The greatest teams in sports are often defined by their rivals. For the past 20 years, the Red Sox measured themselves against the New York Yankees. They were two franchises separated by 200 miles with fan bases that wanted nothing less than the complete annihilation of their archrivals.

Red Sox fans have long loved to hate the Yankees, and the villain they hated most was Alex Rodriguez. You’d think Sunday’s announcement that A-Rod is retiring Friday – that the three games New York will play at Fenway Park this week will be his final complete series – would be met by cheers throughout New England.

Instead, it’s kind of melancholy to think of the Yankees without A-Rod.

It’s truly the end of an era. Last week, Mark Teixeira announced that he’ll retire after the season. Derek Jeter, Mariano Rivera and Jorge Posada are long gone. So is the simmering animosity that once bubbled beneath the surface of these two AL East foes.

Here in Boston, David Ortiz is the last member of the Red Sox team that vanquished the once-mighty Yankees in an unforgettable 2004 ALCS comeback. The side of Big Papi’s first world championship ring reads “Greatest Comeback in History,” reminding him forever that his 2004 team was the first in baseball history to overcome a 3-0 deficit in a best-of-seven series.

Alas, Ortiz will be retiring at the end of the season. Indeed, time waits for no man – not even for the greatest designated hitter in the history of the game.

The Sox feel they are well positioned for life after Papi. They’ve got a young nucleus led by Xander Bogaerts, Mookie Betts and Jackie Bradley Jr., who have already established themselves as big-league regulars. They’ve got a former MVP in Dustin Pedroia ready to take over the mantle of leadership in the clubhouse. They’ve got an ownership group that has seen three championships come to Yawkey Way in the last 13 years.

Things are a bit more unsettled in New York. The Yankees went into sell-off mode before the nonwaiver trade deadline, bringing in an impressive haul of 10 prospects for Aroldis Chapman, Andrew Miller and Carlos Beltran.

It’s the first time since the late ’80s that the Yankees were true sellers at the deadline. It would’ve been unthinkable that they’d go into rebuilding mode under the late George Steinbrenner, but his sons, Hank and Hal, see the thousands of empty seats at Yankee Stadium each night and realize the team’s current course is unsustainable.

New Yorkers have better things to do than watch a muddling fourth-place team.

So the decision was made to step back to step forward. It was the right decision without a doubt, but good luck figuring out who those guys are wearing NY caps at Fenway this week.

The long-term future looks bright for the Yankees now that the decision has been made to rebuild. The Red Sox are hoping their bright horizons are realized much sooner: They were buyers in the weeks leading up to the nonwaiver deadline but have still been a .500 team for the past three weeks.

When the Red Sox visit New York in the final week of the regular season, the Yankees are planning a tribute to send Ortiz off into retirement. It will undoubtedly be an impressive ceremony, along the lines of the goodbye Boston gave Jeter two years ago.

It’s doubtful there will be much of a send-off for A-Rod at Fenway this week.

Once one of the greatest hitters in the history of the game, his career will be remembered for his missteps on and off the field.

Yet Sox fans should take a moment and bid Rodriguez adieu. He was once part of something special that made you pay attention whenever these teams met. It’s been awhile since this rivalry had that feeling.

Tom Caron is a studio host for the Red Sox broadcast on NESN. His column appears in the Portland Press Herald on Tuesdays.