For anyone wondering why the Yankees acquired corner outfielder Matt Lawton for the stretch drive rather than the dynamic center fielder they have needed for several dozen fortnights, it might be helpful to think about the Defensive Spectrum, an ordering of the positions by difficulty created by baseball guru-cum-Red Sox advisor Bill James. It looks like this: DH-1B-LF-RF-3B-CF-2B-SS.

Starting at left, you have the positions that require the least defensive skill. The difficulty level increases as you move rightward. Most of the time, players move leftward along the spectrum, but rarely the other way. As for catcher, it’s not on the spectrum; players generally don’t shift there from other positions or move away once they are there. The truly vexing thing about team building in baseball is that most of the bats are found on the left of the spectrum and most of the gloves are found on the right. Except for the greatest players – like Ken Griffey Jr., in his prime or Cal Ripken – there are few great gloves on the right side of the spectrum that can hit as well as they can field.

That’s why having a Derek Jeter or a Miguel Tejada is so valuable: When two teams are vying for the pennant, its relatively easy for them to achieve parity at first base or right field; team ‘A’ has a big, slow guy who can hit, team ‘B’ has a big, slow guy who can hit. It’s much harder to find parity at shortstop. If, in a given game, all the position players are more or less equal but one team has Jeter at short and the other has Neifi Perez, the Jeter team has an edge. Both teams may have the potential to score four runs, but Jeter gives his team the advantage in finding the decisive fifth run.

The same thing is true of center fielders. There aren’t many who can both field the position with excellence and carry a bat. This season, the typical American League center fielder is batting .271 BA/.324 OBA/.416 SLG. The league average player is hitting .269/.330/.426, so as a group the center fielders are barely treading water. After Boston’s Johnny Damon, Cleveland’s Grady Sizemore, Minnesota’s Torii Hunter, and a few others who can actually hit a little, the wary shopper quickly finds himself in the aisle containing Chicago’s Aaron Rowand (.270/.321/.400), Oakland’s Mark Kotsay (.274/.322/.410), Detroit’s Nook Logan (.265/.300/.342), and, yes, our own Bernie Williams (.257/.332/.405).

That Williams is the eight-most productive center fielder in the league says a lot about the offensive capabilities of the class as a whole. The National League is much the same; after Junior Griffey, Atlanta’s Andruw Jones, and St. Louis’s Jim Edmonds, the potency of the group drops off rapidly.

Some of those players in the lesser center fielder category might be able to play the position with the kind of athleticism that has been missing from Yankee Stadium since Williams passed out of his Gold Glove days, but the cost in lost offense would have been too much to bear. In baseball, a player’s contributions with the bat and the glove must even out. If a player saves 10 runs with the glove over the average fielder but produces 20 fewer runs than the typical player at his position, that’s a net loss of 10 runs for the team, no matter how many times that player makes the Web Gems segment of Baseball Tonight (call this the Rey Ordonez Rule).

The reverse is true as well, though it happens far less often. If a player creates 10 more runs than average with his bat but allows 11 with his glove, the team is down one run. This is the grey area in which Williams now finds himself. Over the course of a season, his glove is likely 10 or 15 runs worse than that of the average center fielder. His bat is not 10 or 15 runs better, which means that every time Williams patrols the middle pasture, the Yankees are operating at a disadvantage. The team can’t afford that, because in order to keep pace in the very competitive AL East and Wild Card races, they’re going to have outhit their still-thin pitching.

That pitching has actually looked pretty good lately, not just the past few days against the generally light bats of the Toronto Blue Jays and Kansas City Royals, but all month. From August 1 through yesterday, Yankees pitchers have posted a 3.77 ERA. There’s a good deal of “too good to be true” in that number. The veterans Al Leiter, Randy Johnson, and Mike Mussina have been erratic, Jaret Wright remains a mystery, and Shawn Chacon is likely to come back to earth soon.

That is why, for the Yankees, chasing after a center fielder this summer would have been an exercise in wasted energy. Andruw Jones isn’t available, and if he was, the Yankees wouldn’t have had enticing prospects to offer anyway. Any player of the class below Jones would have left the team in the Williams Twilight Zone.

That means that their best-case scenario was to take advantage of Hideki Matsui’s ability to play a decent center field. Remember, above-average offensive ability plus average defensive ability equals a net gain for the team. Now all that would be needed was an available corner outfielder who would be able to out-hit the now displaced center fielders (Williams, Tony Womack, et al). Yanks centerfielders have batted .249/.304/.358. Lawton is batting .266/.366/.408. The Yankees are now likely 10 runs better than they were, on which basis they can expect an extra win. Case closed.

Lawton isn’t the outfield gazelle that the Yankees will need to find as soon as this winter, but he neatly solves the problem of providing them with just a little more offense than they’ve had. With the pitching a question mark, with Robinson Cano and Jorge Posada’s bats on seemingly permanent leave, every extra hit will count.

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