The Yankees want a controllable, young starting pitcher. Yes, they would consider a second baseman and want to deepen their bullpen.

But they see a now-and-later rotation problem. In the present, they have uncertainty, particularly with health. In the future, five of the seven pitchers who started the most games for them in 2015 (CC Sabathia, Nathan Eovaldi, Ivan Nova, Michael Pineda and Masahiro Tanaka) can be free agents by the end of 2017.

Hal Steinbrenner has ordered that payroll stay relatively similar to 2015 at a time when the Yankees have little coming off the books. Which is why free agency currently is a secondary source for finding that starter. The Yankees have dismissed signing a mega-deal with a David Price or Zack Greinke.

Because there are so many good starters on the market, a second- or third-tier arm could fall into the Yankees’ price range. But that is unlikely to happen early in the process, and perhaps not at all for someone who could intrigue the Yankees such as J.A. Happ or Scott Kazmir.

This is why you are hearing about the Yankees’ willingness to include Brett Gardner or Andrew Miller in deals as a way to offer something enticing for a young starter while also trimming payroll. To get the right starter, the Yankees also would use their shortstop surplus, notably touted prospect Jorge Mateo.

But who is the right starter?

The Yankees fixate on high strikeout rates, low walk rates and high groundball percentages. Those are the components of QERA (QuikERA), essentially assembling the elements a pitcher most controls: striking guys out, walking them and keeping the ball on the ground (defeating extra-base hits).

Most clubs want this, but the Yankees walk this walk. Just 16 AL starters averaged more than seven strikeouts per nine innings, fewer than three walks per nine innings and induced groundballs 45 percent of the time or better (minimum 10 starts). The Yankees had four — their innings leaders: Eovaldi, Pineda, Sabathia and Tanaka. No other AL team had more than two.

Sabathia’s success in these areas — and the Yankees’ belief that it presaged better things to come — was a big reason he was kept in the rotation while struggling last season.

The top four finishers for the NL Cy Young (Jake Arrieta, Greinke, Clayton Kershaw and Gerrit Cole) hit those stats, as did the pitchers who finished first (Dallas Keuchel), third (Sonny Gray), fifth (Chris Archer), seventh (Felix Hernandez), eighth (Collin McHugh) and 11th (Carlos Carrasco) in the AL.

If you wanted to play junior detective on who the Yankees are targeting, pitchers who excel in those areas are a good start. Some are free agents who had the qualifying offer put on them at a time when the Yankees do not want to give up their first-round pick — so eliminate Greinke, Hisashi Iwakuma and John Lackey.

There is another unavailable group who are Mets, in the AL East, retiring or won’t be moved.

I pinpointed 10 who either hit the strikeout-walk-groundball benchmarks or — like Eovaldi before the Yankees obtained him — come close who I think could be in play:

1. Carlos Carrasco

He is signed reasonably, through 2020, and is at least a high-end No. 2, so I don’t know how the Yankees even get Cleveland deep into conversation without including Aaron Judge, who they say they will not trade. Perhaps Danny Salazar is more plausible.

2. Jose Quintana

Also reasonably under control through 2020. Plus, the White Sox have David Robertson and outfielders, so Miller and Gardner are not ideal exchanges. Would the White Sox move Carlos Rodon, if there would be a bigger package with Mateo or Judge? Also, the Yankees might feel it embarrassing to give up big stuff for Quintana, who they lost for nothing as a minor league free agent after the 2011 campaign.

3. Collin McHugh

The Astros tried to sign Miller last year and still need him. The Yankees probably would want Lance McCullers Jr. if they include Miller. But could they find common ground for someone with McCullers’ upside. McHigh is more likely.

4. Joe Ross

The Nationals also would love Miller and, perhaps, even Gardner. They would move Gio Gonzalez, but his wild penchant probably does not entice the Yankees. The wildness also probably scares the Yankees a bit about Ross’ more established brother, Tyson of the Padres, who also is available and is a strikeout/groundball guy.

5. Raisel Iglesias

The Reds are rebuilding around young starters such as Iglesias and Anthony DeSclafani, who both hit all three benchmarks. Would Mateo be enough to start a dialogue on Iglesias, who just might be El Duque II? I wonder if the Yankees took on the two years at $27 million left on Brandon Phillips to play second whether that facilitates talk.

6. Shelby Miller

The Braves are willing to talk about him, but again, Judge probably has to be in play.

7. Kyle Hendricks

He hit all three parameters, though no one sees a top-of-the-rotation guy here. If the Yankees took Starlin Castro’s contract to have him play second could a deal be worked out?

8. James Paxton

Even with the recent addition of Leonys Martin, the Mariners still could use Gardner to protect them if Martin isn’t good enough or to play a corner with Nelson Cruz becoming a full-time DH again. Paxton has some Andy Pettitte in his delivery, but an injury history.

9. Chad Bettis

An under-the-radar guy. For the Rockies last year, he averaged 7.7 strikeouts per nine, 3.3 walks and induced grounders at nearly 50 percent — plus his numbers were markedly better outside of Coors Field. I am sure Colorado would want to attach Jose Reyes to a deal. I am sure the Yankees would be averse to that idea.

10. Jimmy Nelson

The Brewers are in rebuild mode under new general manager David Stearns, and Nelson and Taylor Jungmann are starters you build with — excellent strikeout and groundball numbers, good walk rates. But Stearns comes from the not-afraid-to-try-something mode, and neither guy projects as an ace. Could the Yankees, for example, send Miller somewhere for prospects Milwaukee wants enough to give up Nelson?