The Yankees have accomplished the near impossible — they had the oldest player in the majors (Mariano Rivera) and the oldest starter (Andy Pettitte) retire and yet somehow have gotten older this offseason.

Thus, the Yankees saw one of their biggest problems — the decay physically and statistically in older players — and doubled down on it rather than run away. This is what happens when you have a putrid farm system combined with a never-rebuild philosophy combined with hundreds of millions of dollars to spend. You buy for today, the heck with tomorrow — and, by the way, today is no given either with this much seniority.

Because this comes at a time when seemingly more effective PED testing has coincided with fewer older players performing well, which only has elevated the value of above-average players in their 20s. Yet, a week after pitchers and catchers arrive at George M. Steinbrenner Field in February, Brian McCann will turn 30, meaning the Yankees will not project a starting position player in his 20s.

Can this work? Maybe. The Yankees are not employing older bums, but players with significant pedigree. However, the problem — like last year — is sheer volume. Maybe a few Yankees graybeards will recall their prime, though two who excelled in 2013 — Rivera and Pettitte — are now gone. But the chances six or seven perform at a high level are not good. And there are no talented youngsters ready to step in to provide quality and energy.

How dependent are the Yankees on the aged? Let us count the ways:

1. Mark Teixeira, who turns 34 in April, will be the third-oldest starting first baseman behind just Adam LaRoche, 34, and Ryan Howard, 34, who like Teixeira is an expensive item who was in decline even before significant injury.

Prior to a 2013 lost mainly to a wrist ailment, Teixeira’s OPS from 2008-12 had sunk from .962 to .948 to .846 to .835 to .807. Even if healthy, can Teixeira stop this trend? And if not, what does that mean for the Yankees, who still owe him $67.5 million the next three years?

2. Brian Roberts, 36, projects as the third-oldest starting second baseman behind Marco Scutaro, 38, and Mark Ellis, who is three months older than Roberts — assuming Ellis starts for the Cardinals over rookie Kolten Wong.

Robinson Cano had many assets, perhaps none more impressive than his durability. Over the past four seasons, he played 640 games, tied for second in the majors with Billy Butler, seven games fewer than Prince Fielder. But Butler is a DH and Fielder a first baseman, while Cano is in the middle of the action at second. Roberts played 192 games the past four years, which ranked 505th. Just to understand how few games Roberts played, that is two fewer than Mets afterthought Mike Baxter.

3. Derek Jeter, 39, is 4 ¹/₂ years older than the next-oldest likely starting shortstop, Jimmy Rollins. He missed most of last season with a twice-fractured ankle. He turns 40 in June. Shortstops who have come to bat even 300 times in an age-40-or-older season: Luke Appling, Honus Wagner, Omar Vizquel and Barry Larkin. None missed most of the previous season with a twice-broken ankle.

4. If Alex Rodriguez, 38, escapes his full suspension and plays in 2014, he would be the oldest starting third baseman by three years over Aramis Ramirez. A-Rod’s OPS has dropped six straight seasons.

And if Rodriguez is not around, then Kelly Johnson is likely to be the primary third baseman. On this team, he is pretty much a baby, not turning 32 until February. Yet he currently sets up as the fourth-oldest starting third baseman behind only Ramirez, 35, and Adrian Beltre and Juan Uribe, both 34.

5. If Raul Ibanez is no longer considered an outfielder — he probably will be the Angels’ primary DH — then the oldest outfielders currently on major league rosters are: 1. Ichiro Suzuki (40), 2. Torii Hunter (38), 3. Alfonso Soriano (38 in January), 4. Carlos Beltran (37 in April), 5. Ryan Ludwick (35), 6. Vernon Wells (35). That’s right, four of the top six — Suzuki, Soriano, Beltran and Wells — are Yankees. It is possible, however, that Suzuki and/or Wells won’t be with the team by April.

Also, Beltran and Soriano should see plenty of DH time, especially if Brett Gardner is not traded.

But keep this in mind: Two offseasons ago, the Yankees stayed away from giving Beltran a two-year contract because they were concerned about the combination of his age and damaged knees. Now, though Beltran is two years older and has two more seasons played on those troubling knees, the Yankees have given him a three-year contract. This is Yankees math: Don’t trust him with a two-year contract at age 35, give him a three-year contract at age 37.

6. Hiroki Kuroda probably will be the third-oldest starter, turning 39 in February, and trailing only Bartolo Colon, 40, and knuckleballer R.A. Dickey, 39. Kuroda has retained excellence into his late 30s. If you are looking for a worrisome sign, however, he finished last season 0-6 with a 6.56 ERA in his final eight starts.

CC Sabathia, at 33, is the seventh-oldest starter currently on an AL roster. But among all active pitchers, only Mark Buehrle (2,882 ²/₃) and Tim Hudson (2,813 ²/₃) have logged more career innings than Sabathia (2,775 ¹/₃), whose pitching age because of wear and tear might be older than his chronological age. He is coming off his worst season by far and yet another dip in his average fastball velocity.

7. When it comes to lefty relievers, age generally is not as big a deal because they have a specific, narrow job — to get lefty hitters out — that they can continue to do into a more advanced age. Nevertheless, in Yankees fashion, they let a 29-year-old (Boone Logan) go for a 37-year-old (Matt Thornton). The only lefty relievers currently on major league rosters older than Thornton are Randy Choate, 38, and Scott Downs, who turns 38 in March.