The New York Yankees were in the playoffs 17 times in the 18 seasons from 1995 through 2012. They played in seven World Series and won five of those, although only one of those championships was since 2000.

The Yankees spent 2013 celebrating the final season of Mariano Rivera, the greatest relief pitcher ever to visit the planet. They also finished 85-77, 12 games out of first place in the American League East, and not in the playoffs.

The Yankees spent 2014 celebrating the final season of Derek Jeter, among the greatest shortstops and the glorious franchise’s all-time hits leader. They also finished 84-78, 12 games out of first, and not in the playoffs.

No specific celebration was planned for 2015, but there was a thought that several players could be looking at last call.

Alex Rodriguez had not played a game since Sept. 25, 2013. He had only 156 at-bats that season with seven home runs, 19 RBI and a .244 average. He missed 2014 because of a drug suspension. The Yankees took him back only because they were on the hook for $22 million this season, and more in the future.

Rodriguez will turn 40 on Monday. He arrived at Target Field on Friday with 20 home runs and 54 RBI, and would have been a worthy member of the AL All-Star team.

Mark Teixeira had missed most of the 2013 season and he batted .216 as he hobbled through 2014. The Yankees owed him $46 million for two more years, so “Tex” was back to hit in the middle of the lineup. Teixeira is 35. He came to Minneapolis with 24 home runs and tied for the league lead with 65 RBI. Rodriguez was quoted as saying Teixeira should be a leading candidate to be a Most Valuable Player.

Those two aren’t the end of it. Brian McCann, a half-year from his 32nd birthday, was awful when he came to the Yankees in 2014, but he’s shown the anticipated power this time: 15 home runs and 58 RBI.

Carlos Beltran is 38 and has another season left at $15 million. He’s the right fielder, but there’s relief available in Chris Young, a 31-year-old journeyman and a threat against lefthanded pitching.

Brett Gardner is approaching 32 and he’s an All-Star. Jacoby Ellsbury is 32; he’s back from injury and hitting.

In other words, everyone contributing notably to the Yankees’ standing as the second-highest-scoring team in the league is well into his 30s.

Most hard-core followers of baseball are looking at Rodriguez’s renewed bat speed in 2015 and want to shout that surely he has found another PED, this one so magical that it is undetectable even from MLB’s more-determined drug testing. I don’t buy that.

Remember, steroids or not, this was one of the greatest young hitters that we’ve seen since baseball’s expansion era started in 1961.

I have no problem with Rodriguez being back with the Yankees, hitting third and producing. He did the longest PED suspension in major-league history: a full year. He did the crime and served his time.

When July started, the narrative on the AL East was that it would be a four-team slog. There was even a thought that the Red Sox, despite their struggles, could make it an open race for the whole division.

Baltimore and Tampa Bay were tied, the Yankees were a half-game behind and Toronto was a game back.

Since then, the Yankees have said goodbye. They won 12 of 16 and were coming off a three-game sweep of the reeling Orioles. The Yankees were 12 games over .500 and the lead was 5½ games.

There are some excellent starting pitchers available before next week’s trading deadline. The Yankees probably will get one of those, but there is a rumor more frightening than the addition of a quality starter.

There has been speculation that the Yankees are prepared to make a real offer for Aroldis Chapman, the Cincinnati closer. A bullpen of Dellin Betances, Andrew Miller and Chapman would be the greatest finishing crew since …

Ah, there would be no “since.”