In this article here, Pinstripe Alley author Caitlin Rogers noted that Yankees' president Randy Levine said the Yankees would not be pursuing Max Scherzer. The current Yankees payroll estimate of around $200M (Cot's contracts pre-Prado trade) would seem to act as a deterrent to adding another $25-$30M AAV to the payroll for the next 6-8 years. However, if there is one team who can spend freely, and there isn't, it's the Yankees. Or the Dodgers. Or the Red Sox. Or the Giants....The point is that if the Yankees really wanted him, they could afford Scherzer.
The starting point is the projections; I'll look at the FanGraphs depth charts. The Yankees are projected to be the #10 team in fWAR from the starting rotation. There are quite a few moving parts to this projection, though. I'll go through them one-by-one.
First, C.C. Sabathia is projected for both a relatively healthy and effective season by garnering 2.3 fWAR in 188 innings. Sabathia's xFIP before he went down last year was a very good 3.11, so it's clear that he still had something in the tank. His walk and strikeout rates were excellent, but for some reason he handed out free dingers like street pamphlets. His .350 BABIP was also way above norms. Sabathia is surely a rebound candidate in performance, but his knee is the question. A Yankees team with a healthy Sabathia doesn't need Scherzer so much.
Second, another health question mark, is Masahiro Tanaka. He's also projected for 188 innings of solid performance. Heck, the projected 3.42 ERA/3.54 FIP might be too high. However, his elbow is the question. Tanaka was shut down in July and returned in September, but he had a partially torn ligament. It's possible that Tanaka could return and pitch with that issue, but there's no telling when his elbow will pop. Luke Hochevar pitched a long and mostly ineffective time with a partially torn UCL. Tanaka is another question mark. A Yankees team with a healthy Tanaka doesn't need Scherzer so much.
Third is Michael Pineda. Surprise, another health question mark! Pineda skipped May, June, and July due to a combination of a suspension for that odd pine tar incident as well as a back injury. For a guy who didn't throw any innings in 2012 and 2013 and missed significant time with injury in 2014, 169 projected innings in 2015 seems a bit high.
Fourth is Nathan Eovaldi. The new guy. He threw 199.2 innings and accumulated 3.0 fWAR in 2014. However, he's a righty with a platoon split. The Yankees' home park treats lefty hitters nicely. 175 projected innings in 2015 is probably a solid estimate, but the projections don't see a repeat of his performance. The Yankees' pitching coach could help Eovaldi harness his stuff better, but Eovaldi also won't have the benefit of throwing to pitchers holding bats anymore.
Fifth is Ivan Nova. Nova made only 4 starts in 2014 before succumbing to Tommy John surgery. He won't be back until mid-season-ish at the earliest, but he is projected for 113 innings.
Chris Capuano, who has quite an injury history himself, is projected for 65 innings, which is what he gave the Yankees last year after joining the team mid-season. He might step out of the rotation when Nova returns depending on his performance. Bryan Mitchell and Chase Whitley finish off the depth chart. The Yankees traded away Shane Greene as well, gaining a shortstop but further reducing their SP depth. The Yankees were unable to re-sign Brandon McCarthy.
After all this, 4 of the top 5 Yankee starters are health question marks, and the 5th is a performance question mark. Should the health question marks have a healthy answer, the Yankees' rotation will be in fine shape. Should the answer be dire and unhealthy, the Yankees will be trolling their minor league system and other teams for pitchers. Unless, of course, they sign Max Scherzer. Scherzer is projected for 208 innings and 4.1 fWAR. He's been healthy and dominant. If the Yankees have any desire to return to the postseason, they'll need another pitcher. There are too many question marks.
It doesn't have to be Scherzer. James Shields is still available. If he wanted to return to the MLB, Hiroki Kuroda probably wouldn't go anywhere else but the Yankees (speculation on my part). The talent level drops off after those guys, though. Now then, to answer my titular question, no, I don't think the Yankees need Scherzer. The Yankees are talented enough, and it's unlikely that all 4 of those pitchers remain unhealthy and ineffective. But they need someone.
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All statistics courtesy of FanGraphs.