They play a game in the Boston Red Sox front office each off-season. A giant magnetic whiteboard is arranged with hundreds of small tiles. Each tile has the name of a player on it, and each tile’s slot on the board gives that player’s position and his location in the organization — Boston, Pawtucket, or Fort Myers. It is more than a depth chart, it is a list of assets as real as the balance sheet or the Green Monster outside.

In this game, one of the team’s operations staff turns away from the board for a moment, and another surreptitiously takes a tile or two off the board. The first staffer then turns around and adjusts the chart to fill in for missing tiles. If Manny Ramirez pulls a hamstring, they’ve played the game enough times to know that Wily Mo Pena takes over in left, that Kevin Youkilis gets slotted in as the emergency left fielder, and that prospect David Murphy is only a phone call away and posting an OBP over .400 down on the farm. If it’s Curt Schilling bleeding from the ankle, the Red Sox quickly shift Devern Hansack up from Pawtucket, or later in the season, they know they will have Jon Lester available.

I was told this story of the whiteboard at the 2005 Winter Meetings by a Red Sox staffer with a sly grin. I’m still not sure if they actually play this game, but every team has its version of the whiteboard, and every team at least considers what happens when — not if — injuries hit. The reason that it’s believable with Boston is that they never seem to be caught unprepared. At any position on the diamond, in the rotation or the bullpen, the Sox have not just one option, but a range of possibilities that cascade out — shifting a player here, another player there, or start the web of phone calls from the front office to other teams when a trade is needed.

In contrast, Brian Cashman and the Yankees have a whiteboard or something similar somewhere in their offices, but when Cashman looks at it, he must only see more problems. The fish-eyed stare that he often gives to a particularly obtuse question must return to his face when he looks at his organization’s depth chart. When they had an injury in the outfield, an organizational filler like Kevin Thompson was their best option. Before turning to Phil Hughes, the Yankees turned to a Double-A starter and then a lesser prospect first; $200 million buys many things, but it doesn’t always buy you depth. In fact, money doesn’t even seem relevant to the process.

Instead, it’s a matter both of planning and understanding a couple of simple concepts that seem to get most teams into this bind. While the Yankees have been stocking up on superstar-level talent, they’ve struggled to fill out a roster — no one wants to be stuck behind a superstar. The ragtag bunch of players that are known as journeymen or “Quad A” players usually don’t come to the Yankees as minor league free agents, both because the team has neglected their value and because when you’ve got Derek Jeter, how much hope can a guy like Andy Cannizaro have when he’s 28 and still stuck in Triple-A? Minor league veterans tend to notice that sort of thing.

These so-called replacementlevel players are freely available and wind up a resource that gets overlooked by an organization like the Yankees. A recent spate of injuries to the starting outfielders in Oakland didn’t force A’s General Manager Billy Beane to make repeated calls to his affiliate in Sacramento. Instead, he looked for help on other people’s rosters, like San Diego and Atlanta, combing for the unwanted toys they might have lying around. The Braves had no idea that Ryan Langerhans would only have a short stay in Oakland, being flipped quickly for a fragile slugger (Chris Snelling) from a NL East division rival, Washington.

More tellingly, the Padres — a team with six former general managers on staff — had no idea that Jack Cust would go from Triple-A journeyman to MLB Player of the Week after they sold him to Oakland. Cust’s home run binge is unsustainable, but his value has already well exceeded his cost. In today’s game, studies done by Baseball Prospectus have shown that a win is worth about no less than $800,000 and can be worth up to almost $5 million to an individual team. Last year, teams paid on average just more than two million dollars for the equivalent of one win from a player. Using the sabermetric law that 10 runs equals a win, with his six homers in seven games Cust has already provided almost a win’s worth of runs, and Cust isn’t making much more than the minimum of $380,000. That’s an arbitrage spread any trader would be happy to use as pocket lining.

Like any number of minor leaguers that don’t make prospect lists, the Jack Custs of the world are available at a relatively insignificant price. Any team could have made the same trade for someone like Cust, and even had he not had his prolific power streak, playing up to his value would be easy. The same could be said for phenom Josh Hamilton, coming back from personal travails and now outperforming the much higher-paid players in the Reds’ outfield, Adam Dunn and Ken Griffey Jr. The game has reached a point where its inability to maximize available resources and fanatical avoidance of risk is in and of itself a risky drain of resources. Creative solutions like Cust or Hamilton are easier, cheaper, and less risky because of the low cost it takes to add them, an expense the team can absorb a lot more easily than a big-money bust from the free agent market.

Around the league, roster problems abound and cost their teams wins. The Twins go eight deep in major league-caliber starting pitchers but wind up using a hitter like Jason Tyner at DH despite his oh-fer-career homerless streak. The Cubs can’t find a slot for their prodigy center fielder, Felix Pie, but also can’t find serviceable middle relief help. The White Sox have four hurlers that could close for many teams but are left using someone like Darin Erstad in the outfield, providing terrible production. Even the Mets, a team who has both one of the smartest collections of talent in the front office and the checkbook to buy almost anything, are still struggling to find a couple guys for the back end of their rotation. You don’t have to break the bank to find options, as long as you invest the time up front to accumulate them.

There’s certainly more than one way to fill a roster. Whether it is the whiteboard theory in Boston or exploiting the free talent pool like Oakland, the best way to win is to have a plan.

Mr. Carroll is a writer for Baseball Prospectus. For more state-of-the-art commentary, visit baseballprospectus.com.