Pitching coach Larry Rothschild and manager Joe Girardi watch New York Yankees injured starting pitcher Masahiro Tanaka throw two simulated innings before the Chicago White Sox play the New York Yankees at Yankee Stadium in the Bronx. Bronx, NY 8/23/14

By Brendan Kuty

Do the Yankees still need to sign a starting pitcher? How about two?

After they signed lefty Chris Capuano to a one-year, $5-million deal Tuesday, general manager Brian Cashman told The Journal News’ Chad Jennings that the 36-year-old, who has recent relief experience, will have a spot in their starting rotation.

That puts Capuano alongside Masahiro Tanaka, CC Sabathia and Michael Pineda as expected Opening Day rotation members.

But do the Yankees need to add more? Let’s discuss.

As it stands, the Yankees have four starting pitchers in a rotation that calls for at least five. (Forget, for now, the Yankees in August discussed possibly of a six-man rotationfor 2015.)

Of those four starting pitchers, who’s the No. 1? It’s likely Sabathia would get the Opening Day start because of the respect he’s garnered throughout the organization, but Tanaka would probably be the so-called ace. Pineda would fall as the No. 2. Then Sabathia would be considered No. 3 with Capuano at No. 4. The fifth guy? Maybe a competition is in order between — deep breath — David Phelps, Adam Warren, Chase Whitely, Bryan Mitchell, Jose De Paula and Esmil Rogers.

So, that’s out of the way. Now, let’s identify the main problems here.

HEALTH? The biggest issue is that it’s unclear whether Tanaka (partially torn UCL), Sabathia (knee) and Pineda (shoulder) will make it out of spring training healthy, let alone last a full season.

All three of them spent significant time on the disabled list in 2014. And while the Yankees maintain that they believe each will have fully recovered by the time pitchers and catchers report to Tampa, Fla., they have to feel at least a little uneasy. In fact, Cashman recently said officials are “keeping our fingers crossed” that Tanaka won’t need Tommy John surgery. He has also said that though Sabathia appears to be “a guy that can pitch in the middle of our rotation … there’s a little bit of a question mark there.” And Pineda hasn’t thrown more than 171 innings since 2011, his rookie year.

SUBSTITUES? All right. Once the possible-injury-risk idea has been digested, there’s the question of who would be among the first candidates to replace a hurt hurler. What if Tanaka goes down in April? Ivan Nova (Tommy John surgery) isn’t due back until sometime in May or June. The Yankees’ top pick, it seems, would be the runner-up in the fifth-starter competition. Out of all those possibilities, not one leaps out — if he did, of course, he’d be the obvious No. 5 starter anyway.

INEXPERIENCE? So that’s an issue. And the third? How comfortable is manager Joe Girardi in trotting out the No. 5 starter competition winner every fifth day?

The Yankees held a battle for that same job last spring before giving it to Pineda, who was simply dominant. But none of this year’s contestants have Pineda’s upside. Phelps filled in admirably for 17 starts — the third most on the team, behind Hiroki Kuroda and Tanaka — but would the Yankees be better served with him in the bullpen, where he’s got more experience? It’s possible.

That brings us to the available external options.

There are too many trade theoretical scenarios out there, and they’re all too complex to detail here. But we do know that, on the free agent market, there’s Max Scherzer and James Shields. But Yankees have repeatedly said they don’t plan to spend big (so, sorry, Scherzer and Shields. Or at least for now.). Kuroda’s out there, too, but he still hasn’t decided whether to retire or pitch in Japan next season. There don’t appear to be any second-tier free agent starting pitchers left outside of Kuroda.