It’s almost always shocking when someone grows on the job, and when the person in question is a baseball manager, it’s an event as rare as a Middle East peace accord. Yet, Willie Randolph, going on 53 years old and therefore no spring chicken in the managerial ranks, has already taken a dramatic step forward this spring by considering placing David Wright in the second spot of the batting order.

Since the game’s earliest days, managers, and the public, have been subject to the received wisdom of batting orders. “The leadoff hitter has to be speedy. The no. 2 hitter has to make good contact so he can hit and run with the first guy. The no. 3 guy should be your best hitter. The no. 4 hitter should be your second-best hitter, but maybe with a little more raw power than your three guy. The no. 5 guy should be your third-best power hitter. We don’t know what a no. 6 hitter is; it’s a mystery. The no. 7 hitter should be someone like a catcher or left fielder, one of those guys who hits a little but doesn’t hit a lot. The no. 8 hitter is the guy whose brother-in-law owns the team. The number no. 9 hitter is the pitcher.”

It sounds like basic common sense, but it’s about 100% wrong. The batting order is not the way that the manager distributes discrete skill sets to set slots that interact in predictable ways to create big innings, but yet another way for the manager to distribute playing time. “Games” may be the accepted measure of the way a manager awards time on the field to each of his players, but a more meaningful measure is plate appearances, the number of times a player brings his bat up to the plate.

Once a player in listed in the lineup, the batting order is what determines how often he plays. In the course of the season, the leadoff hitter is going to bat more often than any other member of the team. The second-place hitter is going to bat about 20 times less often, and the third-place hitter about 20 times less often than the second-place hitter, and so on, down the lineup, to the eighth- and ninth-place hitters, who are going to bat many times less often than the leadoff hitter. Here’s how it worked out for the Mets last year: When a manager picks a player as a leadoff hitter, he may be thinking, “I have to get that speedy, Vince Coleman-type guy up there,” but what he’s really saying is, “I want that Vince Coleman-type guy to bat more often than any other player on my team.” Consider it in the abstract: In 2004, Tony La Russa had Albert Pujols and Tony Womack. No sane offensive scheme would ever have Tony Womack playing more often than Albert Pujols. There is no rational way to justify that. Yet, Womack batted first because he was fast, and Pujols batted third because he was powerful. Womack and other leadoff hitters received 764 plate appearances; Pujols had 692.

In this context, every poorly distributed plate appearance is a lost opportunity. Last year, Randolph had Paul Lo Duca batting second for most of the season. Lo Duca is a good singles and doubles hitter, but he doesn’t hit home runs and he doesn’t walk, neutering his overall offensive package. David Wright can do everything that Lo Duca can do except better, and giving him more chances to hit means more scoring opportunities for the Mets. Last season, Wright primarily batted fifth. Moving up to no. 2 will give him approximately 60 additional turns at the plate if Willie Randolph sticks to the plan. If he’s consistent with his 2005–2006 rates and doesn’t progress further (which would be a surprise and a disappointment), the extra chances will allow him to pick up at least six walks and two or three more home runs. That’s a change worth making.

Some of the best and most surprising lineups of recent memory have featured unorthodox second-place hitters. In 1983, the same Tony LaRussa who batted Tony Womack first with the Cardinals, batted catcher Carlton Fisk second with the White Sox and won the AL West title. The mid-1980s Red Sox often batted Wade Boggs first and Dwight Evans second, which made for an order that lacked speed but forced pitchers to face two of the league’s most patient hitters in the first inning. In 1985, Randolph watched as Billy Martin followed leadoff man Rickey Henderson not with the most obvious candidate in Randolph himself but rather Don Mattingly. Mattingly won the MVP that year.

Randolph may now have put David Wright in the same position.

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