieved with 21 runners on base. Six have scored, a below average rate; the average reliever strands upwards of 50%. Since Embree has been hit hard, he has also left runners behind for other relievers to deal with – 12 in just 19 games. Half of them have scored. Basically, for the Yankees, bringing Embree into a game has been like playing Russian roulette with a fully loaded pistol.

Little of this is Embree’s fault. The Yankees are using him in accordance with a bit of baseball convention which, upon examination, is clearly insane. Not only are the Yankees are guilty of it. Indeed, every team loses games unnecessarily because of their unquestioning adherence to the idea of the situational lefty, the reliever that baseball writer John Sickels has called the “LOOGY” – the “Lefty One Out Guy.”

For the first half of the 20th century, the majority of what passed for baseball’s tactical thinkers ignored that lefty batters were at a disadvantage against lefty pitchers, righties hit better against lefties, and so on. In the absence of solid statistics, superior powers of observation confirmed this to the better managers and the successes of Casey Stengel and Earl Weaver – both ardent believers in what came to be known as platooning – proved that either teams used lefty-righty splits to their advantage or they got left behind.

Ironically, after ignoring platooning for decades, baseball has embraced the concept to the degree that most teams are obsessive-compulsive about keeping two to three lefties lying around in the bullpen so that they can match them up with opposing lefty hitters in the late innings. And a fine idea this would be if those teams had prime versions of Mike Stanton, Dan Plesac, and Jesse Orosco in the pen. The problem is that good lefties are hard to find, so instead the team features Alan Embree, Wayne Franklin, and Buddy Groom, or some combination approximating this one. They can’t pitch, but they survive because they’re left-handed.

Here’s why using these pitchers is a barking-mad thing to do: Every organization has a depth chart of relievers, running from the closer, who is presumably the best relief pitcher under contract, all the way down to the bottom of the minor leagues. Overall, there may be 50 or 60 pitchers on the list. Of these, perhaps the top 20 are suitable to play some role in the majors. If the team chooses its relievers effectively, the top six of these would comprise the major league bullpen. But the teams almost never pick effectively.

If the pitchers were ranked in terms of pure effectiveness, without which side of the rubber they throw from being a consideration, Embree might not make New York’s top six. They might carry another pitcher, a right-hander who is more likely to get an out regardless of who he faces. In most cases, the Yankees (and again, all other teams) would rather carry an ineffective lefty than an effective righty, just so they can pretend to create match-ups.

At that point, another layer of insanity comes into play: A manager on defense cannot create match-ups. This is because of the rule that says that a pitcher must pitch to at least one batter before leaving the game. Game situation: Kenny Lofton is at the plate for the Phillies. Lofton, a left-handed hitter, doesn’t do well against southpaws. A generic lefty is brought into the game to face him. Charlie Manuel reaches for Jason Michaels, a righty hitter. He now gets to face an Embree-class lefty, who has to stay in the game. As a result of this rule, LOOGYs often face more righties than lefties.

All of this strategizing is at best show, at worst self-defeating. The next time Joe Torre needs to retire a lefty batter, he might consider using the best pitcher available, not the best southpaw available. Or the Yankees might sneak up Matt Smith or Ben Julianel, their promising minor league lefty relievers. Anything would be better than using Embree again and again, thinking that the results are going to be different.

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