MLB

ROTATION EQUATION

TAMPA – The Yankees have a math puzzle to solve. Like every club, the Yanks face approximately 1,450 innings of defense.

As a rule, the higher percentage of those 1,450 innings worked by your starters and closer, the better. Middle relievers are middle relievers because they are not good enough to start or close. So the more they pitch, the more a team – in general – is deploying its least-effective arms.

There are exceptions. If Joba Chamberlain, for example, sets up Mariano Rivera, the Yanks are not going to mind the ball in his hand.

Still, like all teams, the Yanks want to limit bullpen innings and, naturally, that burdens the starters. A strong rotation will provide about 950 innings, and 1,000 is exceptional. Now we get to the Yanks’ math puzzle. It revolves around Generation Trey and the prescribed – inflexible – inning totals that will be allotted to Chamberlain, Phil Hughes and Ian Kennedy.

The Yanks are reticent about detailing the inning limitations, but a logical projection for the trio is about 450 innings. That includes the innings Chamberlain likely will pitch out of the pen in the first half and any postseason innings the organization projects.

Thus, the Yanks probably have mentally allocated about 400 starter innings from Generation Trey, even with full health. So now get out your calculators. How do the Yanks get the other 550-600 innings they need?

They keep insisting they are not worried and that a strategy is in place. Pitching coach Dave Eiland said, “There is a way to get it done and we have a plan to get it done.” And he seemed more willing to offer up a finger than that plan. My suspicion is the Yanks are intending to work a sixth starter in regularly to space out Generation Trey’s starts.

The Yanks will have several relievers with minor league options. Therefore, they can plan to send down a reliever at designated periods during the season and summon a starter they feel might match up with a particular opponent. That only heightens the importance of this spring on likely Scranton rotation members such as Alan Horne, Jeff Marquez, Kei Igawa and Jeff Karstens.

“Somebody in there,” Eiland said pointing into the clubhouse, “that most people don’t know right now will almost certainly end up being important for us.”

Of course, the best way to cover the majority of those 550-600 innings is with Chien-Ming Wang, Andy Pettitte and Mike Mussina producing 175-plus strong innings each. That is not an outrageous proposition. Wang is among the majors’ surest 200-inning bets. Not long ago, the same would have been said of Pettitte.

He is due in camp tomorrow to provide a first read on his mental and physical shape. Pettitte is one of just 12 pitchers to log at least 650 innings over the past three seasons. But what if the fallout since his naming in the Mitchell Report impacts his workhorse demeanor?

Mussina, meanwhile, is a wild card. His 2007 season screams that he is on the brink of washed up. But he clearly is in better shape than last year. If he can even rejuvenate to generate a season midway between 2006 and 2007 (think 175 innings, 13 wins, 4.30 ERA) that would help solve the math problems.

Mussina’s last 200-inning season was 2003, and the Yankees starters led the majors in innings (1,066). They have ranked 14th, 18th, 18th and 22nd in the following four seasons. Yet, they made the playoffs each year by relying on the huge edge they almost always enjoy at closer and on offense.

Even if we assume Rivera, at age 38, is same as he ever was, the Yanks have an offensive problem. They still project as a 900-plus run monster. But the AL probably has another half-dozen clubs that will challenge 850 or more runs. That means the Yankees’ edge is not as substantial as in the past, plus Yankee starters must contend with those burgeoning lineups.

So it is difficult to imagine the Yanks can again lag far behind in rotation innings and still reach October. The math puzzle must be solved effectively or the Yanks face the sum of all their fears: No postseason.

joel.sherman@nypost.com