Andy Pettitte has played a lot of roles for the New York Yankees. In 1995, he was a blue-chip prospect called up to replace an injured Jimmy Key. In 1996, he was a postseason hero out-dueling the unflappable John Smoltz. In 2011, he was a retiree riding into the sunset with gas left in the tank. Now, after coming out of retirement for just one year and $2.5 million, he is the seventh Major League starter in the Yankees’ five-man rotation.

Make no mistake, Yankees’ General Manager Brian Cashman would have been a fool to turn down Pettitte at that price. As Cashman reported to ESPN, he had offered the left-hander upwards of $10 million to come back earlier in the offseason. Pettitte wavered, however, and Cashman was forced to bite on deals for starters Michael Pineda and Hiroki Kuroda. By the time Pettitte finally decided to make his comeback, Cashman had only $2.5 million left to offer. Pettitte agreed, and the Yankees acquired the crafty veteran for pennies on the dollar.

But the cheap contract leaves the Yankees answering an age old question: can you have too much starting pitching?

Conventional wisdom says no. Starters get injured. They become ineffective. They disable their fragile bodies punching walls (Kevin Brown) or playing Guitar Hero (Joel Zumaya). As the theory goes, it’s foolish to enter the season expecting all five hurlers to rack up 32 starts. It’s not just sensible but also necessary to have viable fill-ins waiting in the wings. Teams that begin a season with six starting pitchers almost always find use for all of them.

But seven? Between C.C. Sabathia, Kuroda, Pineda, Ivan Nova, Phil Hughes, Freddy Garcia and now Pettitte, the Yankees have seven Major League starters on the 2012 roster. None of these are fringe candidates, either. Sabathia, Kuroda, Pineda and Nova appear locks for the Opening Day rotation. That leaves just one spot for Hughes, Garcia and Pettitte, all of whom deserve to be Major League starters. No other team in the Major Leagues has comparable depth at the position. What can the Yankees reasonably expect to happen?

For that, we dive into the data. To accurately reflect the Yankees’ predicament, we need to look at a subset of pitchers who enter with the expectation of starting for a full season (as was the expectation at some point this offseason for each of the Yankees’ seven). While it’s difficult to accurately capture this expectation in the data, we’ll use the following group as a close approximation: pitchers who signed Major League contracts between 2004 and 2011, who started at least 20 games in the season before signing, and who made fewer than five relief appearances in the season after signing.

What did teams get out of these pitchers? Given that the season lasts 162 games and that teams use five-man rotations, we can estimate that a full season amounts to 32.5 starts per pitcher. By this definition, only about 30% of starters in our pool actually pitched a full season in the year after signing a contract. In fact, the average starter threw just 25 starts. Five pitchers throwing 25 starts equals only 125 games started, leaving teams with an additional 37 starts to “fill.” Thus, it actually takes about six and a half league average starters to complete a starting rotation for a full season. When you consider that even a healthy sixth (and perhaps seventh) starter isn’t able to start games when the other five are in rotation, this number bumps up closer to seven.

Obviously, this number varies tremendously team-to-team and pitcher-to-pitcher, so the calculation is oversimplified. That said, the data suggests that seven starters might not just be an acceptable number, it might actually be the optimal number. Even a roster with six full starting pitchers might not be able to fill the rotation for a full season, given starters’ remarkable tendency to miss games. In order to maintain quality, Major League talent in the starting rotation, seven guys might be a team’s best bet.

But this analysis skirts the bigger problem and the quandary the Yankees currently face: what do you do with the sixth and seventh starters when the other five are healthy? You can send them to the bullpen, although this carries the considerable risk that they’ll have a difficult transition back to starting. You can trade them, although this defeats the purpose of carrying seven starters to begin with. You can send them to the Minor Leagues, although this is impossible for Major League pitchers without Minor League options (meaning their contracts prohibit such demotions) and is generally upsetting to veterans. You certainly can’t just have them ride the bench, as their fragile arms get too cold.

For the time being, the Yankees won’t have too much trouble managing this game of musical chairs. Pettitte, who showed up to camp a month after the rest, won’t be ready to start in the Majors until May. My guess is that Garcia will be thrust begrudgingly into a long relief role, while Hughes (who has been dominating hitters this spring) will take the fifth rotation spot. But this calculus gets much more complicated when Pettitte returns, particularly if the five starters remain effective and if Garcia dominates out of the pen.

But as Brian Cashman would tell you, this is the wrong question to be asking because this is a good problem to have. Is it difficult to find a role for a sixth and seventh starter? Yes, considerably. But this situation (in which a team’s top five starters are healthy and pitching) is actually the best-case scenario. Sixth and seventh starting pitchers are not signed in order to improve the best-case scenario. Rather, their value comes in improving the worst-case scenario and a number of scenarios in between.

Of course, this does imply that teams would be silly to value a sixth and seventh starter the same as a fourth and fifth starter (even if those starters are all of similar ability), given that their value is only realized if another starter goes down. But it also implies that they are worth carrying on the roster.

Pettitte ($2.5 million), Garcia ($4 million) and Hughes ($3 million) combined are costing the Yankees less than Kuroda’s entire salary ($11 million) or half of Sabathia’s salary ($24 million). $9.5 million is not pocket change, and it’s more than most teams can afford for a fifth, sixth and seventh starter. That said, it’s an incredible value for the Yankees that will protect specifically against a downside risk. The “what do we do with our extra starters” question is the one the Yankees should be hoping to ask, not the one they should be hoping to avoid.