Injury has been a big part of the New York Yankees over the last few seasons. Derek Jeter broke his ankle, Alex Rodriguez had hip surgery, CC Sabathia has knee problems, Masahiro Tanaka's elbow flared up, Jacoby Ellsbury's knee was a mess, Carlos Beltran fell apart, and Mark Teixeira's wrist and leg were problems. You name it, and the Yankees have probably hurt it and and been placed on the disabled list for it. Now Brian Cashman seems to be a bit more proactive about it and has constructed a team that looks like it can hold its own in the event someone goes down for the count, which is something you can't really say about the team for the last few years.
If the Yankees lose Mark Teixeira for a long period of time, Greg Bird is there to fill in. If they lose Alex Rodriguez, Greg Bird is still there to fill in. At second base, they have Dustin Ackley and even Rob Refsnyder in case Starlin Castro gets hurt. Castro can also slide over to shortstop if Didi Gregorius goes down. In the outfield, Brett Gardner and Jacoby Ellsbury can play center field, while Aaron Hicks and Ackley can back up at all three outfield positions, not to mention the group in Triple-A that can be called up just in case. For the most part, everyone seems to have a backup and the Yankees won't be stuck with a below-average replacement.
The only positions where things get a little dicey are at third base and catcher. Now, their backup at third base relies entirely around Starlin Castro's ability to learn a new position, however the Yankees seem fairly confident he will be fine after seeing how well he transitioned to second base last year. Otherwise, they won't have many other options outside of someone like Pete Kozma, who would probably be a disaster.
At catching, the Yankees would have been fine if Brian McCann went down with John Ryan Murphy as his caddy, but now that he's gone, they would have to hope that Gary Sanchez can step up to a starting role in his first full year in the majors. Of course, no decision has been made on the backup catcher for the 2016 season, but I have a hard time believing they will pick Austin Romine when he has already made it through waivers after getting designated for assignment last year. Sanchez is their man all the way, so if the reports that he has greatly improved behind the plate are accurate, the Yankees won't have a lot to worry about.
As for pitching, the Yankees have things well in hand in the bullpen. They currently have three closers available to them, so if anyone were to get hurt out of Aroldis Chapman, Andrew Miller, and Dellin Betances, two should work just fine, like it did last year. As for middle relief, the Yankees have enough interchangeable MLB-ready talent to put together a second bullpen, so someone should be able to get the ball to the backend.
Starting pitching, though, is a completely different story and probably the weakest depth the Yankees have. Masahiro Tanaka, Michael Pineda, and CC Sabathia will all be in the 2016 rotation and are all serious injury risks. Now that Adam Warren is gone, they will have to hope that Ivan Nova can improve after another year away from Tommy John surgery. He really can't get much worse than he was last year. I am personally not a huge fan of Bryan Mitchell, but he exists and the Yankees must have had some form of confidence in these two in order to trade Warren and not sign someone else. One of them should be able to amount to a major league fifth starter until help arrives.
It's quite optimistic of me to declare that the Yankees are all set against injury. It's not that I feel confident that they will stay healthy–they almost definitely will not–but you can see that they have put together a much better group of bench players and have really valued versatility over the last year or two. Maybe the Yankees will need a bit of luck with the rotation in 2016, but I'm confident (read: hopeful) that they took that into consideration and already have a plan in pace.